Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Laser spectroscopy of some transition metal-containing free radicals Kingston, Christopher Thomas 2002

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-ubc_2002-73188X.pdf [ 9.9MB ]
Metadata
JSON: 831-1.0061350.json
JSON-LD: 831-1.0061350-ld.json
RDF/XML (Pretty): 831-1.0061350-rdf.xml
RDF/JSON: 831-1.0061350-rdf.json
Turtle: 831-1.0061350-turtle.txt
N-Triples: 831-1.0061350-rdf-ntriples.txt
Original Record: 831-1.0061350-source.json
Full Text
831-1.0061350-fulltext.txt
Citation
831-1.0061350.ris

Full Text

LASER SPECTROSCOPY OF SOME TRANSITION METAL-CONTAINING FREE RADICALS by CHRISTOPHER THOMAS KINGSTON B. Sc. (Chemistry-Physics), The University of New Brunswick, 1996 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF CHEMISTRY We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October 2001 © CHRISTOPHER THOMAS KINGSTON, 2001 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 The University of British Columbia Vancouver, Canada Date 11 Abstract Laser induced fluorescence (LIF) studies have been performed on the transition metal-containing free radicals nickel cyanide (NiCN), niobium oxide (NbO), niobium methylidyne (NbCFf) and tantalum methylidyne (TaCH). All molecules were produced by the reaction of laser-ablated metal atoms with a reactant gas under supersonic jet-cooled conditions. Precise rotational constants and bond lengths have been obtained for the Xi2As/2 state of NiCN. The vibrational structure "of this state is dominated by a Fermi resonance interaction, as are those of the low-lying X 22 A 3 / 2 and W i2 n . 3 / 2 states. Four excited electronic states have been identified, showing that the electronic structure of NiCN is remarkably similar to that of NiH. High resolution spectra of NbO have given the rotational and hyperfine constants for the levels v=0-3 of the B T I state. Strong irregularities in the vibrational dependences of these constants can be interpreted in terms of spin-orbit interaction between the B T I state and the f T I , e 2 0 and d2A states. The hitherto unknown 4A state is estimated to lie near 17500 cm"1, from the vibrational dependence of the spin-rotation parameter y of the B4IT state. Thorough vibrational, rotational and hyperfine analyses were performed on the X 3 Ai state of NbCH. The hyperfine widths of this state vary considerably as a result of spin-uncoupling. The A3c&2 and B 3Ai excited states are heavily perturbed, with as many as nine I l l levels appearing where only one is expected, which complicates the vibrational and rotational analyses. Tantalum methylidyne was found to have an X Q=0+ (llf) ground state, with bond lengths r0(Ta-C)=1.7714 A and r0(C-H)= 1.080 A. The rotational lines exhibit unusually large quadrupole hyperfine splittings caused by the nuclear spin, 1=7/2, of the 1 8 1 Ta nucleus. This effect is normally too small to appear in optical spectra. Interaction between the A Q=l ('n) and B Q=0+ (3TIo+) states has been identified through the transfer of magnetic hyperfine character to the B state from A. TABLE OF CONTENTS Abstract " Table of Contents iv List of Tables viii List of Figures ix Acknowledgements xii Chapter 1 Introduction 1 Chapter 2 Theory 3 2.1 Introduction 3 2.2 Angular Momentum Operators 4 a) Angular Momentum Operators and their Wavefunctions 4 b) Coupling of Angular Momenta 6 c) Coordinate Rotations 10 d) Spherical Tensor Operators 11 2.3 Molecular Hamiltonian 17 a) The General Hamiltonian and the Born-Oppenheimer Approximation . 17 b) The Separation of Vibrational and Rotational Motions 21 (i) Vibrational Energy Levels 23 (ii) Rotational Energy Levels 24 c) Electron Spin 27 (i) The Spin-Orbit interaction 28 V (ii) The Spin-Rotation interaction 31 (iii) The Spin-Spin interaction 33 d) Nuclear Spin 36 (i) Magnetic Hyperfine interaction 37 (ii) Electric Quadrupole interaction 40 2.4 Hund's Coupling Cases and the Effective Hamiltonian Matrix 43 a) Hund's Coupling Cases 44 b) Matrix elements of the Hamiltonian operator in a Hund's case (ap) basis 51 2.5 Symmetry, Parity and A-doubling 61 a) A-doubling Matrix Elements for a case (a) IT State 63 2.6 Intensities and Selection Rules 65 Chapter 3 High Resolution Spectroscopy of Nickel Monocyanide, NiCN 69 3.1 Introduction 69 3.2 Experiment 71 3.3 Appearance of the Spectrum 76 3.4 Results 86 a) The X i 2 A 5 / 2 State 86 (i) Vibrational Analysis: Fermi Resonance 86 (ii) Rotational Analysis 93 b) The Low-lying Electronic States 97 (i) The X 2 2 A 3 / 2 State 97 vi (ii) The W i 2 n 3 / 2 State 101 c) The Excited Electronic States 104 (i) TheA 2 A 5 / 2 State 104 (ii) T h e B 2 n 3 / 2 State 112 (iii) TheC 20 7/ 2 State 115 (iv) TheD 20 5/ 2 State 117 3.5 Discussion 119 3.6 Summary and Conclusions 127 Chapter 4 Anomalous vibrational dependence of the rotational and hyperfine parameters in the B ' l l -X 4 !" transition of NbO 128 4.1 Introduction 128 4.2 Experiment 131 4.3 Results .132 a) Rotational and hyperfine structure in the B4TI electronic state of NbO . 132 b) Vibrational analysis of the 520 - 650 nm region 142 4.4 Discussion 148 4.5 Summary and Conclusions 154 Chapter 5 Laser Spectroscopy of the Transition Metal Methylidynes NbCH and TaCH. .155 5.1 Introduction 155 5.2 Laser Spectroscopy of NbCH 156 a) Experiment 156 b) Appearance of the Spectrum 158 c) The Ground Electronic State, X 3 Ai 163 (i) Vibrational analysis of the X 3 Ai state 163 (ii) Rotational and hyperfine analysis of the X 3 Ai state 167 d) The excited electronic states of NbCH 174 e) Discussion 178 5.3 Rotational and Hyperfine analysis of TaCH 180 a) Background 180 b) Experiment 182 c) Appearance of the Spectra 185 (i) The Al^nO-XOYr*), (001-000) band at 16380 cm - 1 185 (ii) The B0+(3n0+)-X0+(1I+), (000-000) band at 16398 cm - 1 . . .188 d) Results and Discussion 189 (i) The X0+(JS+) State 189 (ii) The Alf/rii) and B0 +( 3n 0 +) excited electronic states 191 Bibliography 200 Appendix 1 Rotational Line Frequencies for the Bands of NiCN 209 Appendix 2 Hyperfine Line Frequencies for the Bands of NbO 231 Appendix 3 Hyperfine and Rotational Line Frequencies for the Bands of NbCH 263 Appendix 4 Hyperfine Line Frequencies for the Bands of TaCH 275 vm List of Tables 3.1 Constants from the Fermi resonance modeling of the low-lying electronic states of NiCN 90 3.2 Rotational constants for vibrational levels in the ground states of each of the observed isotopomers of NiCN 95 3.3 Rotational constants for some excited state levels of NiCN 113 4.1 Rotational and hyperfine constants for the levels v = 0-3 of the B 4 n state of NbO .138 4.2 Measurements of zero gaps from low-resolution spectra of NbO 148 5.2.1 Observed ground state frequencies of NbCH and NbCD 166 5.2.2 Matrix elements for the rotational and spin parts of the Hamiltonian for a 3 A state, as used in this work 170 5.2.3 Ground state rotational and hyperfine constants for NbCH, NbCD and NbN 172 5.2.4 Rotational constants and term energies for some ground state vibrational levels of NbCH and NbCD 173 5.2.5 Rotational constants for some of the observed upper state levels of NbCH and NbCD 177 5.3.1 Derived constants for the ground state of TaCH and TaCD 190 5.3.2 Derived constants for the upper states of TaCH 198 IX List of Figures 2.1 Representations of Hund's coupling cases (a), (b) and (c) 45 2.2 Representations of the extended Hund's coupling cases (ap), (bpj) and (bps) 49 3.1 "Smalley" type ablation source 72 3.2 Schematic representation of the major components of the experimental setup. . . . . . 74 3.3 Portion of the survey spectrum of NiCN 78 3.4 Portion of the high resolution spectrum of the A - X i l\ band of NiCN showing the 2rj.3/2-2n3/2 and 2<!>7/2-2<I>7/2 transitions 80 3.5 Portion of the high resolution spectrum of the A 2As/ 2-Xi 2A5/2 (0,0) band of NiCN showing a number of rotational perturbations in the upper state 81 3.6 Portion of the high resolution spectrum of the C207/2-Xi2A5/2 (0,0) band of NiCN . . 82 3.7 Portion of the high resolution spectrum of the A 2 A 5 / 2 -Xi 2 A5/2 (021-000) band of NiCN 83 3.8 Portion of the high resolution spectrum of the A2A5/2-Xi2A5/2 (020-020), P=9/2-9/2, /=2-2 transition of NiCN 84 3.9 Observed vibrational levels in the ground state, Xi2As/2, of NiCN illustrating the irregular vibrational intervals resulting from the Fermi resonance interaction 87 3.10 Dispersed emission spectra from the v-0 (top) and V2 - 1 (bottom) levels of the A 2 A5/2 state of NiCN 88 3.11 Observed (top) and simulated (bottom) dispersed emission spectrum from the v'=0 level of the A 2 A 5 / 2 state of NiCN 92 3.12 Dispersed fluorescence spectra from the v'=0 (top) and V 2 - I (bottom) levels of the B2ri3/2 state showing strong emission features to the vibrational levels of the X 2 2 A 3 / 2 low-lying state of NiCN 99 3.13 Observed vibrational levels of the X22A3/2 and Wi 2n 3/ 2 low-lying states of NiCN . . 100 3.14 Dispersed fluorescence spectrum from the v'=0 level of the D 2 0 5 / 2 state of NiCN. . 103 3.15 Observed vibrational levels in the excited electronic states of NiCN 105 3.16 Dispersed fluorescence spectrum from the V3=l level of the A2As/2 state of NiCN. . 107 3.17 Reduced rotational energy plots for some vibrational levels of the A 2 A 5 / 2 electronic state of NiCN 110 3.18 Comparison of the observed low-lying doublet states of NiCN, NiH, NiF and NiCl. 120 3.19 Energy level diagrams of the observed electronic states in NiCN and NiH 122 4.1 Hyperfine structures of the first lines of the s Q3i and T R3i branches of the NbO, B ^ / a - X 4 ! " ^ (3,0) band 134 4.2 The first P R. 3 and °R. 4 lines of the NbO, B ^ i / a - X 4 ! " ^ (2,0) sub-band, showing the rapid decrease of the hyperfine widths with J in both electronic states 136 4.3 The spin-rotation parameter y plotted as a function of v for the B 4 n state of NbO . . 139 4.4 The diagonal magnetic hyperfine parameters \\Q for the B4IT state of NbO 140 4.5 The nuclear spin-rotation parameter ci for the B4IT state of NbO, plotted as a function of v 143 4.6 Excitation spectrum of jet-cooled NbO in the region 550 - 575 nm, recorded using a monochromator whose frequency was scanned so as to remain always 981 cm"1 (i.e. AGi/ 2, X 4!") to the red of the tunable laser 144 4.7 Vibrational levels of NbO in the region 13500-20000 cm"1, as presently known . . . 147 4.8 Vibrational intervals AG for the B4IT state of NbO, plotted against v 150 5.2.1 A vibrational progression in the ground state bending vibration of NbCD, showing the alternation in polarization with v2" 160 5.2.2 A portion of the high resolution spectrum of the A3<D2-X3Ai (0,0) transition of of NbCH showing the hyperfine structure due to the 1=9/2 spin of the 9 3Nb nucleus 162 5.2.3 Dispersed fluorescence spectrum obtained by pumping the 16748.3 cm"1 band head of NbCD 164 xi 5.2.4 Assigned ground state vibrational levels of NbCH and NbCD, as measured from the dispersed fluorescence spectra 165 5.2.5 Vibrational levels of NbCH and NbCD belonging to the A3<P2 and B 3Ai excited electronic states 175 5.3.1 Observed vibrational levels of the X0 + and al states of TaCH 181 5.3.2 Medium resolution spectra of the A l ^ n ^ X O * (1I4), (001-000) and B0+ ( 3 n 0 + ) - X 0 + C^), (000-000) bands of TaCH 183 5.3.3 Vibrational structures of the excited electronic states of TaCH and TaCD 184 5.3.4 Hyperfine structure in the low-J rotational lines of the A l (1TIi)-X0+ (1E+), (001-000) band of TaCH .186 5.3.5 Reduced rotational energy plots for the a) A l and b) B0+ states of TaCH 193 5.3.6 Plot of the effective value of 'aAQ' as a function of J for both the A l and B0+ states of TaCH 195 Acknowledgements Xll I would sincerely like to thank my supervisor Prof. Anthony Merer for welcoming me into his group and guiding me through the various projects we have worked on. His enthusiasm for the research and seemingly endless patience has made my time here truly memorable. I hope that one day I might know as much about spectroscopy as he does! I am very grateful to Dr. Jim Peers for his passing along his laser wizardry. I would probably still be standing in front of the 899 struggling to get it to lase if not for him. I am also grateful for the help he gave me on the TaCH and NbCH projects. I would like to thank Dr. Mark Barnes, Dr. Dave Gillett, Dr. Greg Metha and Dr. K. 'Peggy' Athanassenas for their work on the TaCH and NbCH projects prior to my arrival at UBC. I would like to thank Dr. Shuenn-Jiun 'SJ' Tang for his assistance in recording the numerous high resolution spectra for the NbO project, as well as for the many interesting conversations we had. I am also grateful to Dr. Gretchen Rothschopf for the many useful discussions on spectroscopy and the Ph.D. thesis experience. I also wish to acknowledge my only fellow graduate student, Scott Rixon, for all of the discussions we have had. Our lab was a popular destination for visiting scientists. Of these, I would especially like to thank Dr. Dennis Clouthier of the University of Kentucky for his help with some of the NbCH experiments and allowing me to assist in two of his research projects. Through working with him, I learned a great deal about being creative and resourceful in the lab. Next, I would like to thank Dr. Leah O'Brien of Southern Illinois University for her xm contributions to the TaCH project and for inviting me to Kitt Peak National Observatory to assist in some of her FTIR experiments. I must also thank Dr. Thomas Varberg of Macalester College for his help in the early stages of the NiCN project. The support staff in the Chemistry department were indispensable in keeping our lab up and running. Brian Snapkauskas of the mechanical shop and Martin Carlisle of the electronics shop were particularly helpful in minimizing the amount of downtime due to equipment malfunctions. Finally, I would like to thank the most important people in my life. First to my parents for their endless love and confidence. Last, I must thank my fiancee Christine for everything; I could not have accomplished this without her. 1 Chapter 1 Introduction Transition metal-containing molecules have always posed a challenge to experimentalists and theoreticians alike because of the partly filled d orbitals of the transition metal atoms. This has a significant influence on the chemical bonding and properties of these molecules. Nevertheless, molecules of this type are very important to a number of areas of research. Astrophysicists have identified a number of small transition metal molecules in the atmospheres of cooler stars. In organic chemistry, many catalytic reactions use transition metal molecules or substrates as active sites. Solid state researchers are interested in many transition metal alloys for their superconductive properties. Many theoreticians attempt to model the complex electron correlation effects in hopes of predicting molecular properties. The spectroscopy of transition metal molecules presents a unique challenge. The unpaired d electrons give rise to many electronic states that lie relatively close in energy. Further complications arise because of the presence of large electron spin and orbital angular momenta. The interactions of the angular momenta tend to make the spectra of these types of molecules very complex. Analysis of these spectra ultimately yield valuable information on the electronic structures and chemical bonding. Basic molecular properties, such as vibrational frequencies, bond lengths and dipole moments, are accessible. Hyperfine parameters, which describe the electron-spin nuclear-spin interaction, afford a great deal of information on orbital structure. To characterize weak interactions such as these requires techniques with high resolution and sensitivity. The use of laser spectroscopy with a laser ablation molecular beam spectrometer is well suited to studying transition metal molecules. The aim of this thesis is to study the electronic spectra of the transition metal molecules nickel monocyanide (NiCN), niobium oxide (NbO), niobium methylidyne (NbCH) and tantalum methylidyne (TaCH). Chapter 2 presents a basic theoretical background for the study of the molecules presented here, including the coupling of angular momenta, the construction of effective Hamiltonians and the evaluation of their matrix elements. Chapter 3 describes the electronic spectrum of gaseous NiCN, and includes the analyses of the Xi 2 As /2 state and each of the six excited electronic states. Chapter 4 deals with the high resolution study of the v = 0-3 vibrational levels of the B T I state of NbO, detailing the unusual vibrational dependence of the rotational and hyperfine constants that results from interactions with nearby doublet excited states. Chapter 5 is divided into two sections. The first gives the analysis of the A 3 0 2 - X 3 A i and B 3 A i - X 3 A i band systems of NbCH. The final section presents the rotational and hyperfine analyses of the Al( 1 r i i ) -X0 + ( 1 S + ) and B0 + ( 3 n 0 + )-X0 + ( 1 S + ) transitions of TaCH. 3 Chapter 2 Theory 2.1 Introduction Molecular spectroscopy is the study of the transitions between the energy levels of a molecule involving an interaction with photons of electromagnetic radiation. These energy levels are given by the solutions of the time-independent Schrodinger equation: Jfxi, = Ex¥. [2.1] In this equation J{ is the Hamiltonian operator, *F are the molecular wavefiinctions and E the energies of the stationary states of the molecule. Unfortunately, this equation can only be solved exactly for the hydrogen atom and requires a number of approximations in order to be useful in describing molecular systems. One of the most important approximations involves the assumption that the nuclear and electron motions occur independently of one another. This idea was first proposed by Born and Oppenheimer (1) and will be discussed in greater detail in Section 2.3.a. The result of this approximation is that the Schrodinger equation can be separated into nuclear and electronic parts. Further approximations can be used to divide the nuclear wave equation into vibrational and rotational motions; these will be discussed in Section 2.3.b. Finally, the effects of electron and nuclear spin will be examined in Sections 2.3.c and 2.3.d. 4 For nearly all aspects where rotation is involved in molecular spectroscopy it is convenient to write the Hamiltonian operator in terms of angular momentum operators. Section 2.2 will focus on the properties of angular momentum operators and how to couple them. Spherical tensor methods will be used to derive the matrix elements of the various angular momentum operators in the Hamiltonian. The specific forms of the matrix elements needed for the molecules of this thesis are presented in Section 2.4, with some additional details of A-doubling effects given in Section 2.5. The relative intensities of the lines in a spectrum are described in Section 2.6. 2.2 Angular Momentum Operators a) Angular Momentum Operators and their Wavefunctions A quantum mechanical operator, L, is defined as an angular momentum operator if its space-fixed Cartesian components, Lx, Ly and Lz, obey the following commutation relation: [L i .Lj^ i f t e^Lk [2.2] where e1Jk = < + 1 if ijk is a cyclic permutation of X Y Z 0 i f i = j [2.3] -1 if ijk is an anticyclic permutation of X Y Z . Each of the components of L also commutes with the operator L 2 : [ L ; , L 2 ] = 0, i = X,Y,Z. [2.4] This means that wavefunctions can be chosen that will simultaneously be eigenfunctions of L 2 and one of its Cartesian components; Lz is usually chosen because of its simple differential form in a polar coordinate system. The explicit functional forms of the eigenfunctions are not needed in order to determine the eigenvalues of the angular momentum operators. It is sufficient to represent them by the quantum numbers L and M L associated with the operators L 2 and L z , respectively; in Dirac notation they are written I L M L >. The eigenvalues of the angular momentum operators acting on these basis functions are: L 2 | L M L > = h 2 L(L+l) |LM L > [2.5] L z | L M L > = h M L | L M L > , [2.6] where h is Planck's constant, h, divided by 2K. In general, the quantum numbers can be either integers or half-integers, with M L having the (2L+1) possible values M L = L, L - l , L-2, ..., - L for each value of L. The effects of the Lx and L Y operators on the angular momentum basis functions are not as straightforward as those of the L 2 and Lz operators. They are most easily treated in terms of the raising and lowering operators L+ and L_, which are defined by L± = Lx±*'L Y [2.7] L ± | L M L > = h V L ( L + l ) - M L ( M L ± l ) | L M L ± 1 >. [2.8] Equation [2.8] shows how the raising and lowering operators transform the wavefunction I L M L > into multiples of | L ML±1 >. For this reason they are often referred to as "ladder" 6 operators. From Equations [2.5] to [2.8] it is straightforward to determine the matrix elements of the angular momentum operators: <LM L|L 2|L'M L'>=h 2L(L+l )6LL'6 M M' [2.9] < L M L | L z I L' ML' > = h M L 8LL' 5 M M' [2.10] < L M L I L ± | L' ML' > = h ^ /L(L + 1)-M' L(M L ±1) 8LL' 5MM'±I [2.11] where 5ij is the Kronecker delta, defined as 1 i f i = j 0 i f i * j . The significance of these angular momentum operators in molecular spectroscopy lies in the fact that the square of the total molecular angular momentum, J 2 , commutes with the Hamiltonian operator, JC. The eigenfunctions of #"are therefore eigenfunctions of J 2 and can be represented as linear combinations of the angular momentum basis functions I J M >. b) Coupling of Angular Momenta The motions of the electrons and nuclei within a molecule give rise to a number of angular momenta. Moving charges are known to generate magnetic moments, so that each of these angular momenta is associated with a magnetic moment. These moments are free to interact with one another, generating different energy terms in the Hamiltonian. The 7 magnetic interactions can be described as couplings between the associated angular momenta. This section will discuss the methods of coupling angular momenta. The coupling of two angular momenta, j i and J2, to form a resultant angular momentum, J , can be described in two ways. In the first method the system is represented by the wavefunctions | j i j 2 J M >, which are often abbreviated as I J M >. These wavefunctions are eigenfunctions of the operators ji 2, J2 2 , J 2 = ( j i + J2) 2 a n d J z = jiz + J2z- This is called the coupled representation. In the second approach the system is described by the wavefunctions I j i mi ; J2 m.2 > = I j i mi >| j 2 m2 >, where I j i mi > and | J2 ni2 > are eigenfunctions of the operators ji, j i z and J2, J2z respectively. This is known as the uncoupled representation. Both descriptions are equally valid and are related to each other by a unitary transformation where the quantities < ji mi ; j 2 m2 I J M > are the vector coupling coefficients (or Clebsch-Gordan coefficients). Methods have been developed for evaluating these coefficients; however it is more useful to write them in terms of the Wigner 3-j symbol The Wigner 3-j symbols are much simpler to work with as they have higher symmetry properties than the Clebsch-Gordan coefficients. Closed form expressions also exist for evaluating the most common 3-j symbols (2). We can now recast Equation [2.13] in terms of a 3-j symbol JM>= X I ji mi ; j 2 m2 ><ji mi ; j 2 m2 I JM>, [2.13] < ji mi ; j 2 m2 I J M > = ( - l )J ' -^ + M V2J + 1 [2.14] |JM>= V (-l) j ' - J 2 + MV2jTlf J l h [ l | j i m i ; j 2 m 2 > , [2.15] which provides a convenient means of transforming between the coupled and uncoupled bases. The coupling of three angular momenta can be treated as the successive couplings of two angular momenta. Consider the angular momenta ji, j 2 and J 3 which add to give a resultant J. Three mechanisms exist for this coupling. The schemes involve the addition of two of the angular momenta to give an intermediate angular momentum, followed by the addition of the third to give J. The intermediate angular momenta for the three schemes would be ji 2 , j 2 3 and J 1 3 , respectively. The three methods are equivalent since they produce the same resultant angular momentum, and any two are related by a unitary transformation l j 2 3 j l J M > = ^ < J 1 2 J 3 J M I ji j 2 3 JM> I J12 J3 JM>. [2.16] J12 The coefficients <[ j i 2 J 3 J M | ji j 2 3 J M > are called recoupling coefficients and can be shown, using Equations [2.14] and [2.15], to involve the products of four Wigner 3-j symbols. The Wigner 6-j symbol can now be introduced because it is a simpler method for dealing with the coupling of three angular momenta. The Wigner 6-j symbols are defined as | J l Jr J l 2 l = lSl)ZT=^ < J i 2 J 3 J M l j 1 j 2 3 J M > . [2.17] [h J J23J V(2Ji2+l)(2j23+l) The 6-j symbols can be written as sums of products of four 3-j symbols or, alternatively, products of 3-j symbols can be expressed in terms of a 6-j symbol. As in the case of the 3-j symbols, the 6-j symbols possess high symmetry properties and are relatively easy to evaluate. The coupling of four or more angular momenta can be treated in a similar manner to the coupling of two and three angular momenta. Naturally, the number of possible coupling schemes increases with the number of angular momenta being added. The coupling of four angular momenta is best described using the Wigner 9-j symbols. The 9-j symbol, whose general definition is rather cumbersome, represents the recoupling coefficient between two schemes of combining four angular momenta. The classic example for which a 9-j symbol is used is for the transformation between LS and j-j coupling in atoms. The first coupling scheme involves U coupled to 12 to give L, si added to s2 to give S, and finally L coupled to S to give J. The second scheme has h couple to Si to give j i , 12 couple to S2 to give J2 and ji added to J2 to produce J. The transformation between these schemes would be I 0isi)ji (l2s2)J2 JM > = S SI (lil2)L (siS2)S JM> L S ^ L + ^ S + l X ^ + l X ^ + l ) li 12 L Sj S2 S Jl J2 J [2.18] where the quantity in braces is a Wigner 9-j symbol. Nine-j symbols are usually evaluated as sums of products of three 6-j symbols or of six 3-j symbols. The Wigner 3-j, 6-j and 9-j symbols are extremely valuable in evaluating the matrix elements of angular momentum operators, which can be used to construct the molecular Hamiltonian matrix. The symmetry properties of the 3-j, 6-j and 9-j symbols have been thoroughly discussed in the literature (2,3); they will not be given here. 10 c) Coordinate Rotations In spectroscopy, we often encounter the situation in which a molecule interacts with an external field. An example is the interaction between the electric field of a photon and the electric dipole moment of a molecule. External fields are not well defined in the coordinate system of the rotating molecule, but are defined with respect to the laboratory or space-fixed axis system. To describe such an interaction properly the various quantities must be transformed into the same reference frame. This is accomplished through coordinate rotations. One axis system can be brought into coincidence with another by three successive rotations by the Euler angles a, P and y. If we rotate the space-fixed axis system onto the molecular frame, this process would be accomplished by the rotation operator R(apy) = e"iaJz • e _ i p j Y • e_ i Y J x , [2.19] where Jx, J Y and Jz are the space-fixed Cartesian components of the angular momentum operator J. The effect of this rotation operator acting on an angular momentum eigenfunction, | J M ) , is to produce a linear combination of all M components R(apy) | J M > = £ <D^M (aBy) | J M' >, [2.20] M' where the coefficients © ^ . M (aPy) are the matrix elements of the rotation operator R ©M'M(apY) =<JM' |R| JM>. [2.21] These matrix elements comprise the Wigner rotation matrix and often appear in the evaluation of Hamiltonian matrix elements. There are a number of useful properties 11 associated with the Wigner rotation matrix elements which are discussed in detail in reference (3); these will not be presented here. d) Spherical Tensor Operators The matrix elements for the coupling of angular momenta are often evaluated using spherical tensor algebra since spherical tensor operators are much simpler to use than ladder operators for second rank (and higher) interactions. An irreducible spherical tensor operator of rank k is a set of ( 2k + 1 ) quantities which transform into each other under coordinate rotations according to It can be shown from Equation [2.22] that tensor operators of rank zero, T 0 , are invariant to rotation, behaving like scalar quantities. For this reason zero rank tensor operators are called scalar operators. A tensor operator of rank one has three components that behave like the components of a vector under rotation. Therefore, all vector operators, including angular momentum operators, can be represented by spherical tensors of rank one. The relationship between the components of a first-rank spherical tensor and the Cartesian components of an angular momentum operator are given by [2.22] q Jz [2.23] T i = * £ J ± = T £ ( J x ± i J y ) . [2.24] 12 Compound tensor operators are extremely useful in describing systems of coupled angular momenta. Spherical tensor operators behave similarly to the spherical harmonics, the eigenfunctions of angular momentum operators; therefore compound tensor operators can be constructed in a similar manner to the coupling of two angular momenta. Using Equation [2.15] we obtain the result ^kj k 2 k ^ [ T k l (1) 0 T k 2 (2)]k = £ ( - i ) k i - k 2 + i V2k + 1 W2 T£(1)T£(2), [2.25] where T k l (1) acts on the first part of the coupled system and T k 2 (2) acts on the second part. The Wigner-Eckart theorem is used to calculate the matrix elements of a spherical tensor operator in the basis of the angular momentum wavefunctions. Its effect is to factorize a matrix element into two parts that can be dealt with individually. With the notation |r|JM>, where r\ represents all the other quantum numbers of the system, the Wigner-Eckart theorem takes the form (2) < rj' J' M' | T k | rj J M > = (-1)J'-M' { V k J ) <n' J' || T k || ri J >. [2.26] ^ - M q MJ The first part of the matrix element consists of a phase factor and a 3-j symbol. This part contains all the information about the orientation of the angular momenta (i.e. the geometry). The second part is a reduced matrix element, <n/ J' || T k || r\ J >, which contains all of the physical properties of the system. The reduced matrix element is independent of the magnetic quantum number, M, which means that it is independent of the choice of reference frame. 13 Evaluation of reduced matrix elements is performed by solving for a simple matrix element and then substituting back into the Wigner-Eckart theorem. This can be quite easy for a tensor operator acting on an uncoupled wavefunction, but becomes more challenging if the wavefunction is part of a coupled basis. A few examples of reduced matrix elements will now be discussed. Consider the evaluation of < J II T!(J) || J >. From Equation [2.23] we know that TQ1 (J) = J z so that <JM|T 0 1 (J ) | JM> = < J M | J Z | J M > = M . [2.27] If we apply the Wigner-Eckart theorem to the left hand side of Equation [2.27] we obtain (-i)J_M [_JM J M ) ° I I T l ( J ) 1 1 J > = M [ 2 2 8 ] Substituting for the 3-j symbol using reference (3) and simplifying, we find < J || TX(J) || J > = VJ(J + 1)(2J + 1) . [2.29] The reduced matrix element of the Wigner rotation matrix is an important quantity since rotation matrix elements are used to project internal angular momenta expressed in space-fixed axes back into the molecular axis system. It can be shown that for symmetric top wavefunctions | J K M > = B ± i (D^K (aPy), [2.30] V Sn2 where (D^K ( A P Y ) 1 5 t n e complex conjugate of the Wigner rotation matrix defined as £>MK (<*PY) - (-1)M_K © J M - K (aPY). [2.31] 14 Applying the Wigner-Eckart theorem to the (D^*(to), where co represents the Euler angles and p and q represent the space-fixed and molecule-fixed components respectively, we obtain < J' K' M' | ©J5r(co) | J K M > = (-1)J,"M' f V k J ^ <J'K'|| <D. ( a k ) l JK>, [2.32] M' p M , where the dot subscript means that the value of p is not specified. Using Equation [2.30] the left hand side of Equation [2.32] may be rewritten as < J' K' M' I © J f (co) IJK M > = ^ S f ^ ( f f l ) ^ ( f f l ) ^ ( f f l ) d m . [2.33] There is a useful relationship that equates the integral over three rotation matrix elements to a product of two 3-j symbols (3). Using this relationship we have < J' K' M' I < D < ! f I J K M > = (-l)K'-M'V(2J + i)(2J' + l) [2.34] ( r k •0 f J' k j) P MJ V - K ' q K j Substituting this result back into Equation [2.32], we finally obtain J' k J ^ < J ' K' || <D.(qk)*|| J K > = (-1)J'"K'V(2J + 1X2J' + 1) K' q K [2.35] which is the desired result for the reduced matrix element of the Wigner rotation matrix. The reduced matrix elements of compound tensor operators (Equation [2.25]) are needed when considering coupled angular momenta. When the Wigner-Eckart theorem is applied to a compound tensor operator whose components are acting on separate parts of a coupled system we have 15 < j i ' j 2 ' J ' M ' | X £ ( l , 2 ) | J ! J 2 J M > = (-!)• ,J'-M' J ' K J - M ' Q M x<j i ' j 2 ' J ' l |X K ( l ,2 ) | | j 1 j 2 J> , [2.36] where X Q (1,2) = [ T k l (1) ® T k 2 (2)]Q . The most general expression for the reduced matrix element of Equation [2.36] is written using a 9-j symbol The derivation of this formula is very involved and will not be presented in this thesis. In practice, this formula is rarely used because all the operators in the Hamiltonian must be scalar quantities so that the index K is zero. A 9-j symbol possesses the symmetry property that if one element is zero, it reduces to a multiple of a 6-j symbol. The matrix element for the scalar product of two commuting tensor operators of the same rank is also frequently used. The scalar product of tensor operators is defined as < j i ' j 2 ' J ' || XK(1,2) || j i j 2 J > = < j i ' II Tk> (1) || j , >< j 2 ' || Tk> (2) || j 2 > xV(2J + l X 2 J ' + l)(2k + l) j ' 2 j 2 k 2 l . [2.37] r J K [2.38] q and its matrix element is given by < j i ' j 2 ' J' M ' | T k ( l ) • Tk(2) | j , j 2 J M > = ( - l ) j ' + j ' 2 + V6 x E< y' J i ' II T k Q) II Y" ji>< Y" jY II Tk(2) || y j 2 >. [2.39] 16 Two other scenarios arise when calculating Hamiltonian matrix elements. The first involves a single tensor operator acting on one part of a coupled system, while the second has two parts of a compound tensor operator acting on the same system. For the first situation, the reduced matrix element will have a different form depending on whether the operator is acting upon the first or second part of the coupled system. The equations describing these cases are < ji» j 2 ' J II T k ' (1) II ji j 2 J > = 5j, J 2 (-l/>+^+ J + k' V(2J +1)(2J' +1) \)[ J' J^^'llT'MOllJ!) [2.40] < ji'jz' J II T k 2 (2) || ji j 2 J > = 6 j ; j | (-l)J'+J>+J'+k> V(2J + 1)(2J' + 1) <j 2'||T k'(2)||j 2>. [2.41] [J2 J ' Jl I / • , l l r p , [J J2 k l . For the case in which both parts of a compound operator act upon the same system the reduced matrix element takes the form <r ,7l lx K | |rij> = ( - i ) K ^ 'V^T5 : j k l k? *] V J ' U J J J x < -n' j' II T k ' || TI" j" >< TI" j" || T k 2 II -n j >. [2.42] A final note regarding spherical tensor operators brings us back to the topic of coordinate transformations. Using Equation [2.22] we know that the molecule-fixed components of a tensor operator can be obtained by rotation of the space-fixed components T k (A) = X © S } (apy)Tk (A). [2.43] 17 To obtain an expression for the reverse transformation we multiply both sides of Equation [2.43] by <D<K)* and sum over all of the molecule-fixed components, q, to give This expression is used when calculating Hamiltonian matrix elements of internal angular momenta in a space-fixed axis system as it projects the operator back into a molecule-fixed frame. 2.3 Molecular Hamiltonian a) The General Hamiltonian and the Born-Oppenheimer Approximation In the most basic sense, a molecule can be viewed as a collection of charged particles. The total energy of the system is then the total kinetic energy of the particles together with the potential energy associated with the various electrostatic interactions between them. Since a molecule consists of nuclei and electrons, the Hamiltonian operator (or total energy operator) has the form [2.44] q [2.45] 18 where pe and pn are the linear momenta of the electrons, e, and nuclei, n, respectively, and V(q,Q) is the potential energy operator, with q and Q representing the electron and nuclear coordinates respectively, given by V f e Q ^ - E E ^ Z Z ^ + X X ^ 1 . [2 46] n e en e e'>e ee' n n'>n nn' The first sum of Equation [2.45] represents the kinetic energy of the electrons while the second is the kinetic energy of the nuclei. The three terms of the potential energy expression of Equation [2.46] are the nuclear-electron Coulombic attraction, and the electron-electron and nuclear-nuclear electrostatic repulsions, respectively. In principle the energy levels of a molecule can be obtained by solving the Schrodinger equation using the Hamiltonian operator of Equation [2.45]. However, it is not possible to solve the equations of motion analytically for more than two bodies; the hydrogen atom is the only chemical system for which the Schrodinger equation can be solved exactly. Approximations must be used in order to solve for the energy levels of a molecule. Nuclei are substantially heavier than electrons. Electrons will therefore move much faster than nuclei. Born and Oppenheimer (1) proposed that, as a result of the small mass and fast motion of the electrons, the electrons will adapt themselves instantly to the current nuclear configuration. The electrons can then be treated as if they are moving in the field created by the nuclei that are held in a fixed position. This allows us to describe the motions of the electrons and nuclei separately. The total wavefunction can therefore be expanded as a complete set of functions represented by a product of electronic and nuclear parts ^ = Evi(q.Q)vL(Q)- P.47] 19 I n the l imi t o f fixed nuclear posit ions (or inf inite nuclear mass) the Hami l ton ian operator is reduced to the electronic Hami l ton ian # - . = ; T - 2 > 2 + V ( q , Q ) , t2-48^ 2 m e e o f wh ich the electronic funct ions v|/ e(q,Q) are eigenfunctions according to tfX(q,Q) = EX(q,Q). [2 .49] The energies, E' e , o f Equat ion [2.49] are the energies o f the stationary electronic states. Us ing the wavefunct ion o f Equat ion [2.47] and the Hami l ton ian o f Equat ion [2.45] in the Schrodinger equation, mul t ip ly ing bo th sides by M / k * ( q , Q ) and integrat ing over all o f the electronic coordinates, q, w e obtain .2 £ ^J" + E k ( Q ) + jVe * (q, Q ) Z ^ - (<b Q ) d ( l r ^ n ( Q ) n n n n + Z JZ f v e ( q , Q ) — V U q , Q ) l p n M / n ( Q ) = E v | / k ( Q ) , [2.50] where E, the to ta l energy, is the sum o f the electron and nuclear energies ( E = E k + E n ). I f , f o r the moment, w e neglect the terms in Equat ion [2.50] that contain integrals, we are left w i t h a simple Hami l ton ian operator fo r the nuclear mot ion (v ibrat ion and rotat ion) ^ „ = Z / ^ + E e ( Q ) [2 .51] n 2 m „ in wh ich the electron energy acts as a potential energy funct ion fo r the mo t ion o f the nuclei. The integral in the first te rm o f Equat ion [2.50] involves the nuclear kinet ic energy operator act ing on the electronic wavefunct ions. This te rm gives rise to a small nuclear 20 mass-dependence of the electron energy, which is therefore an isotope-dependent correction to the potential energy curve for the vibrational motion. The second term involving an integral is a cross term that contains the nuclear momentum operator acting between different electronic wavefunctions. This represents a coupling between the vibrational and electronic motions of different electronic states (vibronic coupling). The essence of the Born-Oppenheimer approximation involves the assumption that the interactions arising from the vibronic coupling term will be very small and can be ignored. If the separation between electronic states is large, the effects of this cross term are usually small and the Born-Oppenheimer approximation is a valid description. In situations where the energy separation between electronic states becomes small the cross term of Equation [2.50] can produce sizeable effects. Some of the most important effects occur in degenerate electronic states where the two components of the degenerate state are coupled. This results in the phenomena called the Renner-Teller effect in linear molecules and the Jahn-Teller effect in symmetric and spherical top molecules (5,6). These breakdowns can often be treated by perturbation theory, in which corrections are added to the Born-Oppenheimer Hamiltonian. The energies associated with electronic transitions are generally orders of magnitude greater than those associated with vibration, which are in turn significantly larger than the energy of rotation. For this reason, the zero of energy of the vibrational energy scale is usually taken as the electronic energy, E^ (Q), associated with the minimum of the potential energy well. The rotational energy levels are then defined relative to the different vibrational states. The total energy of a molecule can be expressed as the sum of the electronic, vibrational and rotational energies, 21 E = E k ( Q ) + G ( v i V 2 . . . ) + Fv(J). [2.52] b) The Separation of Vibrational and Rotational Motions It is convenient to separate the nuclear Hamiltonian of Equation [2.51] into vibrational and rotational parts (7). This can be accomplished by recasting the kinetic energy operator in an appropriate form. Several quantities must be defined in order to do this: R the position vector of the centre of mass of the molecule in space-fixed axes n the position vector of atom i in molecule-fixed axes ai the equilibrium position of atom /' in molecule-fixed axes dj the displacement of atom / from equilibrium in molecule-fixed axes, such that The velocity of atom /' in the space-fixed axis system, Vj, would be the velocity of the centre where the dot means time derivative. The molecule is rotating relative to the space-fixed frame so f, can be written dj = n - ai of mass of the molecule, R, plus the velocity of atom i relative to the centre of mass, r{, r, = d, + <o x ^ , [2.53] where ro is the angular velocity. The nuclear kinetic energy could then be written [2.54] Expanding Equation [2.54] gives 22 2T = ^ m i R 2 + ^ m i ( ( o x r i ) ( c o x r i ) + ^ m i d ? i i i + 2 ^ m i R ( t o x r i ) + 2 ^ m i R - d i [2.55] i i + 2 ^ m i ( c o x r i ) - d 1 To proceed further we must define what is meant by a vibrational motion. A convenient definition is that no set of vibrational displacements can cause a translation of the whole molecule ( Si mirj = 0 ), and the centre of mass must remain at the origin as the molecule vibrates ( S, m i r ; =0 ). Using these restrictions in conjunction with Equation [2.53] it is simple to show that the second line of Equation [2.55] must equal zero. The conditions for the absence of rotation must be defined next. For this we turn to the Eckart condition: ^ m i ( a i x d i ) = 0. [2.56] Differentiating this expression gives ^ m i ( a i x d i ) = 0, [2.57] i which states that the molecule must possess no angular momentum in its equilibrium configuration. Using the differentiated form of the Eckart condition as well as the vector product relationship A * B C = A B x C w e can simplify the cross product of the third line of Equation [2.55]. The final form of the nuclear kinetic energy expression then becomes 2T = 2]miR2 + ^ m i ( « x r i ) ( t o x r l ) + 2mjd? +2^miCO-(d , xdj). [2.58] i i i i The first term of Equation [2.58] represents the translational motion of the entire molecule, which can be factored off for molecules in free space; the second term is the rotational 23 motion, the third corresponds to vibrational motion and the final term is the cross term describing the coupling between vibration and rotation. This coupling is called Coriolis interaction. It arises because, for polyatomic molecules, certain combinations of vibrations can give rise to a vibrational angular momentum that can couple to the rotational angular momentum (consider the two degenerate bending vibrations of a linear triatomic molecule acting ninety degrees out of phase). The net result is that vibrational and rotational motions cannot be completely separated for polyatomic molecules, although the effects of the Coriolis interaction are often quite small. This effect does not occur for diatomic molecules and the separation of the two motions is complete. (i) Vibrational Energy Levels The procedure for solving the vibrational Schrodinger equation to obtain expressions for the vibrational energy levels of a molecule has been described previously (8) and will not be discussed in detail here. The vibrations of a polyatomic molecule are often approximated as a superposition of harmonic oscillators. For this reason, the vibrational energy level expressions are usually written as a sum of harmonic oscillator energy terms with anharmonic corrections G(v ; v } . . . ) = X co s ( V i + i) + X x s (v, + i ) (v } +1) [2.59] k>j>i 24 In this equation G ( v i V j . . . ) is the vibrational energy, v; are the vibrational quantum numbers, © i are the harmonic vibrational frequencies, and Xy and y y k are the quadratic and cubic anharmonicity constants respectively. A simpler form of this equation is also commonly used: G ( v i V j . . . ) = Z ( ° i V i + Z X i J V i V J + Zy>JkViVJVk+"- [ 2 6 0 ] i j>i k>j>i Neglecting anharmonic effects, the wavefunctions associated with the eigenvalues of Equation [2.59] are the harmonic oscillator eigenfunctions, which have the mathematical form M/Vj (Q ;) = N V i e- ( a ' / 2 ) Q ' H V j (V^Qi), [2.61] where Qi are the vibrational normal coordinates, cti = ccoi / h ( where c = speed of light ), N v i = ^ y . 1 ! ( ~ - ) 4 is a normalization factor and H v i is the Hermite polynomial of order V i . (ii) Rotational Energy Levels The derivation of the rotational energy level expressions is also very well known (8). This problem is often approached by assuming that the internuclear distances are fixed (i.e. that the molecule is a "rigid rotor") and then applying corrections to deal with the "flexibility" of the molecular bonds. The rotational Hamiltonian most commonly used has the form 25 fl"rot = B V R 2 - D V R 4 + H V R 6 + ... [2.62] where B v is the rotational constant, D v and H v are centrifugal distortion parameters and R is the rotational angular momentum operator (the end-over-end rotation of the molecule). The angular momentum R is often not the most convenient quantity to use in calculating rotational matrix elements, because other angular momenta may be present, and it is the total angular momentum that interacts with the field of the photons. Neglecting hyperfine effects, the total angular momentum, J, is the sum of the rotational angular momentum R, the total electron orbital angular momentum L and the total electron spin angular momentum S, i.e. J = R + L + S. A more usable Hamiltonian for open shell molecules is obtained by substituting for R with R = J - L - S . [2.63] For closed shell linear molecules, R = J, and the rotational energy levels can be written FV(J) = B v J(J + 1) - D v J2(J + l) 2 + H v J3(J + l) 3 + ... [2.64] where FV(J) is the rotational energy of level J. Because a molecule is constantly vibrating, the rotational constant, B v , represents an average over the structure of the molecule throughout the vibrational motion. For linear polyatomic molecules, where there are many vibrational degrees of freedom, B v represents an averaged moment of inertia about the axis of rotation. B v = -4- [2.65] In this equation the moment of inertia, I, is defined by the general formula I = £m;r 2 where n is the perpendicular distance of atom i, of mass mj, from the axis of rotation. For diatomic 26 molecules there is only one vibrational degree of freedom so the rotational constant depends only on the internuclear distance, r B v = 2 H 2 , [2.66] 87t cpr where p = minimi + m2) is the reduced mass. In this equation it is implied that r is an average internuclear distance B v = — < v | 4 lv>. [2.67] 871 cp r The magnitude of the rotational constant varies with the vibrational level since the average geometry of the molecule will be different in each vibrational state. This dependence upon v is usually expressed as a power series which, for polyatomic molecules, has the form B v = B e - J ] a i ( v i + i ) + ... [2.68] In this equation B e is the equilibrium rotational constant, evaluated using the moment of inertia of the molecule in its equilibrium geometry, and ai is a parameter describing the vibration-rotation interaction. For a diatomic molecule there is only one term in the sum of Equation [2.68] and the vibration-rotation parameter is given the symbol a e. The equilibrium geometry corresponds to the nuclear configuration at the minimum of the potential energy surface, which is not the same as that in the zero-point level where all the vibrational quantum numbers are equal to zero. The centrifugal distortion parameters, D v and H v , appearing in Equation [2.62] arise from the centrifugal forces that act on the nuclei as the molecule rotates. These forces have 27 the effect of stretching the bonds with increasing rotation. It is often sufficient to use just one centrifugal distortion parameter, D v, when modelling rotational energy level positions. The vibrational dependence of the centrifugal distortion constant D v is also expressed as a power series D v = D e - Z P . ( v . + T ) + - [2.69] c) Electron Spin Up to this point the effects of electron spin have been mostly omitted from the discussion. The concept of electron spin is not present in classical theory, but arises solely as a result of applying relativity theory to the electronic wave equation (9). The inclusion of electron spin angular momentum and its interaction with other angular momenta account for a number of observed effects that are not explained by classical mechanics. According to relativistic theory an electron possesses a magnetic moment, u,, that is proportional to its spin angular momentum p = _ £ e M . [ 2 7 0 ] h In this equation g e is the electron gyromagnetic ratio, U.B = eh / 2me is the Bohr magneton with e being the electron charge and me the electron mass, and s is the electron spin angular momentum. The interaction of this magnetic moment with the magnetic fields generated by the orbital motions of the electrons, the magnetic field generated by the rotation of the nuclei 28 and the spin magnetic moments of other electrons give rise to effects called the spin-orbit interaction, the spin-rotation interaction and the spin-spin interaction, respectively. These effects, which will be discussed below, are generally added as correction terms to the non-relativistic Hamiltonian. Jf= Ho + Xso + #"SR + #"ss [2.71] (i) The Spin-Orbit interaction Consider an electron with non-zero orbital angular momentum moving through the electric field, E, produced by a positively charged nucleus. Maxwell's equations (10) state that the electron will experience a magnetic field, B, given by Ex v B [2.72] where v is the linear velocity of the electron relative to the nucleus and c is the speed of light. The electric field of the charged nucleus is given by the gradient of the potential V dr j [2.73] where r is the position vector of the electron relative to the nucleus. Substitution into the magnetic field expression gives 1 fdV^ B c 2r V dr j r x v [2.74] 29 The magnetic moment of the electron, given by Equation [2.70], will interact with this magnetic field according to 'dv^  Hso = -n -B = hc2x dr (r x v ) • s , [2.75] For discussing a multi-particle system we must clarify our definitions of the various quantities. The position vector r will be written r c n, which represents the displacement of electron e from nucleus n. The velocity of the electron will be labelled v e n , corresponding to the velocity of electron e relative to nucleus n. The electron spin also receives a subscript label s e for electron e. To proceed we must substitute for the velocity, v e n - Classically this would be the vector difference of the electron and nuclear velocities ( v e n = v e - v „ ). However, due to the extremely rapid motion of the electron a relativistic treatment must be used. A phenomenon known as Thomas precession (11) introduces a factor of Vi as a result of the electron's acceleration through the Coulombic field generated by the nuclei and other electrons Ven 2 Ve V n . [2.76] The interaction Hamiltonian now becomes ' d V ^ so hc2r. dr„ L X ( i v e - V „ ) ] - S e [2.77] en V u l e n J For a system of multiple electrons and nuclei the energy corrections are additive. For a molecule, the Hamiltonian is written ^so ~~ S Zr-f k n X ( i V e - V „ )]• S { he2 e n en V d r e n y [2.78] 30 which expands to + 2hc2 he2 e T r e n W e n J (>*en X V e ) - S e (ren X V n ) - S e [2.79] The second term of Equation [2.79] deals only with the nuclear velocity and gives rise to the spin-rotation interaction, which will be discussed in the next section. The significance of the first term can be made more clear by multiplying and dividing the term by the electron mass, me, and using the definition 1 = r x mv. Equation [2.80] clearly describes the interaction of the electron orbital and spin angular momenta, or spin-orbit interaction. The discussion thus far has not taken into consideration the effects of the charges of the other electrons in the molecule. This has been done explicitly by Van Vleck (12); however, it can be approximated satisfactorily by taking the potential, V, as a Coulomb potential with an effective nuclear charge, Zn(efl)C, to describe the screening effect of the other electrons where so is the permittivity of free space. Afier differentiating Equation [2.81] we can write [2.80] V = [2.81] [2.82] 31 By summing over all nuclei Equation [2.82] can be rewritten where a e l e = - ^ M L Y . ^ l e „ . [2-84] 4TO 0 c 2 f t 2 f d Equation [2.83] is called the microscopic spin-orbit Hamiltonian. The spin-orbit Hamiltonian is often approximated as ?fSo = A L ' S [2.85] where L and S are the total electron orbital and spin angular momenta respectively. L = Z , e S = Z S e t 2 ' 8 6 ] e e This form of the spin-orbit Hamiltonian is generally used in the situations where the interacting states have the same total spin quantum number S, while the microscopic form is needed to describe interactions between states of different multiplicities. (ii) The Spin-Rotation interaction The spin-rotation interaction is described by the second term of Equation [2.79] 32 As with the previous derivation, the shielding effects of the various electrons can be approximated by using an effective nuclear charge, Ze(eff), m a potential with the same form as Equation [2.81]. Since we are concerned with the rotational motion of the nuclei, v„ can be expressed as (12) v„ = a x r n , [2.88] where r„ is the position of nucleus n from the centre of mass and co is the angular velocity. Differentiating the potential and using Equation [2.88] with the definition R = I ra for the rotational angular momentum we can express the spin-rotation Hamiltonian as *"« = - 7 l £ ^ Z S ^ f I [ r e „ x ( R x r n ) ] . S e [2.89] 4 7 t 6 0 c K ^ ^ ren which can be expanded to te'Cl»' • r » [2.90] where the vector product rule A x B x C = ( C • A )B - ( B • A )C was used. The second term of Equation [2.90] is often omitted because it is generally very small in magnitude and connects different electronic states. If we take the first term only and sum over the nuclei we obtain the microscopic spin-rotation Hamiltonian # S R = 5 > e R - S e > [2.91] e where 33 b - = - ^ ^ ? ^ ( r " ' r - ) 1 2 9 2 1 A simplified form of the Hamiltonian is usually used in practice: # S R = Y R - S [2.93] which represents a direct coupling of the rotational and total spin angular momenta with coupling constant y. A second contribution to the spin-rotation parameter, which is often greater in magnitude than the direct spin-rotation coupling, results from the off-diagonal elements of the spin-orbit operator. These second order contributions have been shown (13) to have the same form as Equation [2.87]. As a result, the effective value of y obtained by fitting spectral data is an unseparable combination of the direct spin-rotation interaction and the second-order spin-orbit interaction y = y S R + y s o [2.94] where y s o is usually larger than y S R . (iii) The Spin-Spin interaction The magnetic vector potential at point i, arising from an electron at a point j with a magnetic moment p.j, is given by (10) H= xr a 4 34 where rji = rj - n. By Maxwell's equations (10) the magnetic field at point i would be Bi = V x Aj [2.96] where V is the directional derivative operator. If we place a second electron at point i its magnetic moment will interact with the magnetic field generated by the electron at j according to #ss,ij = -M-i • Bi 2 2 n2 r \ 1 V x Sj x rji 3 r ^ J 1 J Si [2.97] where the expression was expanded using Equations [2.96], [2.95] and [2.70]. We now use the vector identity V x A x B = A x ( V - B ) - ( A - V ) x B + ( B - V ) x A - B x ( V x A ) [2.98] and make note of the fact that the directional derivative, V , only acts upon spatial coordinates so that V x s = V - s = 0. After simplification Equation [2.97] can be rewritten #ss,i 2 2 g eu-B h2 + 2 2 g e ^ B h2 S j x ( V r j i ) (s j -V)xrj , 1 r 3 V J' J -• Si 1 3 V J' J Si. [2.99] This equation appears to have a complication in that it becomes infinite when rjj=0. Gauss' divergence theorem can be used to treat this problem and simplify the expression further. The theorem is expressed mathematically as 35 r3-V J' J 4% 8(ry), [2.100] where 8( ry ) is the Dirac delta function which has a value of zero except when = 0. The Dirac delta function is defined in such a way that it picks out the square of the amplitude of electron j's wavefunction at the coordinate origin, or, when electron j is at the same position as electron i <S(rji)> = |v(/j(0)|2. [2.101] Upon using the Gauss divergence theorem the first term of Equation [2.99] can be written 2 2 #-ss,ij (contact) = - 4K | \|/J(0) | 2 S i • S j . [2.102] This is known as the electron contact term since it describes the interaction of the electron spins when they are located at the same point in space (i.e. they are in contact with one another). After some considerable algebra, the second term of Equation [2.99] can be reduced to the following form 2 2 n2 4% Vj(0) s= s, 3 ( s 1 r j i ) ( s j r j i ) [2.103] To account for the total interaction in a molecule we combine Equations [2.101] and [2.103] and sum over all electrons ^ss ~ CfeM-B V - 87C + 2 2 »J s.-Sj 3 ( s i r j i ) ( s j r j i ) [2.104] 36 The first term of Equation [2.104] is just a constant factor and is usually included in the Born-Oppenheimer potential. The second term has the same form as a classical interaction between dipoles and is called the dipolar electron spin-spin interaction. As was the case for the spin-orbit and spin-rotation interactions a simpler more approximate form is used for the spin-spin interaction. The phenomenological form most commonly used in practice for diatomic molecules is ^ S S = | X ( 3 S | - S 2 ) [2.105] where X is the electron spin-spin interaction parameter. d) Nuclear Spin Nuclei have intrinsic spins that originate from the same relativistic treatments as the electron spin. Unlike electrons, most nuclei are composed of more than one elementary particle ( i.e. protons and neutrons ), each with an intrinsic spin of one half. The total spin for a single nucleus, I (not to be confused with the moment of inertia, I), is the resultant of the interactions of the intrinsic spins of each of the nucleons, and has an integer or half-integer value that is greater than or equal to zero. In fact, the largest observed nuclear spin for a single stable nucleus has been found in the tantalum isotope I 8 0 Ta, which has 1 = 9. Nuclei with a non-zero spin angular momentum will have a magnetic moment that is free to interact with other magnetic moments within the molecule. These interactions give rise to magnetic hyperfine structure (14,15). The magnetic moments of nuclei are generally weaker 37 than those of electrons and give rise to much smaller corrections to the energy. Nuclei that have a spin angular momentum with a magnitude greater than or equal to one also have an electric quadrupole moment due to the non-spherical charge distribution. This quadrupole moment can interact with the electric field gradient at the nucleus generated by the charge distribution of the electrons to give rise to nuclear quadrupole hyperfine structure (16). Both of these effects will be discussed below. (i) Magnetic Hyperfine interaction The theory of the magnetic hyperfine interaction in diatomic molecules was first developed by Frosch and Foley (14). They recognised the equivalence between the interactions of the nuclear spin magnetic moments and those of the electron magnetic moments and derived the hyperfine Hamiltonian from the relativistic Dirac equation for the electron. A simplified derivation of the same Hamiltonian expression was later given by Dousmanis (15). The nuclear spin magnetic moment can undergo similar interactions to the electron spin magnetic moment. The principal interactions are with the orbital magnetic moments of the electrons, the spin magnetic moments of the electrons, the rotational magnetic moment of the nuclei, and the spin magnetic moments of other nuclei. This last type, the nuclear spin-nuclear spin interaction, is generally very weak and is usually negligible. It will not be discussed in this thesis. 38 The Hamiltonian for the nuclear spin-electron orbit interaction can be obtained from the electron spin-orbit interaction described in Section 2.3.c(i) by replacing the electron spin magnetic moment with that for the nucleus ui = g„u«.l [2.106] where g n is the nuclear g-factor and u.n is the nuclear magneton ( p n = eh I 2mp , mp is the proton mass ). The expression for the interaction is given by * F IL=E5>- I -- | e' [2.107] where a en = 2hc m„ dV dr [2.108] The Hamiltonian for the nuclear spin-electron spin interaction is derived identically to that of the electron spin-spin interaction. After substituting the nuclear magnetic moment for that of the electron into Equation [2.104] we obtain #"is -g e W n h2 ESg . ^k .<o) |V . . g e ^ B ^ n h2 I „ s e 3 ( I „ r e n ) ( s e r e „ ) [2.109] In this case the first term of Equation [2.109] is not a constant energy correction, but represents the Fermi contact interaction between the electron and nucleus when the electron is in an orbital with non-zero amplitude at the nucleus (i.e. an s-type orbital). The second term describes the dipolar nuclear spin-electron spin interaction. 39 The nuclear spin-rotation interaction is also generally very small and is often omitted from the analysis of magnetic hyperfine structure. In our studies on the niobium oxide molecule (Chapter 4), the data were precise enough to observe the effects of this weak interaction. The Hamiltonian for the nuclear spin-rotation interaction, which can be derived by analogy with the electron spin-rotation interaction, is given by ^ I R = Z C I . n I n - J [ 2 1 1 ° ] where gnM-n C l ' n ~ fc 2 T he I dV — [2.111] dr and I in the denominator is the moment of inertia. J is used instead of R in Equation [2.110] because the effects of I • L and I • S have already been incorporated in the hyperfine spin-orbit and spin-spin interactions. The total magnetic hyperfine Hamiltonian is obtained by combining all of the terms described above as ^ " M H F = S a e I - , e + Z b F . e I - S e + C l I - J e e [2.112] -Z h2 I s e 3(I.r e )( V r e ) r 3 r 5 where the second term has been used to represent the Fermi contact interaction and it has been assumed that there is only one nucleus contributing to the hyperfine structure. As with the electron spin interactions it is useful to approximate the sum over electrons as the vector sum of the various electron angular momenta. The usual form for the magnetic hyperfine Hamiltonian is 40 MHF = aI-L + bI-S + cI z S z +c,I- J [2.113] where a = g e g n w h2 n [2.114] 87t g e g n u . B p 3 h2 n k(o)| [2.115] c = 2 e gnM-B^n / 3 C 0 S 2 6 - 1 h2 \ r 3 [2.116] b = b F - | c [2.117] and Ci is defined above. In Equation [2.113] only the diagonal part of the dipolar spin-spin Hamiltonian has been used. The experimentally determinable parameters are a, b, c, and ci, although b is not a fundamental physical quantity. The Fermi contact parameter, bF, and the diagonal dipolar parameter c are the fundamental quantities describing the nuclear spin-electron spin interaction, but bF can only be evaluated indirectly through b and c. (ii) Electric Quadrupole interaction Although magnetic hyperfine effects dominate the hyperfine structure of open shell molecules, an additional effect, the electric quadrupole interaction, will always be present for any spin multiplicity, as long as I > 1. 41 Quadrupole hyperfine structure is caused by the interaction of the nuclear electric quadrupole moment with the electric field gradient at the nucleus generated by the charge distribution of the electrons (16). It can be understood as follows. From Coulomb's law, the electrostatic interaction between a nucleus at point r„ and an electron at point r e is given by Ze2 [2.118] where r^ = | r e - r„ | is the separation of the electron and the nucleus. This separation can be expanded in the form ^ =V r e 2 + r n-2r e r n cose e n [2.119] where 6en is the angle between r e and r„. Equation [2.119] can then be rewritten as fr } ( \ r 1 - 2 cos6en + Kre J [2.120] which has the form of the generating function for the Legendre polynomials (2). The Coulomb interaction can now be recast in the form tfc—Ze^-^PkCcose.) [2.121] k=0 re where Pk(cos 9en) is the Legendre polynomial of order k. At this point the nuclear and electronic coordinates can be separated by using the spherical harmonic addition theorem (3) P k (cosco) = X (-l)m C k , _ m (9, C t a (9', 40 [2.122] m=—k 42 where Ckm = -v/47r/2k + l Ykm(9,(t>) is a modified spherical harmonic (2). The Coulomb interaction now takes the form of a multipole expansion muttipole - Z e2 £ £ (-1)' k=0 m=-k Z re" k _ 1 C k ,-m(6e,4)e) t-Ckm(e„,*B)] [2.123] where we have summed over all electrons. The first term of the expansion ( k = 0 ) represents a monopole interaction and is simply the Coulomb attraction between the electrons and the nucleus. This term has been accounted for in the electronic Hamiltonian. The next term ( k = 1 ) represents an electric dipole interaction which can be shown to be zero by symmetry arguments (17), as are all higher order terms of odd order. The first non-vanishing term is that with k = 2, which represents the interaction between the electric quadrupole moment, Q, with the electric field gradient, VE, at the nucleus due to the charge distribution of the electrons. The Hamiltonian for this interaction becomes ^ = e i ( - l ) m [ r „ 2 C 2 , m ( 9 n ) i ) ] m=-2 Ze c2)_m(ee,(t)e) which can be written 7 r Q = e £ ( - l ) m T m ( Q ) T 2 m ( V E ) . [2.124] m=-2 Equation [2.124] represents the scalar product of the nuclear electric quadrupole tensor and the electric field gradient tensor. The electric quadrupole hyperfine Hamiltonian can therefore be written as (18) #-Q = eT 2 (Q) -T 2 (VE) . [2.125] 43 The quantum mechanical observables associated with the nuclear electric quadrupole moment and electric field gradient tensor operators are the electric quadrupole moment, Q, and the field gradient coupling constant, qo, respectively. These quantities are defined as '/2 eQ = e < I, mi= 11 T 0 2(Q)| I, mi = I > [2.126] '/2 q 0 = < J , mj= J | T 0 2(VE) | J , mj= J >. [2.127] The experimentally measurable parameter is the quadrupole coupling constant 'eQqo'. 2.4 Hund's Coupling Cases and the Effective Hamiltonian Matrix In general we have complete freedom to choose a set of basis functions with which to calculate the Hamiltonian matrix; for rotational problems they need only be combinations of eigenfunctions of the appropriate angular momentum operators. In practice the choice is a matter of convenience. For example, one might choose a basis set for which it is easy to evaluate the Hamiltonian matrix elements but whose diagonal elements do not approximate the energy levels of the molecule, since matrix diagonalization can be easily performed on modern computers. In other situations it may be better to choose a basis set that gives the most diagonal representation. The choice of basis functions is usually based on the relative sizes of the angular momentum couplings in the molecule. 44 a) Hund's Coupling Cases A useful classification of the different angular momentum coupling schemes in molecules has been made by Hund (19). Although there are potentially many ways in which the angular momenta can be coupled, Hund identified five important limiting cases that have come to be known as Hund's coupling cases (a) to (e) (19). These original studies did not include the nuclear spin angular momentum, but they can easily be extended to include hyperfine structure. Hund's cases (a) and (b) are the most commonly observed coupling schemes in molecules. Case (c) occurs when the molecule contains very heavy atoms and case (d) describes the coupling for molecules in Rydberg states where one of the electrons has a large value of the principal quantum number, n. Case (e) is only rarely met in Rydberg states with open shell cores. Hund's case (a) is the simplest of the coupling schemes. It applies when the spin-orbit coupling is not unduly large, and the electron orbital (L) and spin (S) angular momenta can be considered as precessing independently about the internuclear axis. A vector diagram representing Hund's coupling case (a) is given in Figure 2.1(a). For a linear molecule the orbital angular momentum, L, represents the quantized circular motion of the electrons round the axis containing the nuclei. The component of L along this axis (the eigenvalue of L z) is called A. Similarly, the spin angular momentum, S, precesses round this axis with component Z. The sum of the two components, A + E, is called Q; it represents the projection of the total electron angular momentum. The end-over-end rotation of the s Figure 2.1 Representations of Hund's coupling cases (a), (b) and (c). The coupling scheme and angular momentum basis functions are given for each case. 46 molecule, R, adds to the two electron angular momenta to give the total angular momentum excluding nuclear spin, J . Since R is perpendicular to the internuclear axis for linear molecules, its z-component is zero, so that the z-component of J arises solely from the electron angular momenta, and is equal to Q. = A + Z. Since the angular momenta L , S and J are considered to be independent, the basis functions for Hund's case (a) can be written as the simple product where the index r\ represents all other coordinates needed to fully describe the electronic state. It implies that the angular momenta S and J are well defined, as are the z-axis projections L z , Sz and J z. L is not well defined because molecules do not have spherical symmetry. Electronic states in Hund's case (a) are labelled with the term symbol 2 S + 1 A Q , where the superscript (2S+1) is called the spin multiplicity. Hund's case (b) coupling represents the situation where the spin-orbit coupling is small (smaller than the rotational energy) so that the spin angular momentum S is not coupled to the internuclear axis. A pictorial representation of case (b) coupling is given in Figure 2.1(b). The orbital angular momentum L precesses round the z-axis just as in case (a) coupling. L then adds to the rotational angular momentum R to form the resultant N. This is then coupled to the electron spin angular momentum S to form the total angular momentum excluding nuclear spin, J . This coupling scheme is summarized by L + S + R = J [2.128] I rjA ; SZ ; JH > [2.129] L + R = N N + S = J . [2.130] 47 Since S is uncoupled from the z-axis the projection quantum numbers £ and Q are no longer defined; only K, the z-component of N, is defined in case (b) coupling. For linear molecules K = A because R is perpendicular to the molecular axis so that the projection of N must also be the projection of the orbital angular momentum L. The basis functions appropriate for a linear molecule in Hund's case (b), labelled with the term symbol 2 S + 1 A , are lti;NASJ>. [2.131] Multiplet states of non-linear molecules can also follow case (b) coupling, with basis functions I ri(A) ; NKSJ >. [2.132] The transformation from case (a) to case (b) is given by (20) S N ' r\A ; NKSJ > = ^ ( _ I ) N - S + Q ^ 2 N + 1 r|A;SE;JQ>. [2.133] We must now include the nuclear spin angular momentum. If there is one 'spinning' nucleus in the molecule, the nuclear spin angular momentum may couple with varying strength to the various electronic and rotational angular momenta. The classification of these coupling schemes is based on Hund's cases (a) and (b) which are subdivided according to whether the nuclear spin is coupled more strongly to the molecular axis (subscript a) or to another angular momentum within the molecule (subscript P). In reality the cases (aa) and (ba) are not encountered because the small size of the nuclear magnetic moment makes it very unlikely that it will interact with the molecular fields strongly enough to couple it to the internuclear axis. For case (ap) the nuclear spin I couples to the total angular momentum 48 excluding nuclear spin J to give the total angular momentum F. The complete coupling scheme for case (ap) is L + S + R = J ; J + I = F [2.134] and the appropriate basis functions are | TTA ; SE ; JQIF >. In Hund's case ( b p ) the coupling scheme is further divided according to which molecular angular momentum I couples to most strongly; cases (bpj), (bps) and ( b p N ) are possible. Case ( b p N ) is not expected to occur because the coupling between I and S or I and J is expected to be much stronger than the coupling between I and N. The coupling scheme for case (bpj) is L + R = N ; N+S = J ; J + I = F [2.135] which is best described using the basis functions | TTA ; (NS)JIF >; case (bpj) is the most commonly encountered of the extended case (b) coupling schemes. Case (bps) applies when the Fermi contact interaction ( b F I • S ) is larger than any other electron spin interaction. In this situation I couples to S to form the resultant G, which in turn couples to N to give the total angular momentum F: L + R = N ; I + S = G ; G + N = F [2.136] The basis functions appropriate to case (bps) are | r\A ; (IS)GNF >. Pictorial representations of the three most common of the extended Hund's coupling cases, cases (ap), (bpj) and (bps), are given in Figure 2.2. Hund's coupling case (c) applies to molecules containing one or more heavy atoms. The presence of heavy atoms generally results in extremely large spin-orbit interactions. In this situation L and S couple very strongly to form J a , the total electron angular momentum. 49 a) Hund's case (ap) L + S + R = J ; J + I = F I nASIJQIF > b) Hund's case (bpj) L + R = N ; N + S = J J + I = F I riA(NS)JIF > c) Hund's case (bps) L + R = N ; I + S = G G + N = F I r|A(IS)GNF > Figure 2.2 Representations of the extended Hund's coupling cases (ap), (bpj) and (bps). The coupling scheme and angular momentum basis functions are given for each case. 50 J A then couples to the rotational angular momentum R to give J. A diagram of case (c) coupling is given in Figure 2.1(c). Unlike cases (a) and (b), the electron spin angular momentum S is no longer well defined in case (c) coupling, so the spin multiplicity is also undefined. Case (c) states are labelled with the only defined projection quantum number, fi, and are best described by the basis functions | r | J a f i ; J f i >. Case (d) coupling applies to Rydberg states in which an electron has been promoted to an orbital with a very high principal quantum number n. Because the Rydberg electron is mostly far from the ion core, its orbital angular momentum is coupled only weakly to the molecular axis. The coupling scheme for case (d) has L couple to the core rotational angular momentum N c o r e to give N . The coupling of N and S to give the total angular momentum J is usually very small and is often not included in the coupling scheme. Hund's case (d) is very similar to case (b); the difference is that N (or NCOre) is coupled to L instead of S. The basis functions for case (d) coupling are | NC Ore A L N >. Hund's coupling case (e) will not be discussed here since no well established examples have been observed. The details of this coupling case can be found in the literature (21). Hund's cases (a) to (e) (and the extended cases (ap), (bpj) and (bps)) are essentially choices of basis functions, and represent ideal limiting cases of angular momentum coupling. In reality, they represent the electronic states of many molecules quite closely though all states are intermediate cases to some degree. In fact, in degenerate states where the spin-orbit coupling is moderate, the most nearly diagonal representation can change from case (a) to case (b) with increasing rotation; this process is known as 'spin-uncoupling'. As is shown 51 in the next section, it occurs because the term -2B J • S that arises in the expansion of the case (a) rotational Hamiltonian progressively couples the electron spin angular momentum S more strongly to J than to the orbital angular momentum L . At this point S is said to be uncoupled from L as well as the internuclear axis, which is the coupling scheme described by Hund's case (b). b) M a t r i x elements of the Hamiltonian operator in a H u n d ' s case (ap) basis The electronic states discussed in this thesis are best described using Hund's case (ap) coupling; therefore the Hamiltonian matrix elements calculated in a case (ap) basis will be presented in this section. The appropriate operators have been outlined in Section 2.3 and are expressed in terms of the total orbital and spin angular momenta; only when different electronic states interact with each other is it necessary to use the microscopic forms of the Hamiltonian operators. The total Hamiltonian operator for a case (ap) state can be written H= %ot + XCD + #SO + XSS + #SR + #MHF + # Q + #LD [2.137] where Kot — B R 2 [2.138] Hen = - D R 4 [2.139] Xso = A L • S [2.140] flss= fM3S z 2-S 2) [2.141] 52 #SR = Y R - S [2.142] #MHF = a I - L + bI-S + cI z S z + c i I -J [2.143] i% = eQqo 3I Z2-I 2 41(21 +1) = e T 2 ( Q ) - T 2 ( V E ) [2.144] The term Hm of Equation [2.137] refers to A-doubling effects, which will be discussed in detail in the next section. It is not necessary to use the powerful tools of spherical tensor algebra to evaluate all of the matrix elements to be presented in this section. The vector forms of the operators will be used to calculate the matrix elements of the rotational and electron-spin fine structure operators; spherical tensor methods will be used to evaluate the various hyperfine matrix elements. Full details will not be presented for all of the elements of the total Hamiltonian. Instead, a specific example is made of the magnetic hyperfine spin-orbit interaction to show the general methods by which the final expressions can be calculated. From Equation [2.128] we see that the rotational angular momentum can be rewritten as R = J - L - S. Substituting this into Equations [2.138] and [2.139], expanding and omitting the terms off-diagonal in A (since they can be included in the A-doubling operator) the following forms are obtained for the rotational and centrifugal distortion Hamiltonian operators Hrot = B [ J 2 + S 2 - J 2 - S2 - ( J+S_ + J_S+ )] [2.145] # C D = -D [ J 2 +S2 - J 2 - S 2 - ( J+S_ + J_S+ )]2 [2.146] 53 where ( J+S- + J_S+ ) is the spin-uncoupling operator. Making use of Equations [2.9] to [2.11], the matrix elements of the rotational Hamiltonian (Hot) are < TTA ; S Z ; J O | %oi I nA ; S Z ; J Q > = B [ J(J+1) + S(S+1) - O 2 - Z 2 ] [2.147] < TIA ; SZ+1 ; J O + 1 | HROI \ r\A ; S Z ; J O > = - B V[ J(J +1) - 0(0 ± 1)] [S(S +1) - Z(Z ± 1)] [2.148] and those of the centrifugal distortion Hamiltonian (HCD) are < TIA ; SZ ; JQ | #CD I r|A ; SZ ; JO > = - D {[ J(J+1) + S(S+1) - O 2 - Z 2 ] 2 + 2 [ J(J+1) - O 2 ][ S(S+1) - Z 2 ] + 2 OZ } [2.149] < -nA ; SZ±1 ; JO±l | JCCD I TiA ; SZ ; JO > = 2 D [ J(J+1) - 0(0±1) + S(S+1) - Z(Z±1)-1] x ^ [JfJ +1) - 0(0 ± 1)][S(S +1) - Z(Z ± 1)] [2.150] < r]A ; SZ+2 ; JO+2 | 9fCD I r)A ; SZ ; JO > = - D V[J(J +1) - (O +1)(0 ± 2)][S(S +1) - (Z ± 1)(Z ± 2)] x ^[1(1 +1) - 0(0 ± 1)] [S(S +1) - Z(Z ± 1)] [2.151] The matrix elements for the spin-orbit interaction can be easily evaluated after expanding the operator in terms of its Cartesian components as !Hso = A L • S = A [ L ZS Z + V2 ( L+S- + L_S+ ) ] [2.152] < TiA ; SZ ; JO | #so I r|A ; SZ ; JO > = AAZ [2.153] < riA+1 ; SZ+1 ; JO | Xco I TJA ; SZ ; JO > = ± Aj. VS(S +1) - Z(Z +1) [2.154] 54 where the effects of the L+ and L_ operators have been absorbed into the off-diagonal spin-orbit parameter A L . The electron spin-spin interaction has only diagonal Hamiltonian matrix elements, given by < r]A ; SE ; Jfi I Kss I -nA ; SE ; JO > = § X [ 3 E 2 - S(S+1) ] [2.155] Centrifugal distortion corrections are also needed for the electron spin-orbit and spin-spin interactions because of the rotational motion of the molecule. The centrifugal distortion correction for any Hamiltonian operator, H, can be obtained from flb= i C D [ 7 < R 2 ] + = ^ C D [#-R2 + R V ] [2.156] where C D is the centrifugal distortion parameter. For the spin orbit and spin-spin interactions of Equations [2.140] and [2.141] the centrifugal distortion corrections have the form # b ( s o ) = i A D [ L 2 S z , R 2 J + [2.157] # b ( S S ) = ^ D [ f X ( 3 S z 2 - S 2 ) , R 2 ] + [2.158] where the operator R 2 can be substituted for as before. The matrix elements for these correction terms are < r | A ; SE ; Jfi | #b ( so) I r | A ; SE ; Jfi > = A D A E [ J(J+1) + S(S+1) - fi2 - E 2 ] [2.159] < r | A ; SE+1 ; Jfi±l | 7% 0 ) I r\A ; SE ; Jfi > = - A D A ( E ± V 2 ) V[ J(J +1) - fi(fi ± 1)] [S(S +1) - E(E +1)] [2.160] 55 and < r)A ; SZ ; JO | #b ( S S ) I r\A ; S I ; JO > = f X D [ 3Z 2 - S(S+1) ][ J(J+1) + S(S+1) - O 2 - Z 2 ] [2.161] < r|A ; SZ+1 ; JO+1 | #b(SO) I r|A ; SZ ; JO > = -A,D[ Z 2 +(Z+1)2 - f S(S+1)] x ,j[JQ +1) - 0 ( 0 ± 1)][S(S +1) - Z(Z ± 1)] [2.162] To evaluate the matrix elements of the spin-rotation interaction we substitute for the rotational angular momentum R as before. The expanded spin-rotation Hamiltonian and its matrix elements become 7/ S R = y R - S = y[ S 2 -S 2 +'/ 2 ( J+S- +J-S+)] [2.163] < T I A ; SZ ; JO | XSR I r|A ; SZ ; JO > =y [ Z 2 - S(S+1) ] [2.164] < -nA ; SZ+1 ; JO+1 | ^ S R | r\A ; SZ ; JO > = i Y > / [ J ( J + 0 - ± 1)][S(S +1) - Z(Z +1)] [2.165] The matrix elements for the magnetic hyperfine Hamiltonian are most easily evaluated using spherical tensor methods. As an example of this procedure, the matrix element for the hyperfine spin-orbit interaction a I-L = a T^IJ-T^L) will be examined in detail. From Equation [2.39] we can write the matrix element for the nuclear spin-electron orbit interaction as < r|A ; S'Z'; J'O' IF | a T^I) -T !(L) | r\A ; SZ ; JOfF > = a (-1) J + I + F j j j x< nA ; S'Z'; J'O' || T ! (L) || ^ A ; SZ ; JO >< 11| T^I) || I >. [2.166] 56 The reduced matr ix element O II T ^ I ) || I > is easily evaluated using Equat ion [2 .29] , whi le the tensor operator T X ( L ) must be projected f r o m space-fixed to molecular axes before evaluating its reduced matr ix element. W i t h the help o f Equat ion [2.44] the Hami l ton ian matr ix element can be recast as < r |A ; S T ' ; J 'O ' IF | a T ' f l ) - T ^ L ) | n A ; SE ; J O I F > = a ( - 1 ) J + I + F | ^ J * x Vl(I + 1)(2I + 1 ) < nA | T 1 ( L ) | nA >< J 'O' || ©.^(aPy)!! JO >. [2.167] q Only the q = 0 component o f the tensor operator T q ( L ) need be considered since the q = ±1 components w o u l d have matr ix elements that l ink different electronic states, wh ich is highly unl ikely considering the small magnitude o f the nuclear magnetic moment. Us ing Equat ion [2.27] t o evaluate < n,A | T o ( L ) | nA > and Equat ion [2.35] to project out the q-dependence, w e obtain the result < nA ; SE ; J 'OIF | a Tl(T) - T ^ L ) I n A ; S E ; J O I F > xJ+J'+I+F-Q / l Y T , 1 \ / " 1 T , 1 \ / 1 T , 1 \ / 1 T ' , 1 \ [ F I J'l T J ' 1 P = aA (-l)J+J'+I+F-QVl(I + l ) ( 2 I + l ) (2J + l ) ( 2 J ' + l ) J T 0 o ^ J . [2.168] The matr ix elements for the other terms o f the magnetic hyperf ine Hami l ton ian can be evaluated in a similar manner. The results are < n A ; S E ' ; J 'O ' I F | b T\T) ^(S) | n A ; SE ; J O I F > = b ( - 1 ) J + J ' + S + I + F - Q _ S ^/SfS + l ) (2S +1)1(1 + 1)(2I + 1)(2J + 1)(2J' +1) [F i j'l r i JY s I s^  r o X 1 JI I - f f q Q - E ' q E [ 2 ' 1 6 9 ] 57 < ^ A ; S I ; J'OJT | c I* ( I )^ 1 (S) | nA ; SI; JOIF > = c i ( - I ) " ' ™ V K I + 1)(2I + 1)(2J + 1)(2J' +1) J ] ^ r Q J ^ j [2.170] < TIA ; SI; JOTF | ci T ^ I ) -T\j) \ nA ; SI; JOIF > = ci (-1)J+I+FVl(I + 1)(2I + 1)J(J + 1)(2J +1) | * ] j | [2.171] After substitution of the appropriate 3-j and 6-j symbols (2,3) the non-vanishing matrix elements of the magnetic hyperfine Hamiltonian are (22) < nA ; SI; JOIF | T ^ H F | r|A ; SI; JOIF > = + ^ci R(J) [2.172] 2 J(J + 1) 2 < rjA ; SI; J - l OIF | 7 /MHF I riA ; SI; JOIF > = h ^ J 2 -O^P(J)Q(J) [2.\iy\ 2jV4J2 -1 < -nA ; SI±1 ; JO+1 IF | # M H F I rp\ ; SI; JOIF > _ bVCJ + OXJ + O + l) R(J)V(S) 4 J(J +1) < r|A ; SI+1 ; J - l 0 ± 1 IF | 7/~MHF I T y \ ; SI; JOIF > [2.174] _ + bV(J + 0)(J + 0 + l) P(J)Q(J)V(S) 4JV4J2 -1 [2.175] where R(J) = F(F+1) - J(J+1) -1(1+1) [2.176] P(J)= V(F-I + J)(F + I + J + 1) [2.177] Q(J)= V(J + I- FX F + I - J + 1) [2178] 58 V(S) = V S ( S + 1)-E(E±1) [2.179] and h = aA + (b + c)Z. [2.180] The matrix elements of the electric quadrupole Hamiltonian operator can be calculated in much the same way as those of the magnetic hyperfine Hamiltonian operators. The quadrupole operator is expressed as a scalar product of the electric quadrupole tensor T2(Q), which acts upon the nuclear spin eigenfunctions | I >, and the electric field gradient tensor, T2(VE), which operates on the electron orbital functions I A >. Using Equation [2.39] the matrix elements can be written The reduced matrix element of the tensor operator T2(Q) can be evaluated by applying the Wigner-Eckart theorem ( Equation [2.26] ) to the right side of Equation [2.126]: where Q is the nuclear quadrupole moment. The field gradient tensor T 2(VE) must then be projected into molecule-fixed axes with Equation [2.44]. Using Equation [2.35] for the reduced matrix element of the Wigner rotation matrix, the electric quadrupole matrix element becomes < TI'A' ; S Z ; J ' Q T F | !HQ | r\A ; S Z ; J O I F > = e (-!)• x< III T2(Q) || I >< ri'A'; J ' Q ' || T2(VE) || nA ; J Q >. [2.181] <I||T2(Q)||I> [2.182] 59 < r i 'A' ; SZ ; J 'QTF | HQ \ r\A ; SZ ; JOIF > = | eQ (-1) J+J'+I+F-Q V(2J + 1)(2J' + 1) 2 J I - l J' 2 J F I J ' l f I 2 I'| y i - I 0 i j ^ i - O ' q O <il 'A' | T 2 ( V E ) | n A > . [2.183] For linear molecules the only non-vanishing matrix elements of the field gradient tensor are for q = 0 and ± 2 . These are related to the field gradient coupling constants, q q , by (11,23) q 0 = 2 < A | T 0 2 ( V E ) | A > [2.184] q ± 2 = 2 V 6 < A ' | T ± 2 2 ( V E ) | A >. [2.185] This allows us to recast Equation [2.183] into two final equations; for the elements diagonal in Q , < n A ; SZ ; J'QIF | HQ | n A ; SZ ; JOIF > = -J-eQq0 (-1) F I J ' lf I 2 i V f J' 2 J J+J'+I+F-Q 2 J I - 1 0 1 - n o n V(2J + 1)(2J' + 1) [2.186] and, for elements off-diagonal in Cl, < nA ; SZ ; J'fiTF | HQ \ r\A ; SZ ; JOIF > = —•= e Q q ± 2 ( - i ) J + J ' + I + F " Q 4V6 I 2 I q=+2 J' 2 J" [2.187] Upon substituting for the 3-j and 6-j symbols in the above expressions, we obtain six non-vanishing matrix elements for the nuclear electric quadrupole Hamiltonian operator 60 < n A ; S E ; JOIF | XQ \ r\A ; S E ; JOIF > = eQq0 [3Q2 - J(J + 1)]{3R(J)[R(J) +1] - 4J(J +1)1(1 +1)} 81(21 -1)J(J +1)(2J -1)(2J + 3) < n A ; S E ; JOIF | HQ \ r\A ; S E ; J - l OIF > eQq03O[R(J) + J + l ] y / J 2 - O 2 P(J)Q(J) 8 J(J -1)( J +1)1(21 - 1)V4J2-1 < TIA ; S E ; JOIF | # Q \ r\A ; S E ; J-2 OIF > _ eQq0 3 V(J2 - O 2 )[(J -1)2 - O 2 ] P(J)Q(J)P(J - 1)Q(J -1) 16 1(21 -1)J(J -1)(2 J - 1)^(21-3X21 + 1) < n.A+2 ; S E ; JO+2 IF | KQ \ r\A ; S E ; JOIF > = eQq2 yj[ J(J +1) - 0(0 ± 1)] [J(J +1) - (O +1)(0 ± 2)] v 3R(J)[R(J) +1] - 4J(J +1)1(1 +1) 161(21 - 1)J(J + 1)(2J - 1)(2J + 3) < n.A+2 ; S E ; J - l 0+2 I F | JWQ | n A ; S E ; JOIF > [2.188] [2.189] [2.190] [2.191] _ eQq2[R(J) + J + 1]V[J(J +1) - Q(Q +1)][(J + O - 1)(J + O - 2)] P(J)Q(J) 161(21 -1) J(J -1)(J + 1)V4J 2-1 < n.A±2 ; S E ; J-2 0+2 IF | HQ \ r\A ; S E ; JOIF > eQq2 Vt(J + ^ )(J + O -1)][(J + O - 2)(J + O - 3)] P(J)Q(J)P(J - 1)Q(J -1) 321(21 - 1)J(J - 1)(2J - 1)^(21-3X21 + 1) where R(J), P(J) and Q(J) have the same definitions as in Equations [2.176] to [2.178] [2.193] 61 2.5 Symmetry, Parity and A-doubling The concept of parity deals with the behaviour of the molecular wavefunction when the space-fixed Cartesian components of all particles are reversed. This is done using the space-fixed inversion operator, E*, defined by E* ( Xi, Y i , Z; ) = ( - X , - Y , -Zi ) [2.194] or, equivalently, by the reflection operator in the molecular plane, av(xz) (3), Gv(xz) ( X j , y j , Zj ) = ( X j , - y ; , z; ) [2.195] o-v(xz) ( X , Y, Z i ) = ( -Xi, - Y , - Z i ). [2.196] If we represent the total wavefunction, \|/, by a case (a) basis function | t]ASEJfi >, where we assume that | rjASS > represents the non-rotating molecule basis function and | nA > represents the electron orbital part of the electronic wavefunction, \|/e, then the actions of these operators can be shown to be (24,25) E* | TIASZJQ > = (-1)J-S+S | n -AS - IJ - f i > [2.197] rjv(xz) | TIASZ > = (-l)A + z- s + s | n -AS - I > [2.198] av(xz) | T|A > = (-1)A+S I ri - A > [2.199] where s = 1 for I T electronic states and zero for I + and all other states. The eigenvalues for these operators must be +1 since two successive operations must give the original eigenfunctions. Therefore E* | riASEJfi > = p | x] -AS -EJ - f i > [2.200] 62 av(xz) | r|A > = pe I r| - A > [2.201] where p ( = + or - or 'even' or 'odd' ) is the parity of the total wavefunction and pe ( = + or - ) is the symmetry of the electronic wavefunction. It follows that there are two eigenfunctions associated with the two eigenvalues E*v|/ = + \j/+ ; E*\ | /" = -v | / " [2.202] °v(xz) v|/+ = + \\i+e ; Gv(xz) 1 ) / ;= - v iv [2.203] States with |A| > 1 that are isolated from other states will be doubly degenerate as a result of the two possible values ± |A|. However, the case (a) basis functions would not be eigenfunctions of E* and Qv(XZ) for these states. We can take linear combinations of these basis functions to form proper eigenfunctions, provided they are linearly independent. The eigenfunctions of E* would be W ± = [ I riASZJO > ± | r| -AS - I J - f i > ] [2.204] and for ov(xz) V e = ^ [ l r i A > ± | r , - A > ] . [2.205] The eigenfunctions of Equation [2.204] form a parity basis, since each function has a definite parity of ± ( - l ) J _ s + s . The parity of these levels alternates with J for given |A|, | l | and |fi|. It is convenient to use a different parity label to avoid the alternation with J. The modern scheme is to use the labels e and f to distinguish the two A-components. The convention is that levels with a parity of ± (-1)J_<T are ef levels (26) 63 f=±(-l) [2.206] where a = V2 for states with even spin multiplicity and a = 0 for odd-multiplicity states. With this definition all of the e levels of a given |A| > 1 state will have electronic wavefunctions with the same symmetry ( either + or - ) and all of the f levels will have electronic wavefunctions with the same symmetry but opposite to that of the e levels ( - or + ). Electronic E states (with A = 0) are not doubly degenerate. A given E state will have either positive or negative symmetry (i.e. it will be either E + or £~) and each spin component has either e or f parity levels. Since the Hamiltonian operator is invariant to inversion, parity must be conserved in interactions between two states ( e f> e or f f> f ). Interactions between E and IT states result in the lifting of the degeneracy of the e and f parity components of the n state, because the E state only perturbs the energies of one of these components. This effect is known as A-doubling. a) A-doubling matrix elements for a case (a) II state The operators responsible for the A-doubling effect are the L-uncoupling operator -2B ( J -L ) , which comes from the rotational Hamiltonian, and the spin-orbit operator Ej ajlj-si [2.207] 64 The specific form of this interaction can be worked out using degenerate perturbation theory (27). If we consider an electronic II state, the A-doubling interaction must be at least second order because the | A = 1 > state must interact through distant £ states ( A = 0 ) to affect the I A = -1 > component. Applying perturbation theory to this type of interaction generates very complicated expressions and will not be shown here. It is more convenient to construct an effective Hamiltonian operator that acts directly between the two A components of the state in question. It is found that the expressions from the perturbation theory treatment have the same form as those that would result from the operators (J++J 2 ) , (J+S+ + JLS-) and (S^+S 2.). Therefore an appropriate effective Hamiltonian operator for the A-doubling interaction in TI states is ^ L D = i ( o + P + qXS'+S!)-i(p + 2q)(J+S+ J_S_) + iq(J 2+j!) [2.208] where the coefficients o, p and q are given by (28) x< n,A = 1 I Tf (ai 10 | r)',A' = 0 >< i f , A ' = 0 | fa Ij) I r\,A = 1 > [2.209] P = - 4 1 T| A V < r i , A = l | B T 1 1 ( L ) h ' , A ' = 0> V S ( S + 1)(2S + 1) X 2 < TV,A' = 0 | T l , (a, 1,) I ri,A = 1 >< S' II T 1 ^ ) || S > [2.210] 65 1 = 4SZP K T I , A = 1 | B T 1 1 (L) | n',A' = 0 > | 2 [2.211] The Hamiltonian matrix elements for the A-doubling operator acting within a case (a) TI state are < A = +l;Z = ±2;JQ I #LD I A = ±l;Z;JO > = i(o + p + q)V[S(S +1) - Z ( Z ± 1)][S(S +1) - ( X ± 1)(Z ± 2)] [2.212] < A = +1;Z = ±l;JO +1 | 9fhD | A = ±1;Z;JQ > = - \ (p + 2q)A/[S(S +1) - Z ( Z ± 1)] [J(J +1) - Q(Q +1)] [2.213] < A = +l;Z;jn +2 | #LD I A = ±1;Z;JQ > = \ q V[ J(J +1) - n(Q +1)] [J( J +1) - (Q + 1)(Q + 2)] [2.214] 2.6 Intensities and Selection Rules A spectrum is a collection of individual 'lines' that are produced by an absorption or emission of electromagnetic radiation that causes a transition in the molecule from one discrete energy state to another. The relative intensities of these lines depend upon the population of the initial state in the transition and the 'line strength' factor for that transition. The populations of the energy states are described by the Boltzmann thermal distribution, while the line strength factor is proportional to the square of the matrix element of the 66 operator that causes the transition. The most common transition operator in molecular spectroscopy (and the only one needed for this thesis) is the interaction of the oscillating electric field of a beam of photons with the electric dipole moment of the molecule. This interaction can be expressed as O = - p . E = - T^p.) • T ! ( E ) = - £ ( - 1 ) P T ; ( P ) T ; ( E ) [2.215] where p represents the space-fixed Cartesian components of the two tensor operators. To determine the line strength factor we must evaluate the square of the matrix element of this operator acting between the states involved in the transition. In case (a) the appropriate matrix element expression would be I oc |< iV J ' fl' EF' M F ' I - T V ) • T^E) I T I J Q I F M F > [2.216] where | r| > represents the vibrational and electronic parts of the wavefunction ( specifically I v ; ASE > ). It is relatively straightforward to work out the expression using the spherical tensor methods outlined in the previous sections; the full details will not be included here. If the two states follow Hund's case (a) coupling then the line strength for an electric dipole transition can be shown to have the form Ioc T 1 ( E ) ( 2 J +1)(2J ' + 1)(2F + 1)(2F' +1) n 2 J ' 1 J [2.217] 67 where | T^E) | 2 is related to the strength of the light source and (, r\' | T* (p.) | r\ >, obtained by summing over MF' and MF, is called the transition moment, R q . In order to determine the relative intensities of lines in a real spectrum only a Boltzmann factor needs to be added to Equation [2.217]. The above expression also allows us to determine the general trends for which transitions are allowed and which ones are forbidden. In order for a transition to occur the line strength factor must be non-zero. The symmetry properties of the 3-j and 6-j symbols provide the conditions for when this is true; these conditions are called selection rules. From the 3-j symbol we obtain the rotational selection rules AJ= | J ' - J | = 0, ±1 [2.218] A Q = | Q ' - Q | = 0, +1. [2.219] The 6-j symbol of Equation [2.217] gives us the hyperfine selection rules AF = | F ' - F | = 0, ±1. [2.220] For the selection rules involving the other well defined quantum numbers associated with the wavefunctions we must make a closer examination of the transition moment. The wavefunctions | r\ > can be factored into electronic and vibrational parts (|ri> = |e>|v>)to describe the transitions from the vibrational levels of one electronic state to those of another. The dipole moment operator acts only on the electronic factors so that the transition moment can be written as R q = <e'| T.jGOleXv'lv) [2.221] 68 where < e' I T q (ji)! e > is the electronic transition moment and < v' | v > is the Franck-Condon overlap integral. The only restriction on vibrational transitions is that the Franck-Condon overlap integral be non-zero. The dipole moment operator does not act on the spin parts of the electronic wavefunction. The selection rule for the orbital part of the electronic wavefunction stems from the group theory requirement that the electronic transition moment integral be totally symmetric. In case (a) states the electronic selection rules are AS = 0 [2.222] AZ = 0 [2.223] AA = 0, ± 1 . [2.224] 69 Chapter 3 High Resolution Spectroscopy of Nickel Monocyanide, NiCN 3.1 Introduction The study of ligands such as CN and CO adsorbed on metal surfaces has been the focus of a considerable amount of interest. The main goal is often to understand the catalytic removal of toxins and environmental hazards from exhaust gases. In an effort to understand the nature of the bonding of the cyanide ligand to metal surfaces a number of simple molecules of the form MCN (M = metal) have been examined. The bonding in these species is particularly interesting because three possible isomers can be formed; the linear cyanide MCN, the linear isocyanide MNC and the T-shaped or cyclic configuration. There has also been astrophysical interest in the metal monocyanides. Recently MgCN (1), MgNC (2,3) and the T-shaped isomer of NaCN (4) have been detected in the circumstellar envelope of IRC + 10216. The alkali metal cyanides were among the first molecules with the formula MCN to be studied. Matrix isolation infrared spectra (5) and gas-phase rotational spectra (6) showed that the lithium compound takes the linear isocyanide configuration, LiNC, in its ground 70 electronic state. These results confirmed earlier predictions made by ab initio calculations (7-12). Conversely, sodium cyanide was predicted by ab initio studies to have the T-shaped structure (12-14), which was later confirmed by experiment (15,16). T-shaped structures were also observed for KCN (12,13,17-20) and RbCN (21). For the alkaline earth monocyanides, ab initio studies have predicted that all members of the group should have the isocyanide configuration (22,23). These results have also been confirmed experimentally (3,24-27). The monocyanides of aluminum have been studied extensively by ab initio (28-32), spectroscopic (31-35) and thermodynamic (36,37) investigations; the results show that the linear isocyanide isomer is the most stable. More recently anion photoelectron spectra (PES) have been observed for the cyanides of palladium (38), tin (39), copper and silver (40). In each case the carrier species is presumed to be the linear cyanide isomer based on ab initio results. The near ultra-violet laser fluorescence excitation study of FeNC (41) represents the only observation to date of a transition metal monocyanide in which the structure of the molecule has been conclusively deduced from experimental results. Three bands, representing a short progression in the Fe-N stretching vibration of the excited electronic state, were observed for the FeN1 2C and FeN 1 3C isotopomers. Rotationally resolved spectra with line widths of 0.04 cm"1 were recorded and used to obtain the rotational constants and the molecular geometry. Dispersed emission spectra were also recorded in which progressions in the Fe-N stretching vibration were observed out to V3" = 7. This chapter presents the results of our high-resolution spectroscopic studies on the nickel monocyanide molecule. They represent the first instance in which rotationally 71 resolved spectra of a transition metal monocyanide in the linear cyanide configuration have been observed. The only published works on NiCN are two ab initio studies (42,43) that modeled the bonding of CN to nickel surfaces. The report by Bauschlicher (42) predicts the linear cyanide configuration to be slightly more stable than the isocyanide and that the Ni-C bond should be highly ionic with a transfer of approximately 0.7 electrons from a nickel 3d(a) orbital to the CN group. The more recent study by Zhou, et al. (43), also predicts the linear cyanide isomer to be more stable, by 0.57 eV, and that the bond is even more ionic with the transfer of 0.97 electrons to the ligand. 3.2 Experiment The NiCN molecules were generated in a laser ablation molecular beam spectrometer. The details of this apparatus have been described elsewhere (44). For the sake of completeness, a description is also presented here. The nickel rod (Goodfellow, 99.99+%, 50 mm x 5 mm dia.) was inserted into a "Smalley" type source (Figure 3.1) mounted inside the vacuum chamber. One end of the rod was attached to an Oriel Motor Mike (model 18040) by a flexible rubber coupling. The Motor Mike rotates and translates the rod so as always to present a fresh surface to the ablation laser. The third harmonic (355 nm) of a Nd:YAG laser (Lumonics Inc., model HY400), operating with a pulse energy of approximately 6-8 mJ, was focused onto the surface of the metal rod using a 50 cm focal length lens. A gas mixture 72 Ablation Laser Inlet / , ! — . Figure 3.1 "Smalley" type ablation source. containing 2.5% cyanogen, (CN)2, in helium at a backing pressure of 50 psi was then introduced through a pulsed nozzle valve (General Valve Inc., Series 9) precisely timed to entrain the gas-phase metal plasma. For the production of the NiC 1 5 N isotopomer, a gas mixture of acetonitrile-15N at its ambient vapor pressure in 100 psi of helium was used. The hot mixture then traveled through a short reaction channel (7 mm x 2 mm dia.) before expanding into a vacuum of approximately IO - 6 Torr. The resulting collision-free supersonic jet was probed 5 cm downstream from the exit of the source using a tunable dye laser. Fluorescence excited by this laser was collected in a direction mutually perpendicular to both the expansion and the laser. This fluorescence was directed through a 0.75 m monochromator (Spex, model 1702), detected by a cooled photomultiplier tube (Hamamatsu, R943) and processed by a boxcar integrator (Stanford Research Systems, model SR250). The precise timing of the experiment was controlled with a digital delay generator (Stanford Research Systems, DG535). Absolute calibration was provided by opto-galvanic spectra 73 from a uranium-argon hollow cathode lamp (45). The fringes from a temperature and pressure stabilized etalon servo-locked to a frequency stabilized helium-neon laser allowed interpolation between the uranium lines for precise calibration of the high-resolution spectra (46). The relative precision of unblended features calibrated with this system is better than 15 MHz, even though the line widths were limited by the residual Doppler width of the expansion to a minimum of 110 MHz. Two probe laser systems could be used to excite the fluorescence, depending on the required resolution of the experiment. For low resolution survey work and dispersed emission spectra a pulsed dye laser (Lumonics model HD500) pumped by a second Nd:YAG laser (HY400) was used. Spectra with a maximum resolution of 0.05 cm"1 could be obtained with this system. High-resolution LIF spectra were obtained by using a continuous wave ring dye laser (Coherent Inc., model 899-21) pumped by an argon ion laser (Coherent Inc., Innova Sabre 20-TSM). This laser has a linewidth of less than 1 MHz, but, as mentioned above, residual Doppler-limited line widths of approximately 110 MHz were achieved for these experiments. For less intense molecular bands a pulsed-dye amplifying system (Lambda Physik, model FL2003) pumped by a xenon-chloride excimer laser (Lambda Physik, model Compex 102) was used in conjunction with the ring laser to produce pulses of laser radiation with energies of up to 2 mJ and line widths transform-limited to about 75 MHz. The resolution of the spectra recorded with this system represents the convolution of the Doppler-limited line width and the laser line width, with a slight contribution from power broadening: the observed line widths were about 180 MHz. A schematic representation of the experimental setup is presented in Figure 3.2. 74 75 In this scheme there are a large number of parameters that can be adjusted in order to maximize signal intensity and resolution. The most important factor governing signal strength is the concentration of reactants in the gas mixture. Too little reactant gas limits the molecular production, while too concentrated a mix often quenches the formation of the molecule of interest in favor of other species. Another important variable in optimizing the experimental conditions is the relative timing of the gas pulse, ablation and probe lasers and the boxcar integrator. The triggering of these events was adjusted on a regular basis in order to maximize the fluorescence signal. Additional aspects of the experiment that affect resolution and fluorescence intensity include the ablation laser power and the position of incidence upon the metal rod, the probe laser power and region at which it crosses the molecular expansion, the condition of the surface of the metal rod, the cleanliness of the reaction channel in the Smalley source, the duration and width of the gas pulse and the positioning of the fluorescence collection optics. The process of optimizing signal strength and maximizing resolution involves an iterative adjustment of many of these parameters, followed by regular tweaking in order to maintain optimum conditions. Two types of experiment are carried out using the apparatus described above. The first is a laser induced fluorescence (LIF) experiment in which the tunable dye laser is scanned through a frequency range. If the energy of the laser radiation precisely matches the interval between two energy states within the target molecule for which a transition is allowed to occur, and if the molecule is in the lower of these states, it absorbs that radiation. Once excited, the molecule emits the excess energy as photons of the appropriate frequencies to allow it to relax down to its ground electronic state. In the present experiments, these 76 photons are passed through a monochromator before being detected, as described previously. The monochromator is set to transmit the fluorescence at an offset equal to a vibrational interval of the ground state, effectively functioning as a molecule-selective narrow-band filter, which also serves to remove most of the unwanted plasma emissions and scattered laser light. Using this approach absorption spectra from the vibrational levels of the ground or low-lying electronic states to those of excited electronic states are obtained. Both the low-and high-resolution techniques are used with this type of experiment. The second approach used involved the recording of dispersed emission spectra. For this type of experiment the probe laser is fixed to the frequency of an observed transition within the target molecule. The fluorescence is again collected and directed to the monochromator. The diffraction grating in the monochromator (1200 lines/mm, used in first order), is scanned so as to give a spectrum of intensity against frequency for the molecular emission. This experiment, therefore, gives information about the positions of the vibrational levels of the ground or low-lying electronic states. 3.3 Appearance of the Spectrum The complete excitation spectrum of NiCN observed in our laboratory consisted of 72 bands spanning from 15857 cm"1 to 19980 cm" . All but six of the weakest of these bands have been assigned as upper state progressions in the bending and nickel-carbon stretching 77 vibrations of four excited electronic states. No activity in the carbon-nitrogen stretching vibration was observed, indicating that all of these electronic transitions involve electrons in orbitals that are dominantly nickel in character. Assignments of the bands were made based on the emission patterns of the dispersed fluorescence spectra together with the band positions and intensities, as will be discussed in greater detail in Section 3.4. A portion of the low resolution survey scan, showing the region near the system origins of the A - X i and B-Xi transitions, is given in Figure 3.3. The strongest band, by far, in the spectrum is the origin band of the A 2 A 5 / 2 - Xi 2 A 5 / 2 transition. Lying a mere 80 cm"1 to the blue is the origin band of the B-Xi electronic transition. Due to the proximity of these two system origins and the similarity of their vibrational frequencies, many of the other bands in the spectrum tend to appear in clusters. Some "hot" bands are observed, coming almost exclusively from the bending fundamental of the ground state; these appear as sequence structure on the Ni-C stretching bands and the bands with even quanta of the upper state bending vibration. The exceptions to this are that weak 22 2 sequence bands are observed near the very strong A - X i (0,0) band; also the extremely weak B - X 2 (0,0) band appears weakly. Since the nickel-carbon stretching fundamental and the bending overtone levels lie fairly low in energy (455 cm"1 and 524 cm"1) it is obvious that the vibrational temperature in our experiment is quite low. The bands all share a similar profile at low resolution. In each case there is an intense head formed at low J in the R-branch. The rotational structure is very dense; only in the strongest bands where rotational lines are observed up to J~30!/2 is rotational structure 78 79 observed in the tail of the P-branch at low resolution. Intense perpendicular bands sometimes appear to have two heads because of the strong Q-branch that begins approximately 3 cm"1 to the red of the R-branch head. An example of this can be seen in the B-Xi origin band of Figure 3.3. The sequence bands from the upper state stretching levels show a characteristic double-headed structure. This represents absorption from the 2n3/2 and 2<J>7/2 components of the bending fundamental of the ground state, which are split by 1.3 cm"1. Examples of this can also be seen in Figure 3.3 in the "hot" bands labeled 2\ and 21i310. Figure 3.4 shows a 15 cm"1 portion of the spectrum of the A - X i 21! hot band. This figure illustrates more clearly the double-headed structure of the sequence bands. In the high resolution spectra many more details become apparent. Some examples of portions of high-resolution spectra are shown in Figures 3.4 to 3.8. The dense rotational structure is now completely resolved, as is the nickel isotope structure. Nickel has five naturally occurring isotopes, 5 8Ni, 6 0Ni, 6 1Ni, 6 2 Ni and 6 4Ni, with the relative abundances 68.08%, 26.22%, 1.14%, 3.63% and 0.93% respectively. Only the 6 1 Ni isotope has a non-zero nuclear spin (I = 3/2 ), but it is not observed due to its low abundance. For the most part, only the lines due to the two most abundant isotopes, 5 8Ni and 6 0Ni, were observed with relative intensities of approximately 5:2, although occasionally the R-branch heads and a few isolated rotational lines of the 6 2 Ni isotopomer were also seen. The 6 2 Ni lines were not included in the analysis. The isotope shifts of the rotational lines helped confirm the vibrational assignments of each band. For origin bands the 6 0 Ni lines lie approximately 0.3 cm"1 to the blue of the 5 8 Ni lines (Figures 3.5 and 3.6). The 6 0 Ni lines shift to the red relative to the 5 8 Ni isotopomer by just under 2 cm"1 per quantum of upper state Ni-C stretch and by 80 T 1 • 1 p 1 1 • 1 • 1 1 1 1 1 1 1 1 r 1 1 1 1 1 1 1 1 1 1 1 j 1 • 1 1 r 16545 16544 16543 16542 16541 16540 16539 16538 16537 16536 16535 16534 16533 16532 16531 16530 E/cm Figure 3.4 Portion of the high-resolution spectrum of the A-Xj l\ band showing 2 2 2 2 the FI 3 / 2- F l 3 / 2 and 3>7/2- ®7/2 transitions. The frequncy scale is continuous from the top panel to the bottom. 81 82 83 A ^ - X ^ A ^ (021-000) 58 Ni R 17391 17390 17389 17388 17387 17386 17385 P(101/2) P6o(8^) T ^ ' M '(WWW P(18!/2) P6o(15V4) 17385 17384 17383 17382 E /cm'1 17381 17380 17379 Figure 3.7 Portion of the high-resolution spectrum of the A A 5 / 2 -Xj A 5 / 2 (021-000) band. The isotope shift between the 5 8NiCN and 6 0NiCN band heads is characteristic of having one quantum of Ni-C stretch and two quanta of bend excited in the upper state. 8 4 CN VO VO vo vo I VO. VO i n vo VO o cn C rt +-> CN CN CN ON I CN OA O CN O O X) o HE" * a cn cn C o cn C rt o i o O f N K cu +-» M-H O a a .*-> o cu C H CO C O o cn CU 60 CD 4= +-> M-H o e o o PH 00 rn cu t-< 3 bp g i 3 O T 3 ta rt CJ cn ° he cu -»-> rt o +-» cn -»-» fe espon low espon cu - E ! or H o cu cu o B bra ode -*-> cn -a +-> c o o rt cn o cu 1— VH t-H o 00 c2 ' r t 1 he cn g +-> CD ,c -lin cu -lin c cu t H o H-H ract O cu ract CU cn u-rt inte upper branc nance cu each o Th each res 85 just over 0.1 cm - 1 for each quantum of the bending vibration that is excited. Figure 3.7, a portion of the A - X i 2 2 0 3 1 0 band, is an example of a band whose vibrational assignment was confirmed by the isotope shift. Almost all of the bands that were recorded at high-resolution show some signs of perturbations. Most appear to be random rotational perturbations in which a small number of rotational lines are split into multiple components, however, a few of the upper states appear to be more extensively perturbed. One such level is the 3 1 level of the A state. The high resolution spectrum of the 3l0 band shows most of the rotational lines either shifted in position or split into multiple components, some into as many as six components. The perturbations in this band are so extensive that assigning all of the observed lines is very challenging. An example showing a number of random perturbations is given in Figure 3.5. This figure, showing the R-branch head and band origin region of the A - X i (0,0) band, shows how the J' = 4!/2 level is split into three components, J' = 13 '/2 and I 8 V 2 into four components and the J' = 14Vz and 15 V2 levels are doubled. One of the few unperturbed bands that was recorded at high-resolution is the C - X i (0,0) band shown in Figure 3.6. This band is an unusual case in which the outgoing and returning lines of the R-branch are exactly coincident, making for a very uncluttered spectrum. The high-J lines of the R-branch are also found to overlap with the beginning of the P-branch. Most of the bands of NiCN do not show this degree of blending of the rotational structure. 86 3.4 Results a) The X^As/i State (i) Vibrational Analysis: Fermi resonance An energy level diagram showing the observed vibrational levels of the ground electronic state is given in Figure 3.9. The positions of these levels were ascertained from the dispersed fluorescence (DF) spectra, which were recorded for every band observed in the survey spectrum. Figure 3.10 shows examples of DF spectra from vibrational levels of the A excited state. The upper panel is the emission pattern from the v = 0 level, a totally symmetric level, and shows only emission features down to the totally symmetric levels of the ground state. The lower spectrum is the emission from the non-totally symmetric bending fundamental of the A state, which shows emission only to the non-totally symmetric levels of the ground state. In compiling the list of ground state vibrational levels, emphasis was placed on the DF spectra collected from very intense molecular bands where the monochromator slit width could be reduced. Preference was also given to DF spectra recorded from levels of the C state. The A and B states showed signs of vibronic interaction, characterized by emission down to the levels of the X2 state at 830 cm"1 as well as to the Xi state. Emission features in spectra from the C state (where there is essentially no vibronic coupling) gave the most certain identifications of the vibrational levels of the Xi ground state of the molecule. 87 cu l H 3 o a +-> "3 c o "i§ - H > CU o e rt fi O co 3 cu fe CU fi o o CN O o O IT) jm"cN* <L) O a * w T3 -O o VO VD VD VO^  rn '<N r H © " T 3 « I-H MH <n^  "O <n >n m IT! VI >n o\" VO T t rn CN r—< o" o\* 1—( T t T t T t T t T t T t T t CN - H ~ i-H o" - H VO" m rn cn m m m o" ON" oo" r-~" vo" in" T t " CN CN CN (N CN CN CN CN CN CN CN o" a\ oo" VO" >n" T t " m" CN - 1 — I — I — I — I -o o o TT o o © - H © m g CN ^cj -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 o o o o rt fi o i-H X) '> I-H rt CU cu -f i DO C cO u o % M - C o < cxf CD CO fi O u-00 CU -fi co ~CU 'rt fi O "3 UH X ' > T3 CU CH CU co X> O OV cn cu l-H op fe 00 in H O fi T3 ° ca fi >> cu o ? « fe ^ fe £ IH CU i f o c £ B CU C 00 rt G EI rt CT1 fc fi rt fi cu 2 SH J-j rt m cu > cu cu rt - f i "-3 H &0 fi C <* O cu l H CU , — ± i <-> C X •— CU CD *-> O CD C CD rt co fi w O CU co CD G IH CD . - H -fi fi o H co *H CU ID fe 5 cu >r> -fi o C H £ rt eg fi* • . i f ' § 3 £ co CU CU o rt CU cu -o .5 rt 88 Laser 2,1 J 2,2 4,2 4,1 Excite v' =0 level (16607.2 cm"1) 4,3 6,3 6,2 6,4 8 ' 3 8,4 Laser 1,1 Excite 21 level (16787.5 cm"1) wider slit -1 1 1 1 1~ 500 1000 1500 2000 Displacement from laser line (cm" ) [Ground State vibrational energy] Figure 3.10 Dispersed emission spectra from the v' =0 (top) and v2' =1 (bottom) levels of the A A 5 / 2 state. The v'=0 level gives emission features only to the totally symmetric levels of the ground state, while the v2'=l level emits only to the non-totally symmetric levels. The peaks are labeled using the polyad notation. 89 Close examination of Figure 3.9 shows that twice the energy of the bending fundamental is almost exactly the mean energy of the bending overtone and metal-carbon stretching fundamental levels. Clearly there is a strong Fermi resonance which causes the apparent erratic vibrational intervals. The Hamiltonian used to model this Fermi resonance interaction is a simplified form of that presented by Chedin in his comprehensive study of CO2 (47). The matrix elements for this Hamiltonian are: (v2 v3(\H\v2Vj,C)^ co2v2 + cojvj + x22v\ + + x 2 3 v2v3 + y222 v\ + y 2 2 3 v\v^ + V 2 3 3 ^ + ^ 3 3 3 ^3 [3.1] {v2 V3C\J{]V2-2V3+1C)= k'223 J(v3+l)(v2+C)(v2-C) where a>i and a>i are the harmonic bending and nickel-carbon stretching frequencies, the Jty and Vijk parameters are anharmonic correction terms and &'223 is the Fermi resonance interaction parameter. The levels depicted in Figure 3.9 were fitted to the model outlined by the matrix elements of Equation 3.1. The results of this fit are summarized in Table 3.1. These results show that the 60 observed vibrational levels of the ground state can be reproduced to an RMS of 0.93 cm"1 using this simple model. Although it is intuitive to use vibrational quantum numbers to label the vibrational levels, in this case the levels are so highly mixed by the Fermi resonance that these assignments would be somewhat meaningless. A number of different labeling schemes have been used to describe the vibrational levels of a Fermi resonance interaction. The one we have chosen to use is a polyad notation where each group of interacting vibrational levels is assigned a polyad number, and a second index is used to describe the position of the level in 90 Table 3.1 Constants from the Fermi resonance modeling of the low-lying electronic states ofNiCN. Xi NiCN x 2 Wi NiC Xi N x 2 C03 501.8(29) 511(18) 481.9(67) 487.9(43) 512(26) C02 246.1(16) 225(10) 224.9(58) 246.4(25) 218(11) X33 -5.3(11) -15.2(69) 0 -2.2(11) -19(11) x2 2 -2.84(44) 2.0(24) 0 -2.13(50) 3.4(22) X23 6.93(83) 0 0 0 0 y333 0.200(96) 0 0 0 0 Y222 0.160(25) 0 0 0 0 Y223 -0.302(48) 0 0 0 0 V233 -1.98(15) 0 0 0 0 k'223 16.567(43) 14.39(82) 17.8(13) 17.49(33) 13.9(18) No. of Data 60 15 7 22 15 RMS 0.929 3.287 2.524 1.445 4.199 Error limits (in parentheses) are 3a, in units of the last significant figure quoted. All values are in units of cm"1 except for the number of data points, which are unitless. energy order within the polyad. For completeness, angular momentum quantum numbers are also needed, but it is often not possible to determine the angular momentum values of levels from the dispersed fluorescence spectra alone. For simplicity, the angular momentum quantum numbers have been omitted from the figures. Using this labeling scheme, the v = 0 level of the ground Xi2As/2 state would carry the label (0,1,%), the two components of the bending fundamental would be (1,1,%) and (1,1,%) and the two states resulting from the interaction of the |001> and |020> basis states would have the labels (2,1,%) and (2,2,%). In order to confirm that the model used to describe the Fermi resonance interaction was sufficient, an attempt was made to model the dispersed fluorescence spectrum from the v = 0 level of the A state. The Ni-C stretching vibration should carry the majority of the intensity in this spectrum, although a small contribution can be expected from the totally symmetric 91 bending overtones. A reasonable reproduction of the DF spectrum should be obtained if the emission intensities from the A 0° state to the "bright" levels of the ground state are transformed using the eigenvectors of the Fermi resonance fit in order to obtain the intensity distribution within the Fermi polyads. The intensities were determined by calculating the squares of overlap integrals in the harmonic basis between the v = 0 level of the A state and the totally symmetric levels of the ground state. For the Ni-C stretching vibration the formula for evaluating the overlap integrals has been given by Sharp and Rosenstock (48), while the formula for the doubly degenerate bending vibration was obtained from a paper by W.L. Smith (49). These formulae are presented here in the form used in this study: Ni-C Stretching Vibration: f i V / 2 f 1 p-l N 4iQp Degenerate Bending Vibration: v'W [3.2] where p = v"/v', Hv is the Hermite polynomial of order v, y = 47C2cv/h and Q is the shift in origin of the normal coordinate from the lower to the excited state. The results of this modeling are shown in Figure 3.11. The top portion of the figure is the experimentally observed DF spectrum from Figure 3.10 while the bottom trace is a simulated stick spectrum calculated from the overlap integrals and Fermi resonance eigenvectors. The simulation 92 Laser 2,1 J 2,2 4,2 4,1 L - U 4,3 U 6,3 6,2 Observed Dispersed Emission Spectrum (Excite 16607.2 cm"1) 6,4 8,3 8,4 8,5 Simulated Dispersed Emission Spectrum 500 1000 1500 2000 Displacement from Laser line (cm" ) Figure 3.11 Observed (top) and simulated (bottom) dispersed emission spectrum from the v'- 0 level of the A A 5 / 2 state. The simulation was produced by calculating harmonic overlap integrals and transforming them using the eigenvectors of the Fermi resonance fit. Excellent agreement is observed for the relative intensities of each of the Fermi polyads. 93 accurately reproduces the relative intensities of the Fermi polyads, confirming that the model chosen is sufficient to describe the Fermi resonance in this state. A number of dispersed fluorescence spectra were also recorded for the NiC 1 5 N isotopomer. The data were much less complete than those for the main isotopomer; only 22 vibrational levels were identified. These data were also treated by our Fermi resonance modeling program, giving the results shown in Table 3.1. Since fewer levels were observed for this isotopomer and these were generally restricted to the lower portion of the vibrational manifold, fewer parameters were required to obtain an adequate fit. (ii) Rotational Analysis The bonding in NiCN is assumed to involve transfer of an electron from the nickel atom to the cyanide ligand, resulting in a Ni + CN~ structure, and leaving the nickel atom with the (3d9) electron configuration. The ground state of the molecule should therefore be an inverted doublet state. Based on this, it was assumed from the onset of the experiment that there would be a similarity between NiCN and the nickel monohalides. Nickel fluoride (50-52) and chloride (53-55) have both been found to possess a 2n3/2 ground electronic state and to have several low-lying states below 5000 cm"1. After the strong band at 16607 cm"1 had been identified as a probable (0,0) band, its high-resolution spectrum was recorded (Figure 3.5). The method of combination differences was used to assign the rotational structure and it was observed that the ground state has a 94 total angular momentum projection of P = 5/2, making the ground state symmetry 2As/2. This result suggests that NiCN is actually more similar to the nickel hydride molecule than to the nickel halides, as NiH has also been observed to have a 2 A 5 / 2 ground state (56,57). Further similarities between NiCN and NiH will be discussed later. A total of 11 bands that originated from the v = 0 level of the ground state were recorded at high-resolution. Two additional bands were recorded using acetonitrile-15N. Since only one of the spin-orbit components of the X i 2 As/ 2 state is represented in these data a simplified Hamiltonian was used to describe the rotational structure: 9f= T v + B v J( J+l ) - D v J2( J+l )2 [3.3] Combination differences for all of the unblended pairs of lines in each of the high-resolution spectra were collected and fitted to Equation 3.3 using a least-squares method. The rotational constants of 5 8 NiC 1 4 N and 5 8 NiC 1 5 N were then used to calculate the structure of the molecule. The results of these fits are shown in Table 3.2. The magnitude of the ground state rotational constant observed for the 1 5 N isotopomer confirms the geometry of this molecule. If it is assumed that the molecule is the NiNC isomer and that it has similar bond lengths to those listed in Table 3.2, then it is straight forward to prove that a substitution of the nitrogen atom in the central position would result in a fractional reduction in the rotational constant of-1%. The results of our rotational analysis clearly show a fractional reduction of just over 4%, which is consistent with the substitution of the terminal atom in the bond that does not contain the center of mass. The structure of the molecule is therefore confirmed as being the linear cyanide isomer, NiCN. 95 Table 3.2 Rotational constants for vibrational levels in the ground states of each of the observed isotopomers of NiCN. Isotopomer Level T v /cm"1 B v /cm"1 10* Dv/cm"1 5 8NiCN 0 , L | 0 0.1444334(30) 4.99(26) i , i , f ( 2n 3 / 2) 243.6398(8) 0.1451482(63) 0 l , l , K ® 7 / 2 ) 244.9641(14) 0.145143(14) 0 i , i , - | ( 2 r 9 / 2 ) 482.1(24) 0.145904(8) 0 5 8 NiC 1 5 N 0 0.1386226(61) 4.13(52) 6 0NiCN 0 0.1430605(42) 5.10(41) ( 2n 3 / 2) 243.5534(10) 0.1437649(58) 0 i , i , f ( 2r 9 / 2) 482.1(24) 0.144512(11) 0 6 0 NiC 1 5 N o , i , f 0 0.137268(12) 4.1(10) r 0(Ni-C)/A 1.8292(28) r 0(C-N)/A 1.1591(29) Error limits (in parentheses) are 3o~, in units of the last significant figure quoted. Levels are labeled using the Fermi polyad notation (see text) with the angular momentum quantum number included. The bond lengths were calculated from the B 0 rotational constants of the 5 8NiCN and 5 8 NiC 1 5 N isotopomers. The vibronic characters of the excited vibrational levels are given in parentheses. All parameters with a value of'0' were held fixed in the least squares procedure. Fligh-resolution spectra were also recorded for a number of bands originating from the bending fundamental of the ground state. For a 2As/2 electronic state in Hund's case (a) coupling the bending fundamental has two components with 2 n 3 /2 and 2 ® 7 / 2 vibronic symmetries. Simultaneous analysis of these "hot band" spectra (vi" - 1) with the corresponding "cold bands" (yi" = 0) enabled us to calculate the term energies and rotational 96 constants for both components of the bending fundamental in the main isotopomer as well as the 2IT3/2 component of the 6 0NiCN isotopomer. These results are included in Table 3.2. A weak band observed at a frequency of 16464 cm"1 (see Figure 3.3) was initially puzzling. It appears to the red of the A - X i system origin band, yet does not lie at the expected position for any sequence band based upon the observed vibrational frequencies of the upper and lower states. After much consideration, it was theorized that this band was the 22 2 hot band originating from the / = 2 component (2T9/2) of the bending overtone, which would not suffer from the effects of the Fermi resonance that perturbs the 1 = 0 component. The dispersed fluorescence spectrum from this excited state supports this assignment. The dominant features appear at displacements of 425 cm"1 and 546 cm"1, which do not correspond to any observed vibrational intervals of the ground state manifold. We can use the unperturbed vibrational frequencies and anharmonicity constants extracted from the Fermi resonance analysis (Table 3.1) to estimate the positions of the P = 9/2 vibrational levels, in the absence of any additional anharmonicity. The (0220) level of the ground state is estimated to lie at an energy of 482.1 cm "\ and the (0420) and (0221) P = 9/2 levels should lie at 949.2 cm"1 and 973.7 cm"1 in zeroth order, respectively, where we are using the conventional vibrational labels (v\ vl vi). If we assume that the P = 912 levels follow the same Fermi resonance described by Equation 3.1 and the results of Table 3.1, we can predict that the pair of levels resulting from the mixing of the |0420> and |0221> basis states should lie at energies of 902.8 cm"1 and 1020.1 cm"1. The vibrational intervals between these levels and the (0220) level at 482.1 cm"1 would be 420.7 cm"1 and 538.0 cm"1, which are very similar to the intervals observed in the DF spectrum. Perhaps more striking is the similarity 97 of the peak separations, which is calculated to be approximately 538 cm"1 - 421 cm"1 = 117 cm"1, based on the arguments above, and observed to be 546 cm"1 - 425 cm"1 = 121 cm"1. It was discovered that with neon as a backing gas in the experimental apparatus the intensity of this weak band improved sufficiently for it to be recorded at high-resolution (Figure 3.8). Rotational analysis showed that this band is a P = 9/2-9/2 parallel transition, confirming the proposed assignment. Transitions to the P = 9/2 upper state are not allowed from the P = 5/2 ground state, so that the positions of these energy levels are left "floating". However, since the lower state is not affected by the Fermi resonance, the energy of the (0220) level calculated above should be accurate to within a few reciprocal centimeters. This result is included in Table 3.2. b) The Low-lying Electronic States (i) The X 2 2 A 3 / 2 State Both the nickel halides (50-55) and nickel hydride (56,57) possess a number of low-lying electronic states below -5000 cm"1. It is, therefore, no surprise to observe such states in NiCN as well. Two low-lying states have been identified in nickel cyanide. No absorption spectra strong enough for rotational analysis could be observed for either of these states; however, dispersed fluorescence (DF) studies have provided important evidence for their existence and character. 98 The most prominently observed state, apart from the ground state, in the DF spectra lies 830 cm"1 above the zero point level of the ground state. We have labeled this state X 2 by analogy with NiH; it has been shown to be a 2 A 3 / 2 state. A very weak absorption band was observed at 15857 cm"1, which has been assigned as the (0,0) band of the B - X 2 transition. The signal-to-noise ratio for this band is barely greater than 1, so that no rotational information can be extracted from it. The X 2 state is observed most prominently in the emission spectra from the levels of the B state, though the D state and some levels of the A state emit to it as well. Examples of DF spectra showing emission to X 2 are given in Figure 3.12. This figure is analogous to Figure 3.10 but highlights the emission from the B state to the totally symmetric and non-totally symmetric levels of the X 2 state rather than the ground state as in Figure 3.10. In total, we have identified 15 vibrational levels of the X 2 state. Their energies are shown diagrammatically in Figure 3.13. These levels show a similar pattern to the ground state, suggesting that Fermi resonance is present here as well. The DF spectra which provide data on the X 2 state are generally weaker than those used to compile the level structure of the ground state. For this reason, the slits on the monochromator were generally kept significantly wider in order to maintain sufficient signal-to-noise levels. The measurements of the level positions are accordingly less precise; with a slit width of 1 mm we estimate our uncertainty as being upwards of ±5 cm"1. The observed level positions were fitted by our Fermi resonance modeling program; however, because of the reduced resolution and limited number of data points, the results 99 Laser — i — ' 500 Excite 21 level (16856.1 cm"1) wider slit 1000 1500 2000 2500 Displacement from laser line (cm"1) [Ground State vibrational energy] Figure 3.12 Dispersed fluorescence spectra from the v' = 0 (top) and v2'= I (bottom) levels of the B JJ 3 / 2 state showing strong emission features to the vibrational levels of the X 2 A 3 / 2 low-lying state. 100 4000 3600 E/crri1 3200 2800 2400 1600 \ 1200 \ 800 2 J _ _26_66 0 J _ _2238_ 5,1 1919 4,1 1681 3,1 1493 2,1 1268 1,1 1054 0,1 830 6,3 3694 4,3 3262 A2_ _31_82 _2744 7,3 2484 6,3 2289 6,2 2200 5,3 2099 5,2 2016 4,3 1852 4,2 1776 3,2 1578 2,2 1338 6,4 3784 w 2 n V V1 1 1 3 / 2 6,4 2373 v 2 A ^ 2 ^ 3 / 2 Figure 3.13 Observed vibrational levels of the A 3 / 2 and Wj II 3 / 2 low-lying states. The W 1 levels are represented by the dashed lines. The Fermi polyad assignments and energies are given for each level. 101 were not as good as those obtained for the vibrational structures of the ground states of the two isotopomers mentioned earlier. The results of the Fermi resonance fit to the X 2 state are also included in Table 3.1. The electronic symmetry of this state could not be determined by rotational analysis, as was done for the ground and excited states, since the only absorption spectrum observed was too weak. The assignment of this state was therefore based upon the following argument. The emission features to the X 2 state observed in the DF spectra originated from levels of the A 2A5/ 2 , B2Fl3/2 and D2<S>5/2 states. Assuming that the A character of each of these states has not been compromised through interactions with other states, the X 2 state would have to have 2A symmetry with an angular momentum projection of either P = 3/2 or 5/2 in order to have allowed emission from all three of these excited states. Since the ground state is known to have 2 A 5 / 2 symmetry it is logical to conclude that the X 2 state is 2 A 3 / 2 . (ii) The Wi 2 n 3 / 2 State A second low-lying state with its origin at 2238 cm"1 relative to the ground state has been identified in NiCN. Figure 3.12 shows a single emission feature, labeled Wi, that could not be placed into the vibrational manifolds of the ground or X 2 states. The possibility that this peak was evidence of the C-N stretching vibration could not be ruled out, although the lack of activity in this stretching vibration in any of our absorption spectra led us to believe 102 that another explanation was needed for this emission feature. Confirmation that this level was indeed the origin of another low-lying electronic state came from the dispersed fluorescence (DF) spectra of the levels of the D2<D5/2 state. Figure 3.14 shows the DF spectrum from the v - 0 level of the D state. The relative intensities of the bands making up the D-Xi and D - X 2 electronic transitions are seen to be virtually identical. This same emission pattern, with similar relative intensities within each polyad, is repeated with its origin at 2238 cm"1 displacement. Clearly this is a second low-lying state whose totally symmetric vibrational levels are appearing in emission from the D state. The Wi state is only seen in emission from levels of the B2IT3/2 and D 205/ 2 states. This low-lying state must have an angular momentum of P = 3/2 or 5/2 in order to be observed from the B and D states. A Ni+(3d9) electronic configuration gives rise to 5 doublet 2 ~F 2 2 2 2 2 electronic states with E , IT3/2, Tli/2, As/2 and A 3/ 2 symmetries. Both of the A states have been accounted for in NiCN, which leaves 2n3/2 as the only plausible assignment of the \ V f state. The Wi designation was made by analogy to the W i 2 n 3 / 2 state of NiH which lies at a similar energy. It is obvious from Figure 3.14 that similar vibrational level patterns occur in the Wi, X 2 and Xi states. Clearly the Fermi resonance interaction plays a dominant role in the vibrational levels of all three states. We have only observed a small number of the levels of the Wi state. This is partly due to the fact that this state lies fairly high in energy. In general, our spectrometer is only able to detect emission features in the DF spectra out to a 104 displacement of -4500 cm"1 because the sensitivity of our photomultiplier tube decreases towards the red end of the spectrum. The levels that have been identified are included in the energy level diagram of Figure 3.13. The positions of the levels have also been fitted by our Fermi resonance program, giving results which are included in Table 3.1. c) The Excited Electronic States (i) The A 2 A S /2 State The A2A5/2 - Xi 2 A 5 / 2 electronic transition is the strongest band system observed in our fluorescence excitation spectra. Transitions were observed out to vj = 5, which enabled us to compile a fairly complete picture of the lower portion of the vibronic manifold in the A state. Figure 3.15 shows a schematic representation of all of the observed vibrational levels within the A electronic state, along with those for each of the other three excited states. Vibrational assignments were made by careful consideration of the DF spectra, the band positions and intensities and, where possible, with high-resolution. The band whose R-head lies at 16608 cm"1 (Figure 3.3) is the strongest band at the red end of the NiCN spectrum. Clearly, based upon its position, isotope shift and intensity it is a (0,0) band. This was confirmed from the DF spectrum recorded by pumping this transition (top of Figure 3.10). This spectrum shows emission only to the totally symmetric levels of the ground state, indicating that the excited state is a totally symmetric level, and shows a monotonically 105 e lU e tN CD C D IT) O O O O CN O o m o o o Os o o m 00 o o o 00 o o o o o o o 106 decreasing intensity of the emission features with increasing displacement, with no evidence of a Franck-Condon "hole" resulting from a node in the upper state wavefunction. Figure 3.10 represents a "textbook" fluorescence pattern from a v = 0 level. The high-resolution spectrum of this band (Figure 3.5) established that the excited state has 2As/2 symmetry. The next strong band that can be attributed to the A - X i system occurs at a frequency of 17041 cm"1. A dispersed fluorescence spectrum from this excited state is given in Figure 3.16. Emission features in this figure again correspond to the totally symmetric levels of the ground state. The peaks representing the Fermi polyad containing one quantum of Ni-C stretch in the ground state are clearly the strongest features in this spectrum and there is an intensity minimum at the polyad containing two quanta of Ni-C stretch. These features are consistent with the upper state vibrational wave function for the Ni-C stretching motion having one node, meaning that it has Vi = 1. A high-resolution spectrum was recorded for this transition which confirmed that the upper state angular momentum is P = 5/2, firmly establishing this level as the (001) level of the A state. The pair of weaker bands located at 16779 cm"1 and 16788 cm"1 give identical DF spectra containing only the non-totally symmetric levels of the ground state (bottom of Figure 3.10), with strong emission to the bending fundamental of the ground state. High-resolution experiments showed that these two upper states have P = 7/2 and 3/2, respectively. These upper state levels are therefore assigned as the two orbital components of the bending fundamental of the A state, specifically 2$>7n and 2Il3/2. 107 K o "CD T 8 « 3 IT) o" o" o o o cn o o in C N cn o" in^ oo" 00 cn^  oo" o o o C N vo" vo" C N TT" C N CN" o o in B o CD cd O CD O O O O o in C N CD c o rt H-1 CO CD U o CD O CD H CD < CD +-> C+M O "CD CD CD * ^ +-> C o T3 C o O I M o c cd fe rt CD s -CD H rt +-» CO fi O t-H 00 CD . f i CD CD 1-H o I % CD o s S o CD C H CD CD C CD CD c o CD tH O CD c o )H CD C H CO r! B C+H o g rt CD a o 00 fi •g rt o o rt -a rt O JH~> C H O a, vo cn CD t H 00 fe fe ^ m CD 2 -G -fi +-> -a o ™ + J CD O 108 The assignments of the bending and stretching fundamentals of the A state establish the upper state vibrational frequencies as V2' ~ 172 cm"1 and V3' ~ 435 cm"1. Using these frequencies together with the procedures outlined above, we have been able to assign 18 vibronic levels of the A state up to the (005) level. In the cases where high-resolution data were available the isotope shifts between the 5 8NiCN and 6 0NiCN isotopomer bands helped to confirm the vibronic assignment of the upper state. As mentioned previously, a shift of approximately 2 cm"1 is observed for each quantum of V3 that is excited in the upper state, and a shift of just over 0.1 cm"1 is observed for each quantum of v 2 that is excited. Rotationally resolved spectra were obtained for bands involving ten separate levels of the A state. These experiments revealed that all of the observed levels of the A state contain rotational perturbations. For the most part these appear to be isolated random perturbations in which single rotational levels have been doubled or shifted in position. Rotational constants for these A state levels could still be obtained by simply omitting the transitions involving these individually perturbed levels. The pure Ni-C stretching levels appear to suffer from considerably more severe perturbations. These levels were perturbed to such a degree that establishing rotational assignments for all of the observed lines proved extremely challenging, even despite the fact that the ground state rotational constants were well known. Almost every rotational line is split into multiple components, sometimes as many as six, and/or shifted from their expected positions. Even after rotational assignments had been made there were a considerable number of unassigned features. There were no obvious 109 patterns indicating avoided crossings or giving the nature of the perturbing state or states. No attempt was made to deperturb these levels. Even the zero point level of the A state does not avoid these perturbations. This level exhibits an intermediate degree of perturbation as compared to the other observed levels of the A state. As can be seen in Figure 3.5, a number of upper state rotational levels are split into several components with no obvious pattern to the splittings. Despite this fact, all of the rotational lines of this band can be assigned. Figure 3.17 shows a series of reduced rotational term value plots for different isotopomers and vibrational levels within the A state. The term energies (Tv) and rotational constants (J3V) were estimated from the high resolution spectra and the quantity Tv+ B^J+J) was subtracted from the energy of each of the upper state rotational levels. The uncertainty in each level position is smaller than the dots used in the plots. Under ideal conditions, with a complete absence of perturbations, one would expect these reduced rotational energy plots to be smooth straight lines with zero slope; any deviation from this represents a perturbation. Figure 3.17(a) is the reduced rotational energy plot for the v = 0 level of the main isotopomer, illustrating the extensive and random nature of the perturbations. Figures 3.17(b) and (c) show the reduced rotational energy plots for the v = 0 level of the 6 0 Ni and 1 5 N isotopomers, respectively. The plot for the A, v = 0 level of 6 0 NiCN shows that the perturbations are smaller than in the 5 8NiCN isotopomer. The majority of rotational levels, however, do show signs of small splittings or displacements from their theoretical energies. The 1 5 N plot seems to indicate an avoided crossing in which there are secondary interactions 110 • • o • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • CD > kn O o CD > J D JS o c3 CD I-H a o T3 1) H-> O kH H-> -O 3 c/l C CD CD .O U5 CvS ^ 3 >> ao CD c CD o H—» o kH CD H-> tn—i O >> O 'cc? CD H-» C/> o •a o is o CD "a3 CN -^H K CD 43 H-» t+H o in "CD "3 O o '•ci kH CD S O CH-! O > CD kH CD O OH o u CH-H O "CD _o *OH GO kH c CD 13 ° c ll O a n3 H—' o kH <U o CD L i CD JS H kn' CD B o OH O H-< O I O OH O H-» O 2H % 3 00 PH C+H O "CD J D ( uio) ASJSUJJ paotvpsjj ( uia) X S i s u g p a o n p s y I l l perturbing a number of rotational levels near the vicinity of the level crossing. The final plot, Figure 3.17(d) shows the reduced rotational energy for the P = 7/2 component of the bending fundamental of the A state. One rotational level is shown to be split into four components while the rotational levels on either side are split into two. The plot suggests an avoided crossing with a level with significant P-doubling; however a deperturbation has not been attempted. Because the A, v = 0 level is heavily perturbed, an 'r0' structure is not easily obtained, even though data are available for several isotopomers. Estimates of the bond lengths in this electronic state can be made. No evidence of activity in the C-N stretching vibration was observed anywhere in this study. It is therefore reasonable to suppose that the C-N bond length does not change in any of our electronic excitations. If we assume that the C-N bond length remains at the value obtained for the ground state, r0(C-N) = 1.1591 A, and estimate the rotational constant from the few unperturbed levels as Bo' ~ 0.12886 cm"1, then the Ni-C bond length can be calculated to be approximately ro(Ni-C) ~ 1.984 A. Calculation of the upper state rotational constants from the observed transition frequencies was only carried out on the levels for which the perturbations were not too extensive. Data are only available for the P = 5/2 spin-orbit component of the A 2 A state, so that a full case (a) Hamiltonian could not be used in the fitting procedure. Instead the transition frequencies were fitted to the simplified model: E v J = T v + B v J(J + 1) - D v J 2 (J + l) 2 ± V2[ qJ (J + 1) + q D J 2 (J + l) 2 ] [3.4] 112 where Tv, Bv and Dv have their usual meaning and q and qo are the A-doubling and centrifugal distortion to the A-doubling parameters, respectively. In all cases where the lower state in the transition was the v = 0 level of the ground state, the lower state constants were held fixed at the values obtained from the combination difference fits (Table 3.2). For the rotational analysis of the two components of the bending fundamental of the A state, data were available for both the "cold" bands originating in the v = 0 level of the ground state as well as the vi' = 1 "hot" bands. In this case the bands were fitted together, with the ground state constants held fixed; the constants for the vi' = 1 and vi = 1 were allowed to vary. The results of the rotational analyses of the levels of the A state are included in Table 3.3. (ii) The B 2 n 3 / 2 State The vibrational bands of the B2Tl3/2 -Xi 2As/ 2 electronic transition are generally thirty to forty percent weaker than those of the A - X i transition. For this reason fewer bands were observed in the B-Xi transition and fewer data are available for the levels of the B state. A schematic representation of the observed vibronic levels of the B state is shown in Figure 3.15. In this figure the levels of the B state are interleaved between those of the A state. To identify the levels of the two states, the vibrational assignments for the levels of the B state are placed on the right hand side of each level. 113 Table 3.3 Rotational constants for some excited state levels of NiCN. Level P' T v B v 108DV 10'q 108qD Bv=0 i 8 Ni Vi 16686.0522(6) 0.1311593(23) 7.26(18) 4.07(23) 5.77(24) Bv=0 6 0 Ni % 16686.2516(6) 0.1298941(31) 7.57(32) 3.48(32) 6.60(43) A 2 1 5 8 Ni Vi 16780.4764(11) 0.129788(11) — — ~ A 2 1 5 8 Ni Vi 16787.4647(5) 0.1294016(31) — — — A 2 1 6 0 Ni Vi 16787.5851(6) 0.1281847(34) — — — B2 1 5 8 Ni y2 16856.1164(4) 0.1321844(16) 8.11(11) — — B2 1 6 0 Ni Vi 16856.2607(6) 0.1309053(51) 7.98(82) — — A 22, 7=0 5 8 Ni Vi 16944.3862(4) 0.1300123(28) 1.25(31) — — A 22, 7=0 6 0 Ni Vi 16944.1519(5) 0.1287804(27) 1.74(28) — — A 22, 7=2 5 8 Ni Vi 16945.2062(7) 0.1306218(37) — — — A 22, 7=2 6 0 Ni Vi 16945.4768(6) 0.1293802(32) ~ -- — A 2 3 5 8 Ni Vi 17106.0473(5) 0.1307277(26) -2.16(21) — — A2 1 3 1 5 8 Ni Vi 17231.4929(10) 0.1290309(20) — 2.05(85) 3.3(13) A2 2 3 x 5 8 Ni Vi 17389.3351(5) 0.1293903(30) 1.06(33) — — A223l 6 0 Ni Vi 17387.1160(10) 0.1281696(75) 0.84(109) ~ — Cv=0 5 8 Ni Vi 17811.8475(3) 0.1292373(14) 5.10(13) — — Cv=0 6 0 Ni Vi 17812.0763(5) 0.1280009(37) 5.59(52) — — Di/=0 5 8 Ni Vi 19127.175(23) 0.12917(7) — — — Error limits (in parentheses) are 3a, in units of the last significant figure quoted. All values are given in units of cm"1. Values indicated by were held fixed at zero during the least squares fitting. Vibrational assignments for the levels of the B state were made by the same methods as those for the A state. Levels of the B state could be distinguished because they usually emit strongly to the low-lying X22A3/2 state. Examples are shown in Figure 3.12 which contains the dispersed emission spectra from the v = 0 and vi = 1 levels of the B state. For the most part, vibrational levels of the A state emit only weakly, if at all, to the levels of the X 2 state. Observation of strong emission to this state provided immediate evidence that the excited state belonged to the B manifold. 114 Identification of the level at 16686 cm"1 as the v = 0 level of a second excited electronic state was based upon a number of observations. Firstly, as mentioned in the previous paragraph, the DF spectrum displayed emission features to the low-lying X 2 state. Secondly, the level lies a mere 79 cm"1 from the v= 0 level of the A2As/2 state. This interval is too small to be a vibrational interval in the A state. From the high-resolution spectrum it is clear that the lower state is the ground state and that the upper state has P = 3/2; also there is clear evidence of P-type doubling in the upper state. No P-doubling was observed in the rotational structure of the A2As/2 - X i 2 A 5 / 2 (0,0) band, indicating that the 16686 cm"1 state probably has electronic TJ symmetry. The 5 8 Ni - 6 0 Ni isotope shift observed in the high-resolution spectrum is very similar to that in the A 2 A 5 / 2 -Xi 2 As/ 2 (0,0) band. Finally, the rotational constant given by the high-resolution spectrum (B = 0.1311593 cm"1) was not consistent with this state being either a vibrational level or spin-orbit component of the A 2 A state (Bo ~ 0.12886 cm"1). The conclusion is that the 16686 cm"1 level is the P = 3/2 component of the v = 0 level of an electronic JJ state which we designate B 2JJ 3/ 2. High-resolution spectra were only recorded for two bands involving levels of the B state, specifically the B - X i (0,0) band at 16686 cm"1 and the B - X i 21 0 band at 16857 cm"1. No obvious signs of perturbations were present in either of these upper states. Rotational analyses were performed for both states by fitting the transition frequencies to Equation 3.4 while keeping the ground state rotational constants fixed to those values obtained in the combination difference fit. The results of these rotational analyses are included in Table 3.3. 115 Isotopic substitution experiments using 15N-acetonitrile were not performed at high-resolution for the levels of the B state. Direct calculation of an ' r 0 ' structure was not carried out. The assumption that the C - N bond length remains constant at the value listed in Table 3.2 can be used in conjunction with the observed rotational constant to calculate the N i - C bond length in the B state as r 0 (Ni-C) = 1.9465 A. (iii) The C 20 7/ 2 State The C2<I>7/2 - X i 2 A 5 / 2 electronic transition represents the second strongest band system that has been observed in our spectra. The observed bands are similar in appearance to those in the A - X i system, with fairly strong progressions involving the upper state totally symmetric vibrational levels, and weaker bands from the sequence structure and non-totally symmetric vibrations. A total of thirteen vibrational levels of the C state were observed. These levels are depicted in the energy level diagram of Figure 3.15. Identification of the C - X i system of bands as another electronic transition was quite straightforward. The C - X i (0,0) band, whose band head lies at 17813 cm"1, appears at an energy where the A - X i and B - X i bands are rapidly losing intensity. This strong (0,0) band, as well as the intense vibrational structure, stands out amongst the weaker A and B systems in this region. The DF spectrum from the 17813 cm"1 state is also very characteristic of a v = 116 0 level. Identical emission features appear in this spectrum and in the DF spectrum from the v=0 level of the A state (figure 3.4) with only a few differences in the relative intensities. High-resolution methods were used to obtain a rotationally resolved spectrum of the C - X i (0,0) band. A portion of this spectrum is shown in Figure 3.6. Rotational analysis revealed that the excited state has an angular momentum of P = 7/2, which identified the C state as being a 2 0 7 / 2 state. This spectrum also indicates that the v = 0 level of the C state is free from the rotational perturbations that were observed in the levels of the A state. The constants obtained from the rotational analysis, in which the transition energies were fitted to Equation 3.4 while keeping the ground state parameters fixed, are included in Table 3.3. No other high-resolution spectra of bands involving levels of the C state were recorded. Assignments of the vibrational levels of the C state were made in much the same fashion as those of the A and B states, with the DF spectra playing an important role. The DF spectra from the levels of the C state were unique in the sense that they showed no emission to the vibrational levels of the low-lying X 2 or W i states. Each of the other excited electronic states showed at least some emission to levels of these low-lying states. This represents further evidence that the C state is not affected by vibronic coupling. The structure of the molecule in the C state can be estimated by using the same assumptions used for the A and B states. For a C-N bond length of ro(C-N) = 1.1591 A and an excited state rotational constant of Bo = 0.1292373 cm"1 the Ni-C distance is estimated to be r0(Ni-C)= 1.9669 A. 117 (iv) The D 20 5/ 2 State The D2<I>5/2-Xi2A5/2 transition was the weakest of the four band systems observed in our studies. Only three vibronic bands were observed, representing a short progression in the excited state N i - C stretching vibration. Assignments were made using the same considerations outlined previously and the level positions are included in the energy level diagram shown in Figure 3.15. The v = 0 level of the D state lies too far to the blue (19127.2 cm'1) for us to study using high-resolution methods. Instead, a medium-resolution spectrum was recorded using the pulsed dye laser system optimized for slow scan rate and high dispersion. Line widths on the order of 0.1 cm"1 were obtained using this approach. In the resulting spectrum, the majority of the R- and Q-branch lines were not resolved due to the dense rotational structure. The P-branch, however, was nicely resolved and was easily assigned using ground state combination differences to the R-head. Enough rotational transitions were observed to allow the fitting of the upper state term energy and rotational constant. These results are included in Table 3.3. The first lines of the rotational branches were not resolved in the medium-resolution spectrum. This made assigning the symmetry and angular momentum of the D state slightly more challenging. The dispersed fluorescence spectrum from the v = 0 level of the D state (Figure 3.14) shows strong emission to all three of the X i 2 A 5 / 2 , X 2 2 A 3 / 2 and Wi2IT3/2 states. The D state must therefore have an angular momentum projection of either P = 5/2 or 3/2. 118 The Q-branch of the medium resolution spectrum of the D - X i (0,0) is weaker than the R-and P-branches, suggesting that this is a parallel transition and that P' = 5/2. The interval between the v = 0 levels of the C and D states (1315 cm"1) is very similar to the spin-orbit interval of the Ni+[3d 84s] a2F state (1445 cm"1) (58), which should be the base electron configuration of the C2<I>7/2 state. This suggests that the D state may be the 2<J>5/2 spin-orbit partner to the C state. Further evidence can be obtained from the rotational constants. According to Mulliken (59,60), the spin components of an electronic state that is close to Hund's case (a) coupling have effective rotational constants BQ that are related to the mechanical rotational constant of the entire state, B, by: Bn=B + (2B2/AA)z [3.5] where A is the spin-orbit coupling constant and A and £ are the orbital and spin angular momentum projections, respectively. Using the observed rotational constant for the v = 0 level of the C state (Bm = 0.1292373(14) cm"1) we can estimate using Equation 3.5 the rotational constant of the P = 5/2 spin-orbit component as B5/2 = 0.12926 cm"1. The observed rotational constant for the v = 0 level of the D state is B0 = 0.12917(7) cm"1, which appears to be in acceptable agreement with the prediction of Equation 3.5 considering the limited resolution of the D - X i spectrum. It is reasonable to conclude that the D state is in fact the 2<J>5/2 state. 119 3.5 Discussion From the very beginnings of this study we noticed dramatic similarities between the electronic structures of N i C N and N i H (56,57,61). Once the ground state of N i C N was established as having 2 A 5 / 2 symmetry, comparisons were made to NiF (50-52), N i C l (53-55) and N i H . Figure 3.18 shows an energy level diagram of the observed low-lying doublet states in each of N i C N , N i H , NiF and NiCl . The NiF studies show the molecule to have a 2 n 3 / 2 ground state. At least six low-lying states were observed, of which the assigned doublet states are 2 n i / 2 at 251 cm"1, 2 A 5 / 2 at 830 cm"1, 2 S + at 1574 cm"1 and 2 A 3 / 2 at 2224 cm"1. N iCl was found to share the same 2 n 3 / 2 ground state as NiF. The low-lying excited states in N i C l are analogous to those in NiF; the main difference between the two species being that the two 2 A states in N i C l have dropped in energy relative to the 2 S and 2Ylin states. N i H was found to have a very different low-lying electronic structure than the two nickel halides. The ground state of N i H was observed to be 2 As/ 2 with the 2 A 3 / 2 state being the lowest excited state at 973 1 2 ~F 1 2 2 2 cm" . A S state was observed at 2052 cm" while the two IT states, TT 3/ 2 and ITi/ 2, were seen at the higher energies of 2610 cm"1 and 3456 cm"1, respectively. N i C N seems to have a low-lying electronic structure that is very similar to that of N i H . Both molecules have 2 A 5 / 2 ground states and the two observed low-lying states of N i C N , the X 2 2 A 3 / 2 state at 830 cm"1 and Wi 2TI 3/ 2 state at 2238 cm"1, have analogous states at very similar energies in N i H . Due to the extensive similarities the state designations used for N i H were adopted for the low-lying states of N i C N . 120 U • i-H Hi C N 3 VO i n cn vo C N C N IT) O C N 5 oo cn C N C N oo vo VO vo m o cn oo cn ov o cn oo C N 0 0 m CN < o VO 1 — 1 I T ) C N CO — j " t o II -a CJ CCS r5 y £ B o <+M c CD o m CD CD c CD C+H o co CD 4-* 3 s X> CD o x>r< - V fe I s CD m CD O c CD I CD co O CD +-» o c o co ,to C+-I CD e o fl-l o U 0 0 cn CD t-< =3 i n i n to o c CD t-H M-H CD s O fe £ to t-H CD x l g to ^ CD +-> to I-H CD —i | i r— O O O O O O i n O i n cn m C N o o o o o o o o o i n o i n C N r-! r - i 121 The excited state electronic structure of NiCN is very similar to that of NiH as well. Each of the four excited states observed here in NiCN have counterparts in NiH. Furthermore, the states of NiCN are all shifted to slightly higher energy than those of NiH by almost a constant factor of-700 cm"1. An energy level diagram showing the observed states of NiCN and NiH is given in Figure 3.19. The reason that the electronic structure of NiCN resembles so closely that of NiH, while differing from the nickel halides, can be made using crystal field arguments. The fluorine and chlorine atoms of the nickel halides will draw a significant amount of electron density to them and will appear as negatively charged ligands to the nickel atom. In NiH the hydrogen atom, though technically behaving as FT, will not carry considerable electron density. The proton nucleus will be "visible" to the nickel atom and will appear to be a compact positive charge, which is why NiH and the nickel halides differ in electronic structure. For the case of NiCN, the cyanide group is known to behave as CN". The majority of the electron density surrounding this ligand will be drawn to the large non-bonding orbitals on the back side of the nitrogen. When the carbon atom approaches the nickel it will appear to possess a slight positive charge, therefore resulting in a similar molecular electronic structure to that of NiH. Dispersed Fluorescence spectra from some levels of the B state, primarily those with vi = 1, showed a few very weak emission features to levels that do not fit into the vibrational manifolds of the ground state or low-lying states as they are understood. One of these lies at 586 cm"1. Too few levels were observed to discern any vibrational relationship common to them all. Based upon the similarities between NiCN and NiH discussed above, it is reasonable to assume that there should be a low-lying 2 S + state in NiCN at an energy below 122 NiCN NiH 19127 D 2$ 5/2 AE 756 17812 cr<D 7/2 780 18371 G2<D 5/2 16686 16607 B 2 n 3/2 A 2A 5/2 595 682 17032 15925 F2<£, 7/2 2 16091 D n 3 / 2 B 2A Ni+[d8s]H~ 5/2 3456 w 2 2 n 1 / 2 2238 830 ~ 2 372 2610 W , 2 I I 3 2 j u — - — — 2052 X 2 X 2 143 973 * l \ / 2 0 w 2 n v x 2z + X 2 2 A 3/2 X x 2 A 5 / 2 Ni + [d 9 ]FT Figure 3.19 Energy level diagrams of the observed electronic states in NiCN and NiH. Dramatic similarities are observed in the electronic structures of the two species. The NiH level positions were taken from references 56,57 and 61. 123 2000 cm"1. It is possible that some of these weak unassigned features are emission to this 2 E + state. The Fermi resonance analyses of Section 3.4.a(i) indicate that the vibrational levels of the X 2 and Wi states do not follow the model of Equation 3.1 as well as those of the ground state. The larger uncertainties and poorer fit results may arise because the data for these two states are fewer and less precise than those of the ground state. Another possibility could explain the observed deviation from the Fermi resonance model: both the X 2 and Wi states are P = 3/2 states and their origins are separated by only 1408 cm"1; it is possible that a weak vibronic interaction between the two states shifts the levels away from the expected Fermi resonance patterns predicted by Equation 3.1. Unfortunately, the data available are not sufficient to confirm such an interaction. The rotational perturbations observed in the levels of the A state unfortunately give very little information about the nature of the perturbing state or states. It is possible to make some suggestions for the causes of these perturbations. It was found in NiH (61) that there are quartet states located at similar energies to the B 2 A5/ 2 and D2Fl3/2 states and it is suggested that there should be other quartet states in this energy region. It is safe to conclude that there must be a number of quartet states at similar energies to the A 2 A 5 / 2 state of NiCN as well. If the density of quartet states is high the rotational perturbations could easily be caused by interactions between the A state and one or more of these dark states. It is interesting to note how small the vibronic coupling between the A and B states is in NiCN. The A and B states are separated by only 80 cm"1 and differ in A by one unit. In such 124 situations it is possible for the two states to couple through the bending vibration. Strong interactions of this type have been observed previously in our laboratory in the molecule YOH (62). In that molecule the vibronic coupling between the B 1 ! ! and C 1 Z + states is so strong that the A' component of the bending potential for the B state is forced into a shallow double minimum with a small barrier to linearity, while the potential of the C state is 'pinched' resulting in a bending frequency that is significantly larger than that of the ground state. NiCN appears to lie at the other extreme in which the effects of the vibronic interaction are very small. The result of what little vibronic coupling there is causes the splitting of the two vi = 1 levels of the A state to be larger than that of the Xi ground state. The P = 3/2 (2n3/2) and P = 7/2 (207 / 2) levels of the % state are separated by only 1.32 cm"1. In the A state this splitting is increased to 6.99 cm"1. Discounting the effects of the C2<D7/2 state on the A state, this increased splitting is presumably due to the v = 0, P = 3/2 level of the B state pushing up on the vi - 1, P = 3/2 level of the A state, which is found to lie only 101 cm"1 higher in energy. The weakness of the vibronic coupling seems to be a result of the A and B states both belonging to the same (d8s) electron configuration. There are very few signs of Renner-Teller splittings in any of the electronic states of NiCN. Degenerate electronic states (A > 0) of linear molecules contain two components whose wavefunctions differ by a 90° rotation about the molecular axis. One can associate the two components with the orbital motion of the electrons in either direction about the internuclear axis ( ± A). If the nuclei are in a linear configuration the electrostatic forces felt 125 by the orbiting electrons in the two components will be identical, and they will lie at the same energy in zero order. As the nuclei deviate from a linear configuration (i.e.: as they undergo a bending vibration) the resulting electrostatic field will perturb the motion of the electrons in the two components to different degrees. The result is a breakdown of the Born-Oppenheimer approximation and a lifting of the degeneracy of the components of the electronic state. This process is called the Renner-Teller effect, after the original paper by Renner (63), and can be treated quantum mechanically as a coupling of the vibrational (/) and orbital (A) angular momenta (64). The effect can be observed as a splitting between the vibrational angular momentum components of the bending levels in the electronic state. In degenerate electronic states, excitation of the bending vibration will result in multiple vibronic components as a result of the non-zero values of A and /. These levels are described by the vibronic angular momentum quantum number, in the absence of spin, K = | ± A ± / |. For example, in the 2A 5 / 2 electronic ground state of NiCN, excitation of one quantum of bending vibration (% symmetry, / = 1) results in 2Tl3/2 and 2<I>7/2 vibronic levels with K = 1 and 3 respectively. In zero order, with the two components of the electronic state coinciding, these levels would be degenerate. A splitting will result when the electronic degeneracy is lifted as each of these vibronic levels will be more closely associated with only one of the electronic components. In NiCN the K = 1 and 3 components of the bending fundamental are split by 1.3 cm"1. This can be attributed to a weak Renner-Teller interaction, but can also be explained as a vibronic interaction between the K = 1 P = 3/2 component of the bending fundamental and the P = 3/2 X2 2A3/2 v - 0 level which pushes the P = 3/2 bending level of the ground state down in energy. In Section 3.4.a(ii) we showed that the P = 9/2 components of 126 the bending overtone level (K = 4), the (0420) level and the (0221) level of the ground state should lie very close in energy to those predicted by the harmonic frequencies and anharmonicity constants from the Fermi resonance fit of Table 3.1. This suggests that the Renner-Teller splitting, if any, must be very small. The survey spectrum depicted in Figure 3.3 contains two "hot" bands assigned as 22 2 in the A - X i transition. The band at 16421 cm"1 represents the transition from the (2,2,5/2) polyad level of the ground state (at 524 cm"1) to the P = 5/2 component of the A 22 level; the vibrational angular momentum, /, is zero in both states. The second band at 16465 cm"1 comes from the 7 = 2 component of the ground state bending overtone, which is not affected by the Fermi resonance; it therefore lies at the position expected for the 22 2 sequence band. We do not, however, observe the hot band from the (2,1,%) level of the ground state, at 456 cm"1. The eigenvectors from the Fermi resonance modeling show that the (2,1,%) and (2,2,%) levels are roughly 40:60 and 60:40 mixtures of the |001> and |020> basis states, respectively. One might therefore expect to see the "hot" band from the (2,1,%) level at 456 cm"1 because the lower level contains more |020) character and its Boltzmann factor is more favorable. It should lie near 16490 cm"1, in a clear region of the spectrum. At present we can offer no simple explanation for its absence. 127 3.6 Summary and Conclusions This work reports high-resolution observations of several electronic transitions of nickel monocyanide, NiCN, and represents the first analysis of a transition metal monocyanide in which the molecule is confirmed to have the linear cyanide geometry. Rotational analysis shows that the ground state of the molecule is Xi2Ay2, with bond lengths ro(Ni-C) = 1.8292(28) A and r0(C-N) = 1.1591(29) A. A total of six excited electronic states have been identified; two low-lying states below 2500 cm"1 as well as four states between 16600 cm"1 and 20000 cm"1. The energies and relative positions of these states were found to be remarkably similar to those found in NiH. Crystal field arguments have been presented that attribute these similarities to the ligands presenting positive charges to the nickel centers which results in similar electrostatic interactions in both species. Strong Fermi resonance interaction occurs in the ground state as well as both low-lying excited electronic states. A simple Fermi resonance model was sufficient to reproduce the observed vibrational structure in these states to within experimental uncertainty. A number of unusual rotational perturbations were observed in the levels of the A2As/2 state, but the nature of the perturbing state or states could not be conclusively determined. 128 Chapter 4 Anomalous vibrational dependence of the rotational and hyperfine parameters in the B 4 I I - X 4 Z " transition of NbO 4.1 Introduction Niobium monoxide, NbO, has only two strong electronic transitions in the visible region, but the spectrum is surprisingly complicated because of the quartet spin multiplicity of the states involved and the extensive vibrational structure. In the first detailed account of the spectrum, V.R. Rao (1) classified the bands into three systems, A, B and C, but could offer no conclusions about their assignments. Three years later, he and Premaswarup (2) gave vibrational assignments for the long wavelength system (C), grouping the bands near 660 nm into the four sub-systems of a 4II(a) - 4S(b) transition. Meanwhile, a brief note by K.S. Rao (3) reported a rotational analysis of the strongest band of the A system, at 469 nm, also suggesting that the spin multiplicity was quartet, but this was almost immediately questioned by Uhler (4) who, using higher resolution, re-assigned it as 2 A - 2 A. Some aspects of her analysis, such as the very large values of the spin-rotation parameters, were not entirely convincing, but there was no further progress for 20 years until Brom, Durham and Weltner (5) proved, from the e.s.r. spectrum, that the ground state is 4 E ~ . Subsequent laser studies by 129 Femenias et al. (6) showed that the ground state has a second order spin-orbit splitting of 62 cm - 1 , which means that it is better described by case (a) coupling. This cleared up many of the remaining problems. Rao's A system is now recognized (7) as the transition C4E~(a) -X 4 E ~ ( a ) , and his C system as the transition B4TI - X 4 E _ ( a ) ; only one of his four sub-systems was correctly assigned vibrationally. . One of the problems complicating the analysis of the B4IT - X 4 E ~ system is that its spin structure is very asymmetric. The explanation of this asymmetry was given by Adam et al., (8) following a comprehensive rotational and hyperfine analysis of the (0,0) band. A state lying about 1000 cm - 1 below the B4II state, which had been noted in the matrix isolation work of Refs. (5) and (9), was also seen in their experiments. This state turned out to be a 2T1 state, which is strongly coupled to the B 4 n state by the spin-orbit operator, whose matrix elements have AO = 0. Since a 2TI state only has O = 1/2 and 3/2 components, it raises the two middle components of the 4 n state ( 4 r i i / 2 and 4 n 3 /2) relative to the two outer components ( 4 n_ i / 2 and 4 n 5 / 2) . The sub-band structure of the B4IT - X 4 E ~ transition is even more asymmetric because the two middle components of B 4 n only combine with the 4 E i / 2 component of the ground state, while the outer components combine only with 4 S 3 / 2 , which lies 62 cm - 1 higher in energy; therefore the two middle sub-bands are pushed up by a further 62 cm - 1 relative to the two outer sub-bands. The result, somewhat confusingly, is that the shortest wavelength sub-band of the B4T1 - X 4 E ~ (0,0) band does not involve the B 4 n 5 /2 component, even though this is the highest energy spin-orbit component. 130 Six doublet states are now known, following the detailed Fourier transform emission studies of Launila et al. (10) The state causing the asymmetry in B4IT, now designated c2Tl, is the upper state of the absorption bands near 730 nm discussed in References (5,8,9). Lying at higher energy are the states fill, e 2 0 and d2A. In the present work we show that these three higher doublet states also give rise to absorption bands from the X 4 E ~ ground state; Rao's very complicated B system (1) is now seen to consist of irregular progressions and sequences from the two strong quartet electronic transitions, B - X and C-X, together with weaker bands from the three underlying doublet-quartet transitions, d-X, e-X and f-X. The state labeled D in the matrix spectra of Brom et al. (5) can now be identified as the d 2 A 3 / 2 state of Reference (10); its gas-to-matrix shift is in the opposite sense to that of the B4TI state. The principal results of the present work are the rotational and hyperfine analyses of some of the higher bands of the B4IT - X 4 I ~ transition, with v ' = 1 - 3 and v " = 1. The main reason for undertaking it was to catalogue the exact positions of the NbO bands in the 550 - 650 nm region. In our studies of Nb compounds prepared by reacting laser-ablated Nb atoms in a free jet expansion with species such as CH 4 , we always find strong impurity bands of NbO, arising from traces of oxygen either in the Nb rod or in the helium carrier gas. These present problems when we try to locate weak bands of new molecules. An example is NbCH, whose spectrum overlaps the B4TI - X 4 S~ transition of NbO; our attempts to disentangle the bands of NbCD and NbO showed the need for a fuller understanding of the NbO spectrum. A second reason was astrophysical. The presence of NbO in the spectrum of the S-type star R Cygni has been tentatively established (11,12) by means of the band-heads at 6484 and 131 6591 A. When that work was done the bands had not been assigned, but Femenias et al. (5) later showed that they are the Q = 3/2 - 1/2 and 1/2 - 1/2 components of the B 4 n -X 4 E ~ (0,0) band. The NbO spectrum is extensively overlapped by bands of ZrO in the spectrum of R Cygni, so that a more secure identification might be possible if measurements were available for other less overlapped bands. 4.2 Experiment NbO molecules were prepared by the reaction of laser ablated Nb atoms with 0.5% O2 entrained in helium, in an apparatus which has been described in Chapter 3. In the present experiments a rotating and translating niobium rod was ablated using the third harmonic of a pulsed Nd:YAG laser (Lumonics Inc. FTY-400), focused by a 50 cm focal length quartz lens. The resulting metal plasma then reacted with the helium-oxygen mixture in a free jet expansion, generated by a pulsed nozzle valve (General Valve Inc., Series 9) operating at a backing pressure of about 50 p.s.i. Five centimeters downstream from the ablation point the supersonic expansion was crossed by a tunable laser beam, either from a pulsed dye laser (Lumonics HD 500) pumped by a second Nd:YAG laser (HY-400) or a ring laser (Coherent Inc model 899-21) pumped by an argon ion laser (Coherent Innova Sabre 20-TSM). Laser-induced fluorescence was collected through a monochromator (Spex 1402, 0.75 m), detected by a cooled photomultiplier (Hamamatsu R943) and processed by a box-car integrator 132 (Stanford Research Systems model SR 250). The monochromator was set to record the fluorescence to the x/' = 1 or 2 vibrational levels of the ground state, with a band-pass of 3 nm; in this mode it acts as a narrow-band filter, taking out most of the plasma emission and removing any scattered light from the tunable laser. Calibration was provided by opto-galvanic spectra from a uranium-argon hollow cathode lamp. (13) A temperature and pressure stabilized etalon, servo-locked to a stabilized helium-neon laser, allowed interpolation between the uranium lines for precise calibration of the ring laser spectra; (14) the relative precision of unblended lines measured with this system is about 15 MHz, though the line widths obtained in the present experiments were about 120 MHz, limited by the residual Doppler width in the free jet expansion. 4.3 Results a) Rotational and hyperfine structure in the B 4TI electronic state of NbO High resolution spectra have been recorded in this work for the case (a) allowed sub-bands of the (1,0), (2,0) and (3,0) bands of the B4IT - X 4 £~ transition of NbO. The (0,0) band of the transition has already been recorded by Adam et al, (8) using intermodulated fluorescence from a microwave discharge. Even though the effective temperature in their source was not much above room temperature, lines were observed up to 133 rotational quantum numbers of about J= 50V2. The analysis therefore gave very precise data for the v - 0 levels of both electronic states. We have made no attempt in this work to improve on the constants derived in Reference (8), since our resolution is slightly poorer and our maximum observed J values are less than 20V2; also the data set of Reference (8) included the very precise ground state microwave measurements of Suenram et al. (15) The advantage of our supersonic jet spectra is that they do not show center dips, or cross-over resonances, which are an annoying artifact of intermodulated fluorescence; (16) also the high-J lines are missing. As a result the hyperfine structures of the low-J lines are clearer, so that the diagonal hyperfine parameters are as well-determined as those of the zero-point levels given in Reference (8). The greatest improvement is found for the (2-lines with J ~ IOV2 where the center dips caused by the AF = +1 hyperfine components, on the sides of the strong AF = 0 components, previously had the effect of broadening the lines unsymmetrically; these are no longer present. NbO has particularly impressive hyperfine structure, since the 9 3 Nb nucleus (1=9/2) has the largest magnetic moment of any non-radioactive nucleus. Figure 4.1 shows the hyperfine structures of the first lines of the SQ^\ and TR^\ branches of the 4n 3/ 2 - 4Si/2, (3,0) band. The 5<231(3/2) line contains a good example of a hyperfine intensity cancellation, of the type that occurs in low-./ Q lines of spectra where the carrier molecule contains an atom with large nuclear spin. (17) Such cancellations occur when J < I, at F values where the angle between the vectors F and J (in a classical model) is roughly 90°. Since the intensity is carried by the J vector, the amount of 134 o PQ T.uio 131 £60181 ^3 -2 * J fi ro CD cd CD CD - ° £ v2 , 2 fi H ° 2 8 .S c —| cd 00 o .53 cd 23 co c n CD CD "3-pq O M-I CD XJ -u-> <+H O cn CD -fi CD fi cd CD X > CD T3 Cu, CD T 3 c c TO CD M fi cd CD X J H-> o cn CD fi <4—i o CD CD RO fi fi I d > X ! CD --a X J S *^  -13 CD J4 UH cd s CD" c Si" CD CD X ! -t-> C+H O cn CD UH CD 2 c o - 2 ?S CD ^ cn ^ 2 ^ C cn <e 2 CD - f j i f © CD fi CD CH >, K CD X ! -»-» CD > '5b fi CD fi o I UH O fi cd ] a* ^ ^ 5 PH H-1 O 135 intensity that is projected onto the F vector is small, so that the hyperfine component with that value of F in the upper and lower states almost disappears. In the present case the F = 4-4 hyperfine component of the sQi,\ (3/2) line, marked with an asterisk, is seen to have very low intensity compared to its neighbors. The new bands are sufficiently similar in appearance to the (0,0) band described in Reference (8) that we do not give details of the analysis here. Since the object was to determine the upper state constants, we only recorded enough of each sub-band to chart the courses of the rotational and hyperfine structures for both parities. The most useful regions of the sub-bands were the R branches, where the line density was not excessive, and the rotational assignments were obvious from the numbers of hyperfine components in the low-J lines together with the ground state hyperfine combination differences. Figure 4.2 shows the first R lines of the 4n_1/2 ~ 4 ^ 3 / 2 (2,0) sub-band; the fl-doubling of the lower state is almost zero at these low J values, so that the large splitting between the PR\2 and °R\t\ branches reflects the A-doubling of the excited state. We avoided using the ^-branches as far as possible because the assignments are not immediately obvious as a result of the line density, while the same information is available from the more widely-spaced R and P lines. However since the 4 F I 5 / 2 - 4 l 3 / 2 and 4 n 3 / 2 - 4 E 1 / 2 sub-bands are heavily overlapped, especially in the (1,0) band, use of the Q branches was sometimes unavoidable. It is surprising that there are not more local rotational perturbations in the B 4 n state, considering the density of doublet electronic levels at the same energy. The B 4 n, v= I and 2 levels appear to be unperturbed, at least in the range of J values we have observed, though 137 there is a possible perturbation in the 4 n 3 / 2 , v = 3 level, where the highest-observed /-parity levels, near J= 12V2, appear to have been shifted downwards by a small fraction of 1 cm - 1; unfortunately the affected branch, SQT,\, is weak and not supported by combination differences, so that the perturbation cannot be confirmed. Table 4.1 gives the rotational and hyperfine constants derived for the v = 1-3 levels of the B 4 n state, together with those of the v = 0 level (from Reference (8)) for comparison. The Hamiltonian and its matrix elements have been taken unchanged from Reference (8). Because we have only observed rotational lines up to J ~ 15V2, the various centrifugal distortion parameters are not well determined, and are not considered further. The most significant differences on vibrational excitation lie in the spin-rotation parameter, y, and the diagonal magnetic hyperfine parameters, and Cj. Figure 4.3 shows the parameter y plotted against v, where it can be seen that y increases by nearly a factor of four between the levels v = 1 and 2, after which it changes sign for v =3. The magnetic hyperfine parameters h^, which are coefficients of 2Q[F(F+1) -I(I+\)-J(J+\)]/[4J(J+l)] in the diagonal matrix elements of the Hamiltonian, are shown plotted against x^ in Figure 4.4, with the four values of O for each vibrational level displaced sideways for clarity. In pure case (a) coupling the values of /?Q should vary linearly with Cl for a given vibrational level, according to the relation hn = a\ + (b + c)Z, [4.1] 138 Table 4.1 Rotational and hyperfine constants for the levels v= 0-3 of the B 4 n state of NbOa, in cm"1. Values for the v = 0 level are taken from Ref. (8). v = 3 v =2 V = 1 v =0 T5/2 18167.7058 (3) 17275.1624 (3) 16361.2808 (3) 15414.62783 (13) T 3/2 18076.3139 (11) 17182.8877 (4) 16283.1524 (2) 15378.83368 (12) Tl/2 17762.7621 (30) 16890.9718 (57) 16012.8806 (13) 15 128.40 697 (30) T-1/2 17480.9627 (31) 16615.4106 (58) 15742.9143 (14) 14863.6089J (29) B b 0.407437 (5) 0.409730 (5) 0.411920 (4) 0.4137936 (2) 10s D 0.121 (3) 0.334 (40) 0.290 (21) 0.36308 (13) Y 0.251 (13) 0.7817 (19) 0.2103 (7) 0.16235 (17) 103 A D 0.46 (8) 2.948 (4) 1.364 (3) 0.8968 (14) 104XD 8.87 (44) 1.972 (2) 0 (fixed) 0.167 (11) 103 n c 6.74 (12) 0 (fixed) 1.819 (3) 0.814 (3) 106AH 0 (fixed) 0.85 (7) 0 (fixed) 0.01828 (13) 106 A-H 0.237 (11) 0.350 (25) 0 (fixed) 0.01155 (9) o+p+q 3.39 (5) 6.121 (44) 6.640 (9) 6.3798 (17) p+2q 0.06020 (3) 0.1406 (2) 0.06179 (4) 0.062301 (8) 0.0007 (4) 0.0400 (9) 0.00090 (24) 0.000116 (4) 10 D 0 + p + q 0 (fixed) 13.21 (4) 0 (fixed) 0.0369 (9) 105 D p + 2 q 0.76 (18) 0 (fixed) 0.92 (7) 0.2319 (10) 107 D q 23.5 (90) 49.6 (2) 0 (fixed) 0.100 (21) h5/2 0.01844 (12) 0.01912 (9) 0.01956 (15) 0.01948 (11) I13/2 0.02970 (16) 0.02764 (11) 0.02388 (13) 0.01874 (13) hi/2 0.02421 (19) 0.02398 (40) 0.02417 (55) 0.02393 (30) h-1/2 0.05325 (20) 0.05407 (21) 0.05516 (37) 0.05485 (26) b5 3 0.01706 (43) 0.0765 (111) 0.0202 (9) 0.01879 (6) b3j 0.0569 (9) 0.0018 (33) 0.0354 (15) 0.01906 (18) bi.-i 0.0206 (6) 0.0155 (7) 0.0140 (7) 0.01722 (21) d 0.00522 (4) 0.00556 (7) 0.00564 (7) 0.00603 (3) 104cx 0.875 (35) 0.209 (30)° 0.19 (5) 0.153 (5) e 2 Qq 0 0.0021 (7) 0.0017 (8) 0.0019 (10) 0.00204 (42) r.m.s. error 0.000727 0.000661 0.000757 0.000786 no. of data points 2509d 1483 1330 7327 a Error limits (in parentheses) are 3cr, in units of the last significant figure quoted. For the v= 0 level the following constants were also obtained: e2Qq2 = 0.0247 (10), 107 Db = 0.44 (62) and 105 % =1.2 (9) cm"1. The energy zero is the electronic origin of the X4£~, v = 0 state; on this scale the lowest energy hyperfine level of the molecule, J= V2, F,, F=4, lies at -30.6210 cm"1. (See Ref. 8) 0 Based on data for v = 0 and 1, the equilibrium rotational constants and bond length are Be = 0.414730 cm"1, ae = 0.001844 cm"1; re = 1.7259! A. c 104 D b = 0.547 (21) was also determined for the v= 2 level; the residuals suggest that the parity-dependent nuclear spin-rotation parameter S, could also be floated, but this is not realistic in view of the limited range of/values in the data set. d Includes data for X4E", v = 1. 139 140 0.06 -0.03 . . . . 1 0 1 2 3 V' Figure 4.4. The diagonal magnetic hyperfine parameters /in for the B 4n state of NbO, plotted as a function of O and v. The four Q-components for a given lvalue are shown displaced sideways. Tie lines join points corresponding to the same O and lvalues. 141 where a, b and c are the usual Frosch and Foley hyperfine parameters (18) and Cl = A + Z. The pronounced departure from the linear relation for v = 0 was explained in Reference (8) as the result of spin-orbit mixing of the c2FI state with the Cl = 1/2 and 3/2 components of the B 4n state; this lowers the value of /?i/2 and raises the value of /?3/2, producing the observed zig-zag pattern. The principal difference with increasing v is that the value of /?3/2 increases. Since hy2 does not vary, it appears that the perturbing effects of the c2n state do not change; instead, another perturbation mechanism must be growing in, with another Q=3/2 state presumably responsible. The spin-orbit effects responsible for the breakdown of Equation [4.1] also affect the off-diagonal hyperfine matrix elements. In case (a) coupling there is a hyperfine contribution to the AD = +1 (spin-uncoupling) matrix elements, which subtracts the quantity b[F(F+l1) -J(/+1)]/[4J(J+1)] from the rotational constant B. If the state is unperturbed the effective value of b should not depend on Cl, but it was found in Reference (8) that three different values were needed for the three ACI = +1 matrix elements. These were labeled &QQ', in an obvious notation that suppresses the halves in the values of Cl. The reason why three different values of £QQ- were needed is that the Cl — 1/2 and 3/2 components of the B 4n state are contaminated to different degrees by the c2n state. Table 4.1 shows that the values of vary erratically with v, with no obvious trends being discernible. The values are not as well determined in the higher vibrational levels because the sample molecules are colder in the present experiments, so that the maximum observed J 142 values are lower. However the value of by _y varies the least, again consistent with the idea that a perturbing Q=3/2 state is responsible. Another interesting result is the variation of the nuclear spin-rotation parameter cj. This is shown in Figure 4.5, where the values of Cj are plotted against v. The remarkable similarity of Figures 4.3 and 4.5 is striking, but is in fact an illusion. It was demonstrated in Reference (8) that, for a 4n state perturbed by 4 E and 4 A states, there is a pure precession relation between y and Cj, cj = - ya/(A + 2B), [4.2] where a is the Frosch and Foley parameter (18) for nuclear spin-electron orbit interaction, A is the spin-orbit coupling constant and B the rotational constant. The relation is obeyed closely for the levels v = 0 and 1, but breaks down massively for v = 2 and 3, where the variations are very large and in the wrong sense. Since the only low-lying 4 S states expected in NbO are the X 4 S~ state and the C 4S~ state at 21 315 cm - 1, this strongly suggests that there must be a 4 A state nearby. We return to this point below. b) Vibrational analysis of the 520 - 650 nm region Low resolution excitation spectra have been recorded for the 520 - 650 nm region in order to clarify the vibrational assignments of the NbO features appearing. Absorption bands from 143 144 — i tsm o o N -o o o o o o 0 0 o o OS o o o 0 0 o o CD o Xi O Id CD X ) H "3 3 cd cn -3 C cci X> CD x) H c ro CD o 3 CD cr -a CD CD cn o O a o a ro f cn 3 T 3 CD ~o UH o O CD CD cn jaJ CD 3 3 +-> CD X l H-> C+H o CD t-H CD ' X i X B l ti CD CD "TO CD CD 6 o t-H ^ I « C—I V"! x e •ti  M ro CD "3 CD Id 3 e ro CD a I T ) r-o m 3 o '5b CD X " CD o -a ro I-, . „ ro "3 ^ !£ m ro cn ~" c n X I CN I D CD ob to a 6 X ) oo OQ $ 2 O • .. CN W to "X <f CN C+H O cn CD •3 _3 ' ro cn > "3 CD O O CD CD 3 • a to ro a ' r o to -a J=i o p ' 3 3 x o fi C+H o o to O H cn 3 O ' " r o •y 'CD P-l l-H 3 00 B CD ro i_ CD + ^ - ° - 2 00 "3 .3 o O "rt cd CD X ! H T3 CD 3 T3 "±3 -3 to +-* ro cn T3 3 ro X ) to X ) -*-> U UH ro cn C o 3 .op 'cn CD "3 ro CD X5 ro CD a <D 3 cr CD CD ti ro ro X ) 3 O -3 00 3 O cn s .2 o ro <4-H 145 from X 4 E ~ can be identified in these spectra going to all four of the higher doublet states analyzed by Launila et al. (10), f^ IL e2<D, d2A and c2n. Figure 4.6 illustrates the 550 - 575 nm region, which contains the four components of the B4I1 - X 4S~, (3,0) band, together with weaker f-X, e-X and d-X bands. The selection rules for the doublet-quartet bands are consistent with spin-orbit coupling transferring the intensity from the strong B - X transition by a AQ = 0 mechanism. For instance, the Cl = 1/2 and 3/2 levels of the excited doublet states only appear in absorption from the X 4 ! , - ^ component of the ground state. This is because they are mixed with the Cl = 1/2 and 3/2 components of B 4n, respectively, and these have |E| = 1/2; according to the case (a) selection rule, AE = 0, they can only combine with the |£| = 1/2 component of the ground state. Similarly, Cl = 5/2 doublet levels only appear in absorption from the X 4 E _ 3 / 2 state because they are mixed with B 4n 5/ 2 , which has |E| = 3/2. It is surprising that weak e 2 0 5 / 2 - X 4 Z _ 3 / 2 bands appear in our spectra, because the matrix elements of the spin-orbit operator have AA = 0, ±1; the intensity transfer mechanism must therefore be higher order. No levels of the e 20 7/ 2 component appear in our spectra because there is no Cl = 7/2 component in the B 4 n state from which they could obtain intensity by spin-orbit coupling, even in higher order. Considerable sequence structure appears in these spectra. Even though the NbO molecules were prepared in a supersonic jet source, bands with v " = 3 are clearly visible. Although the Franck-Condon factors for Av = 3 transitions clearly favor the sequence bands over the (3,0) band itself, it seems that the vibrational temperature in our source must be quite 146 high, even though the rotational temperature is only about 50 K. Because of the extensive sequence structure we have been able to follow the vibrational levels of the B 4 n state to v = 5, and assign some higher vibrational levels of the doublet states that were not reported by Reference (10). For example, the band at 17659.5 cm - 1 in Figure 4.6 can be assigned unambiguously as d 2 A 5 / 2 - X 4 E~3/ 2 (4,2). To check the assignment we recorded part of it at high resolution, and could show by first lines and combination differences that it is an O = 5/2 - 3/2 band with v" = 2 andB' = 0.41290 cm - 1 , which is exactly as expected for d 2 A 5 / 2 , v' = 4, extrapolating from the values reported for the lower levels by Launila et al. (10) The hyperfine structure of the upper state is not resolved, even with linewidths of 100 MHz. To the blue of Figure 4.6 the spectrum drops off in intensity very quickly. The B - X, (4,0) and (5,1) bands are comparable in intensity to the f ^ H ^ - X 4 E ~ 1 / 2 (0,0) band, near 18050 cm - 1 , but otherwise there is only a long weak d 2 A 5 / 2 - X 4 E~3/ 2 sequence built on the (3,0) band, possibly going to (8,5). The vibrational level structure of NbO in the 13000 - 20000 cm - 1 region, as given by the present work, combined with the laser spectra of Adam et al. (8) and the Fourier transform emission spectra of Launila et al. (10), is illustrated in Figure 4.7. In this figure the quartet levels are indicated with longer horizontal lines, and the doublet levels with shorter lines. The levels shown include data from some new zero-gap measurements from the present work, given in Table 4.2. 147 I 2 5 19195 4 18342 3 17481 2 16615 1 15743 • 0 14865 B 4 n Figure 4.7. Vibrational levels of NbO in the region 13500-20000 cm'1, as presently known. The data for B 4II, v= 1-5, c 2n 3/ 2, v - 3 and d2A5/2, v = 4 come from the present work; data for B 4 n , v = 0 are from Ref. (8), and the remaining doublet levels are from Ref. (10). The zero of energy is the electronic origin of the X 4Z" state, whose two components lie at -30 cm"1 (2=1/2) and 32 cm"1 (£=3/2). Levels are grouped into columns by Q; quartet levels are shown with long horizontal lines and doublet levels by shorter lines. 148 Table 4.2 Measurements of zero gaps from low-resolution spectra of NbO (cm1) B 4 TI-X 4 E (4,0) (4,1) (5,1) (5,2) (6,2) £1 = 5/2- 3/2 3/2 - 1/2 1/2 - 1/2 -1/2 - 3/2 19013.4 18994.7 18660.7 18310.2 18032.4 18012.7 17679 17329 18899.4 18887.3 18536.7 18181.5 17925.9 17919.2 17562 18414.3 c2n-x4z (0,0) (1,0) (2,0) (3,0) Q = 1/2- 1/2 13551 3/2- 1/2 14331 14454 15212 16088 16956 d 2A-X 4£" (0,0) (1,0) (2,0) (3,0) (4,0) n = 3/2 - 1/2 16648 5/2 - 3/2a 16017 e20-X4E" (1,0) Q = 5/2-3/2 17731 17585 (4,3) 17502 18517? 17815 18716.7 17735 f2n-x4E" Q = 3/2 - 1/2 1/2 - 1/2 (0,0) 18053.0 18285b a (4,1): 18634.0; (4,2): 17659.5 (from high-resolution spectra); (5,2): 18550.0 cm"1. Rotational constants for the i/ = 4 level: B = 0.412895 (34), 106 D = 1.22 (58) cm"1 (3a error limits); theF"= 6 component of thei?(3/2) line lies at 17661.3478 cm"1. b blended with a Nb atomic line 4.4 Discussion The irregularities in the vibrational dependence of the constants for the B4T1 state, described in the previous section, can be largely understood by reference to Figure 4.7. For instance the increase in with v, shown in Figure 4.4, presumably results from the onset of 149 interaction between the B 4 n 3 / 2 state and the d 2 A 3 / 2 state, whose v = 0 level lies between the levels v = 1 and 2 of the B 4 n state. The interaction appears to be fairly strong, because considerable intensity is transferred to the d 2 A 3 / 2 - X 4 E ~ 1 / 2 system, as can be seen in Figure 4.6. A similar interaction must also occur between the d 2 A 5 / 2 and B 4n 5/2 states. Since the d 2 A 5 / 2 , v= 0 level lies between B 4 n 5 / 2 , v = 0 and 1, the interaction must already be affecting the B 4 n 5 / 2 , v = 0 level, with the result that the value of h5/2 does not change appreciably with v, since it is already perturbed at v= 0. The strength of the d 2 A 5 / 2 - X 4 E ~ 3 / 2 system suggests that the interaction between d 2 A 5 / 2 and B 4 n 5 / 2 is quite large, presumably because interacting levels with the same vibrational quantum number lie only a few hundred cm - 1 apart. The spin structure of the B 4 n state is another probe of the various spin-orbit interactions. Figure 4.8 shows the vibrational intervals AG for the four components of B 4n, plotted against v. There are no doublet states with O = -1/2, so that the vibrational intervals for this component are absolutely normal, decreasing regularly with v. On the other hand the first vibrational interval for the 4n 5/ 2 component is 67 cm - 1 higher than that of 4n_y2, showing that its v = 0 level has been pushed down considerably compared to the others. The presence of the d 2 A 5 / 2 , v = 0 level between B 4 n 5 / 2 , v = 0 and 1, as just described, is almost certainly the reason. 150 Figure 4.8. Vibrational intervals AG for the B4IT state of NbO, plotted against v. Data for v = 0-3 are from Table 1; data for v - 4 and 5 are from Table 2. 151 The depression of the B 4n 5/2, v = 0 level causes an interesting change in the appearance of the B - X bands with increasing v. In the (0,0) band, the 4n 5/ 2 - 4 £ ~ 3 / 2 sub-band lies to the red of the 4n 3/ 2 - 4E~i/2 sub-band, even though 4n 5/ 2 is the highest energy O-component; in the (1,0) band the energy order of the sub-bands reverses back to the expected order. However this is only temporary, and the order reverses again at v = 6. In the course of their work on the doublet manifold of NbO, Launila et al. (10) found two new Q=5/2 levels that they could not assign. They remarked that the levels appear to coincide with the estimated positions of the B 4 n 5 / 2 , v = 1 and 2 levels. Having now measured them, we can confirm that this is correct: the strong d 2 A 5 / 2 / B 4 n 5 / 2 mixing induces the d 2 A 5 / 2 - X 4 E ~ 3 / 2 system in our spectra and the B 4 n 5 / 2 - a 2A system in theirs. Interestingly, they do not report any bands from B 4 n 5 / 2 , V = 0, even though this level seems to be the furthest out of place. The vibrational intervals in the B 4 TIy2 component are again instructive. The first three vibrational intervals follow those for the 4n_ 1 / 2 component quite closely, but the next interval is slightly larger than expected, presumably because the v = 0 level of the f^TI^ state falls within it. The interaction must be weak, however, because the shift is only about 3 c m - 1 and the amount of intensity transferred to the f^n^ - X 4 E ~ 1 / 2 system (just beyond the blue edge of Figure 4.6, and similar to the f2n3/2 - X 4 E _ 3 / 2 band shown in that figure) is very small. The 4n 3/ 2 intervals are less easy to understand, being generally about 30 c m - 1 higher 152 than those of 4n_!/2. Possibly this indicates that this component dissociates to different atomic limits from the others. A slight lowering of the third vibrational interval could conceivably be taken as evidence for interaction with the f 2 !^, v = 0 level, which lies just belowB 4n 3 / 2, v =3. The most striking vibrational dependences are those of y and ch illustrated in Figures 4.3 and 4.5. These two parameters take account of perturbations of the 4IT state by distant 4 S and 4 A states (8) and, according to Equation [4.2], the ratio y/cj should be equal to -(A+2B)/a. This is found to be true to within a few percent for v = 0 and 1. The same approximations that lead to Equation [4.2] predict (8) that, if the only important perturbing states are 4 Z states, the spin-rotation parameter y should be equal to half the A-doubling parameter p+2q. The values given for v = 0 in Table 4.1 show that y is five times too large, from which Adam et al. (8) concluded that a 4 A state must lie nearby, and be responsible for the magnitudes of both y and Cj. In this work we have shown that the value of p+2q does not change much with v (barring an excursion at v = 2), meaning that the contribution from distant 4 S states to the parameter y also should not change. The very large variations in y and cj between v = 2 and 3, seen in Figures 4.3 and 4.5, therefore appear to represent a severe breakdown of the pure precession approximation, and the reversal in the sign of y at this point appears to be direct evidence that the v = 0 level of the 4 A state is located there, at an energy near 17500 cm - 1 . We discount the effects on y of the doublet excited states because these 153 only interact with a 4 n state through the spin-orbit and spin-spin operators, where there is no explicit dependence on J; therefore they do not contribute energy corrections that look like rotation-dependent terms in the Hamiltonian such as y (J - S ) • S or Cj I • J . Nevertheless the large centrifugal distortion parameters that are needed to model the B4IT, v = 2 and 3 levels show that they are not innocent bystanders. The 4 A state in question is presumably the o 8 o * 4 A state predicted by the ab initio calculations of Launila et a/.(10) to lie at 18935 cm - 1. This is about 1400 cm - 1 above the mid-point between the B4TI, v = 2 and 3 levels, which is not an unreasonable figure. The mechanism of the mixing that affects the values of y and Cj must be second order, because the a5a* 4 A and nd2 B 4 n states cannot interact directly: however if there is a small amount of configuration interaction between the 7i5 2 B4LT. state and the 07t8 A4T1 state at 11820 cm - 1, interaction between the 4 A and B 4 n states becomes possible through the spin-orbit operator. Such configuration interaction is known to occur in the c2LT. state, which has mixed 07t5/7t52 character. (8,10) Very weak 4 A - X 4 E ~ absorption bands might possibly occur near 17500 cm - 1; we have searched for them, but without success. 4.5 Summary and Conclusions 154 In conclusion, we have clarified the vibrational assignments of the NbO spectrum in the 15000-20000 cm - 1 region, and demonstrated that spin-orbit interaction with the B 4n state causes all the higher excited doublet states seen by Launila et al. (10) to appear in absorption from the ground X 4 E ~ state. At the same time the courses of the vibrational levels of the B4II state become very irregular; only the Q. = -1/2 component is unaffected, which gives a warning about how difficult it will be in general to interpret the hyperfine parameters of excited electronic states. An abrupt change in the sign of the spin-rotation parameter y for the B4IT state, between v = 2 and 3, gives evidence that the hitherto unknown o"5o~* 4 A state probably lies near 17500 cm - 1 . 155 Chapter 5 Laser Spectroscopy of the Transition Metal Methylidynes NbCH and TaCH 5.1 Introduction The bonding between transition metals and hydrocarbon ligands is of great importance to chemistry because of the role it plays in heterogeneous catalysis (1). Transition metal compounds with methylidyne-like ligands ( formula RM=C-H ) are thought to play a key role as intermediates in olefin metathesis reactions (2). For the most part, studies of molecules containing a formal metal carbon triple bond have only been carried out for large organometallic molecules (3-5). Recently our group has reported the spectroscopic observation of some of the simplest molecules of this type, transition metal methylidynes with the formula M=C-H, by reacting metal atoms with methane gas under supersonic jet-cooled conditions. To date we have observed the electronic excitation spectra of VCH (6), WCH (7), TiCH (8), CrCH (9), ZrCH (10) and in the present work, NbCH and TaCH. All of these molecules are linear in both their ground and excited states. In this study we present the results of spectroscopic investigations of NbCH (NbCD) and TaCH (TaCD) in the visible region. Two electronic transitions have been observed in 156 each molecule. They have been identified as A 3 0 2 - X 3 A i and B 3 Ai-X 3 Ai for NbCH and A Q=l Orii) - X X Z + and B Q=0 +( 3n 0 +) - X 1 ^ for TaCH. Details specific to the two molecules will be given in the next sections. 5.2 Laser Spectroscopy of NbCH a) Experiment The NbCH molecules were produced by the reaction of laser-ablated niobium atoms with methane gas (CH4) in an experimental apparatus that has been described in detail in Chapter 3. For the present experiments a rotating and translating niobium rod (Goodfellow Inc.) is ablated using the frequency-tripled output of a pulsed Nd:YAG laser (Lumonics Inc., model HY400). The resulting metal plasma is then entrained in a stream of helium carrier gas seeded with approximately 8% methane; for the NbCD experiments, a mixture of 8% CD4 in helium is used. The mixture passes through a pulsed nozzle valve (General Valve Inc. Series 9), expanding into a vacuum to form a cold free jet expansion. Five centimeters downstream from the point of ablation the molecules are excited by a beam of photons from a tunable dye laser, either from a Nd:YAG-pumped pulsed dye laser (Lumonics HD500) or a pulsed dye amplifier (Lambda-Physik, model FL2003) pumped by a XeCl Excimer laser (Lambda-Phsik, Model Compex 102). Laser-induced fluorescence is collected through a 157 monochromator (Spex 1402, 0.7 m), detected by a cooled photomultiplier (Hamamatsu R943) and averaged by a boxcar integrator (SRS model SR250). The monochromator was set to record the fluorescence to one of the vibrational levels of the ground electronic state with a band-pass of 3 nm; in this configuration it filters out most of the unwanted plasma emissions and laser scatter and acts as a molecule-selective narrow band filter. The linewidths of the fluorescence excitation spectra are about 0.1 cm"1 when using the Lumonics pulsed laser and 350 MHz with the pulsed dye amplifier system. These widths are convolutions of the laser linewidth, the residual Doppler width of the unskimmed free jet expansion and small contributions due to power broadening. The spectra were calibrated using optogalvanic spectra of argon and uranium (11). In the high-resolution spectra a temperature and pressure stabilized etalon servo-locked to a stabilized helium-neon laser allowed interpolation between successive uranium lines (12) providing a relative precision of 15 MHz for the measurement of unblended lines. Dispersed fluorescence (DF) spectra were collected by scanning the monochromator with the tunable laser set to a band head in the excitation spectrum. The slit width of the monochromator was reduced from 3 mm to 1 mm for these experiments, corresponding to a linewidth of 11 A. The frequencies measured in these spectra, which represent fluorescence down to the vibrational levels of the ground state, are expected to be accurate to ±5 cm"1. A number of 'hot band' spectra involving an excited vibrational level of the ground state were recorded with the. pulsed laser system as follows. The monochromator was set to the frequency of a strong band coming from the zero point vibrational level of the ground state. At the same time the tunable laser was scanned through a region to the red that is 158 offset by an amount equal to a vibrational interval of the ground state, obtained from the DF spectra. The noise level is often greatly reduced when the fluorescence is detected to the blue of the laser line so that the 'hot bands' are observed even though they may not appear in the original survey spectra. In the present experiments we found that there was sufficient population in the lower vibrational levels up to about 1200 cm"1 to make them observable. b) Appearance of the Spectrum At least 28 red-degraded bands of NbCH and 15 of NbCD have been identified in the region 710-485 nm. Only a few of these bands are strong in the excitation spectra of either isotopomer. In NbCH, the strongest band head in the spectrum lies at 16056.7 cm"1; there are also strong bands with heads at frequencies of 16167.5 cm"1, 16206.5 cm"1 and 16595.6 cm"1. For NbCD, the most intense band has an R-head at 16118.6 cm"1, with the only other band of significant intensity appearing at 16238 cm"1. The remainder of the observed bands in both isotopomers have intensities that are considerably less than 50% of those of the most intense bands. Considerable care was taken to identify the carrier of the bands in our spectra. We found that NbC (13) appeared persistently as an impurity in our excitation spectra. We also found that emission features due to NbO (14,15), excited by broadband ASE of the laser dye, frequently appeared in our dispersed fluorescence spectra. 159 The most striking features of the excitation spectra as a whole are the large clusters of bands at the long wavelength end of the spectrum in each isotopomer. In NbCH there are seven bands between 16165 cm"1 and 16330 cm"1; in NbCD six bands have been identified in the same region, with at least 3 other very weak bands that could not be confirmed as NbCD by their DF spectra. These clusters have been attributed to perturbations by a comparatively dense manifold of lower lying dark states that are interacting with a single vibrational level of the electronic B state. Two electronic transitions have been identified in the excitation spectra. Based on the first lines of the branches the first has been designated A3<J>2 - X 3 A i and has its (0,0) band at 16056.7 cm"1. On deuteration, the (0,0) band of this transition is shifted to the blue to 16118.6 cm"1. The second transition has been designated B 3 Ai - X 3 A i . The v = 0 level of the B state suffers from the perturbations mentioned above, so that the (0,0) band of the B - X transition is responsible for the clusters of bands that are observed. This will be discussed in greater detail below. No bands originating from vibrationally excited levels of the ground state were originally identified in our survey spectra. By fixing the monochromator to a known transition from the v = 0 level of the ground state and scanning the laser through expected 'hot band' frequencies (as described above), the 'hot bands' from the (010), (020) and (001) vibrational levels of both isotopomers were recorded. Figure 5.2.1 shows the rotational structure of some of these 'hot bands' in NbCD. 160 Figure 5.2.1 A vibrational progression in the ground state bending vibration of NbCD, showing the alternation in polarization with v2". All three bands are plotted to the same scale. The vibrational assignment and band origin positions are given next to each band. 161 All of the excitation bands are red-degraded, with R-branch heads forming at J ~ 12. Figure 5.2.1 illustrates how the relative intensities of the rotational branches change between parallel and perpendicular polarization with excitation of the bending vibration. Many of the observed bands show rotational perturbations at higher values of J. Figure 5.2.1 shows examples of the types of perturbations encountered. In this figure the rotational branches are doubled at J' = 18 which results in the unusual R-branch in which extra lines appear to the blue of the head. The low-J lines in Figure 5.2.1 are broadened by the nuclear hyperfine structure resulting from the I = 9/2 spin of the 9 3Nb nucleus. The A3<I>2 - X 3 Ai (0,0) bands of both NbCH and NbCD, as well as portions of a few other bands, were recorded using high-resolution in order to resolve the hyperfine structure. Figure 5.2.2 shows the first two lines in the R-branch of the A30>2 - X 3 Ai (0,0) band of NbCH. The hyperfine width of the R(2) line is significantly less than that of R(l). The hyperfine structure collapses rapidly with J to near zero width. As a result, only the first few lines of each branch show any significant resolution of the hyperfine structure. 162 163 c) The Ground Electronic State, X 3 Ai (i) Vibrational analysis of the X 3 Ai state Dispersed fluorescence (DF) spectra were recorded by pumping each of the observed excitation bands in our survey spectra. Figure 5.2.3 shows the DF spectrum from the 16748.3 cm"1 level in NbCD. The features of these spectra represent emission down to the vibrational levels of the ground electronic state. The figure shows a long progression in the ground state bending vibration out to (070), where the odd v2 levels are stronger than the even v2 levels; weak features that have been assigned to the C-D stretching frequency (100) and the (110) combination band are also observed. Also shown in the figure is emission to a feature at just over 400 cm'1. This feature is isotope invariant since it has been observed frequently in the DF spectra for both isotopomers; it has therefore been assigned as case (a)-forbidden emission to the X 3 A 2 spin orbit component of the ground state. This assignment is consistent with the results obtained by Azuma et al, for NbN (16), where the 3 A 2 - 3 A i interval in X 3 A is determined as 400.5+0.1 cm"1. Combining the results from all of the DF spectra, we obtain a comprehensive picture of the vibrational structure of the ground state. A listing of all of the observed vibrational levels for NbCH and NbCD is given in Table 5.2.1. The assigned vibrational levels of the ground states of NbCH and NbCD are illustrated in Figure 5.2.4. Assignment of the levels below 2500 cm"1 was straightforward because the Nb-C stretching frequency and the bending fundamental and overtone 164 165 N b C H (070) (060) (050) (031) (040) (021) 3 A , (OH) (002) (030) (Oil) J A 2 (001) (001) J A 2 (010) ""(020) ~ (010) J A 2 (000) (000) N b C D (041) (110) (100) Figure 5.2.4 Assigned ground state vibrational levels of NbCH and NbCD, as measured from the dispersed fluorescence spectra. The levels indicated by solid lines belong to the X Aj component; those indicated by a dashed line belong to the X A 2 spin component. See Table 5.2.1 for the precise level positions. 166 Table 5.2.1 Observed ground state frequencies of NbCH and NbCD NbCH NbCD Level Assignment Level Assignment Level Assignment Level Assignment 409 X 3A 2 ,v = 0 2361 4v2 409 X 3 A 2 , v = 0 2330 5v2 603.41 v 2 2550 466.106 v 2 2529 V i + v 2 904.55 v 3 2665 3v2 + v3 857.375 v3 2674 4v2 + v3 1017 X 3 A 2 , v 2 2894 5v2 932.667 2v2 2783 6v2 1182.63 2v2 2960 1260 X 3 A 2 , v3 2839 1316 X 3 A 2 , v3 3188 1319 v 2 + v 3 2866 1506 v 2 + v3 3450 6v2 1404 3v2 2909 1776 3v2 3558 1688 2v3 3056 1811 2v3 3760 1734 X 3 A 2 , v2+v3 3258 7v2 1907 X 3 A 2 , v2+v3 4116 7v2 1769 2v2 + v3 4027 1942 4312 1865 4v2 2080 2v2 + v3 4684 1901 2114 4785 2099 V i 2176 5043 2228 3v2 + v3 All level positions given in cm"1. Frequencies of v2, v3 and 2v2 were obtained by fitting the rotational transitions of the 'hot bands' (see text); all other frequencies were obtained from the DF spectra. frequencies have been determined to pulsed laser accuracy from the rotational analyses of the 'hot bands'. Because of increasing anharmonicity, and ambiguities resulting from increasing level density, it has proven to be difficult to conclusively assign many of the observed frequencies above 2500 cm"1; this is more true in NbCH since a larger number of levels were observed above 2500 cm"1. Assignment of the levels at 2099 cm"1 and 2529 cm"1 in NbCD as the C-D stretching fundamental and the (110) combination level was made by considering both the positions and intensities of the peaks in the DF spectra. Since the fundamental 167 frequencies for the Nb-C stretch and the bending vibration are 466.106(35) cm"1 and 857.375(36) cm"1, respectively, the only logical assignment for the 2099 cm"1 level is (100), even though the X 3 A 2 , 2v3 level is expected to lie near 2097 cm"1. Figure 5.2.3 shows this feature to be quite weak, which is consistent with our assignment; only a very small change in the C-D bondlength is expected upon electronic excitation so the Franck-Condon factors involving the C-D stretch of the ground state must be quite small. It is probable that this band is only seen because the upper state is perturbed by a level or levels where the C-D stretching vibration is excited. A possible assignment for the level at 2529 cm"1 is 3v3, since this should lie at approximately this energy assuming a constant anharmonicity. However, looking at Figure 5.2.3 we can see that the (001) feature is quite weak compared to the bending features and that the 2v3 peak is completely missing. In view of the strength of the v 2 fundamental we assign the 2529 cm"1 feature as (110). We have not been able to assign the C - H stretching fundamental in NbCH conclusively. (ii) Rotational and hyperfine analysis of the X 3 Ai state The A 3 0 2 - X 3 A U (0,0) bands for both NbCH (16056.7 cm-1) and NbCD (16118.6 cm-1) were recorded at high resolution using the Excimer-pumped pulsed dye amplifier system described in Section 5.2.A. Portions of the bands with heads at 16167.5 cm"1, 16246.4 cm"1 and 16595.6 cm"1 in NbCH and 16177.0 cm"1 in NbCD were also recorded. 168 These spectra revealed that the ground state has an angular momentum of P" = 1; by analogy with the isoelectronic NbN (17) and isovalent VCH (6) this state was assigned as X 3Ai. In these experiments much of the rotational structure is resolved and the hyperfine splittings due to the I = 9/2 spin of niobium are observed. Figure 5.2.2 shows the first two lines of the R-branch in the 16056.7 cm - 1 band of NbCH. The hyperfine width is widest for J" = 1 and decreases as 1/J as is typical when both states follow case (ap) coupling. The appearance of the hyperfine structure can be understood from the diagonal matrix elements of the magnetic hyperfine Hamiltonian (18) #~MHF = aI z L z + bI-S + cI z S z [5.2.1] For case (ap) coupling these are < „ A S s m i F I «-MHP I nASuniF > - k + ( b + c ) s ] n g ^ - i < i + i ) - J(m)] [ 5 2 2 ] The R(l) line of Figure 5.2.4 consists of 9 hyperfine lines representing all the possible AF = 0, ±1 transitions between the rotational levels J' = 2 and J" = 1. Although ten hyperfine levels are expected for a given J value when I = 9/2, the rules of vector coupling limit the number of possible hyperfine levels for low values of J. For the R(2) line all of the 15 possible hyperfine lines can be assigned; however, the hyperfine width has already collapsed to the point where many of the low-F hyperfine lines are overlapped. For lines with medium values of J the hyperfine width rapidly collapses until often only the most intense hyperfine component, with the highest values of F, is partially resolved. The hyperfine structure in NbCH undergoes a dramatic reversal where the hyperfine widths of the rotational lines pass through a minimum and then expand again with the 169 opposite ordering of the hyperfine components. A similar occurrence was observed in the isoelectronic molecule NbN (17). This reversal is a result of the hyperfine widths of the rotational levels of the two states, which evolve at different rates with J, becoming equal and causing all of the hyperfine transitions to be coincident. This indicates that at least one of the two states is no longer represented by case (ap) coupling. Equation [5.2.2] shows that if both states remain in case (a) coupling the hyperfine widths of the two states will decrease at the same rate and will never be equal. In NbCH, as was the case in NbN, spin-uncoupling effects are causing the ground state of the molecule to evolve rapidly towards case (b) coupling with increasing rotation. Azuma et al. (17) showed that the hyperfine splitting must always reverse in this way in a regular triplet state when the Fermi contact interaction is the dominant contributor to the hyperfine structure. This is a result of the correlation between the different spin components of the regular triplet state upon going from case (a) to case (b) coupling. In the case (b) limit the Fermi contact interaction is described by the formula <NSJTF | b I-S | NSJIF > = b[F(F + l)-I(I + l ) -J( J + l)][j(J + l) + S(S + l ) - N ( N + l)] 4J(J + 1) The 3 Ai state (E = -1) in the case (a) limit becomes the Fi component (J = N + 1) in case (b). One only needs to compare Equations [5.2.3] and [5.2.2] to see that the ordering of the hyperfine levels must reverse no matter what the sign of the Fermi contact parameter b. In NbCH it is found that the hyperfine splitting in the ground state passes through zero at J = 17, while it was observed to occur at J = 14 in NbN (17). The difference in J value is because the rotational constant of NbN is larger than that of NbCH while the spin orbit parameter is roughly the same. 170 The Hamiltonian operator describing the rotational and hyperfine structure of a 3 A state in case (ap) coupling can be shown from Equation [2.137] to have the form H= A LZSZ + f A.(3 S22 - S 2) + B ( J 2 - J 2 + S 2 - S2 ) - (B - \ y)(J+S_ + J_S+) - D ( J 2 - J 2 + S 2 - S2 - J+S_ + J_S+)2 + y (S2 - S 2) + aI zL z + bI-S + cIzSz. [5.2.4] In this equation, A is the spin-orbit parameter, X is the parameter for the electron spin-spin interaction as well as second order spin-orbit effects, B is the rotational constant, D is the centrifugal distortion correction and y is the spin-rotation interaction parameter. In the present study we have no rotational information for the Q = 2 and 3 spin components of the 3A ground state, though we have observed the spin-orbit interval between X 3 Ai and X 3 A 2 in several of the dispersed fluorescence spectra. To fit the ground state structure we decided to fix the spin-orbit constant to A = 204.5 cm - 1 and to ignore the terms of the Hamiltonian involving X and y, since we have no data to determine them. The resulting matrix elements for the rotational part of the Hamiltonian are given in Table 5.2.2. Table 5.2.2 Matrix elements for the rotational and spin parts of the Hamiltonian for a 3A state, as used in this work. | 3 A 3 > , 3 A | 2A + B(x-8) V 3 ' - D ( x 2 - 14x + 52) < 3A 2 | < 3 Ai | Symmetric | 3 A 2 > -V2(x-6)[B-B (x-- D ( x 2 -2D(x-5)] 2) -12) -2D v /(x-2)(x-6) -A/2(x-2)[B-2D(x-l)] -2A + Bx - D (x2 + 2x - 4) The matrix is given in the R 2 formalism neglecting all terms in X, y, A D and Xu, and with x = J(J + 1). 171 The hyperfine matrix elements in case (ap) coupling, both diagonal and off-diagonal in fi, are given by Equations [2.172] to [2.175] < JOIF 1 H M H F | JOIF > = h"[F(F+i)-«i+0-jq+i)] [ 5 2 5 ] 2J(J + 1) < mw | HMHF I J-l^HF > - ^ + I + F + 1 ) ( P ^ - W + I-F)(F + I - J + 1) 2JV(2J + 1)(2J-1) < SE,JfiIF | HMHF I SE±l,Jfi±lTF > = bJ[j(J +1) - Q ( Q + 1)|S(S +1) - E(Z + 1)J y[F(F+i)-iq+i)-j(j+i)] 4J(J + 1) < SE,JfiIF | HMHF I SI±l ,J- l , f i±l ,IF > = + bV(J+fi)(J + fi - 1)[S(S +1) - S(S ± 1)J V^(J + I + F + 1)(F + J-I)(J + I-F)(F + I - J + 1) 4JV(2J + 1)(2J-1) where h = aA + (b + c)Z [5.2.9] Azuma et al. (17) found that in NbN there was sufficient spin-orbit contamination in the ground state that they required a separate h parameter for each of their O sub-states and two separate b parameters to obtain an adequate fit to their data. Since data are not available for the fi = 2 and 3 sub-states we do not have to take such measures in this case. The final parameters for the X 3 Ai state of NbCH are given in Table 5.2.2. They were obtained by fitting the combination differences for all unblended pairs of hyperfine transitions. Despite the fact that the hyperfine structure collapsed quickly with J, there was usually at least one hyperfine component in each rotational line that was partially resolved; 172 this allowed the determination of the b parameter. Since only a limited range of J values was available the centrifugal distortion constant could not be determined directly; instead it was fixed at the value determined by the Kratzer relation (19). The same procedure was used to determine the ground state parameters of NbCD, which are also included in Table 5.2.3. The rotational constants for the two isotopomers were used to calculate an 'r0' structure assuming that there was no change in C - H bond length upon deuteration; the bond lengths are given in Table 5.2.3. Table 5.2.3 Ground state rotational and hyperfine constants for NbCH, NbCD and NbNa. NbCH NbCD NbN a A 204.5* 224.28 B 0.414177(13) 0.354054(15) 0.501464 107D 3.44* 2.40* 4.54 h(3A0 -0.04404(17) -.06157 b 0.071(21) 0.079b Structure: r0(Nb-C) 1.77933(9) ro(C-H) 1.0827(5) The bondlengths are given in A; all other values given in cm"1. All values indicated with an asterisk were held fixed in the least squares fit. Values in parentheses are 3 standard deviations in units of the last significant figure quoted, (a) Taken from Ref. (17). (b) Average of b+ and b_, as defined by Ref. (17). Rotationally resolved spectra (linewidth = 0.1 cm-1) of the (000-010), (000-020) and (000-001) 'hot bands' were recorded for both NbCH and NbCD (see Figure 5.2.1). The hyperfine structure is not resolved in these spectra, though hyperfine broadening of the low-J lines is noticeable. A simple case (a) energy expression of the form 173 E = T V + B VJ(J+1) [5.2.10] was used to fit the observed transition frequencies while keeping the ground state parameters fixed at the values from Table 5.2.3. Since all of the hot bands had a common upper state they were fitted simultaneously to obtain the best results. The rotational constants and vibrational term energies for the three ground state levels are given in Table 5.2.4. Table 5.2.4 Rotational constants and term energies for some ground state vibrational levels of NbCH and NbCD. NbCH NbCD Level T v B v T v B v 000 0 0.414177(13) 0 0.354054(15) 010 603.41(10) 0.40731(68) 466.106(35) 0.35469(22) 020 1182.63(10) 0.41416(68) 932.667(37) 0.35474(24) 001 904.55(8) 0.4131(12) 857.375(36) 0.35307(22) All values given in cm"1. Values in parentheses are 3 standard deviations in units of the last significant figure quoted. The (000-020) 'hot band' pictured in Figure 5.2.1 appears to have a larger number of rotational lines than the other two bands in this figure. Since all three share the same upper state (A3<D>2, v = 0) the appearance of these extra lines must be due to the bending overtone level of the ground state. One possible explanation would be a P-resonance between the vibronic components of the bending overtone level. In a 3Ai state, the 020 level has P = 1 (3Ei), P = 1 (3Ai) and P = 3 ( ^ 3) vibronic components. It is possible that the two P = 1 components lie very close in energy and that a second order rotational interaction between them, analogous to 1-resonance in the bending overtones of molecules, causes the 174 forbidden 3 0 2 - 3£i component to pick up some intensity. We have made some tentative rotational assignments for these extra P-branch lines; however, none of the corresponding R-branch lines could be identified among the stronger lines of the main R-branch. No further conclusions can be drawn at this time. d) The excited electronic states of NbCH Two excited electronic states have been identified in NbCH. Assignment of the two states as A 3 0 2 and B 3Ai was based on intensity, isotope shift and rotational information. All of the observed excited state vibrational levels of NbCH and NbCD are depicted schematically in Figure 5.2.5. The most intense band in the excitation spectra of each isotopomer is found at the long wavelength end of the spectrum. High resolution spectra reveal the upper state to have an angular momentum of P' = 2. A 3<J> state was observed in NbN (17) with the fi = 2 sub-state lying at an energy of 15711 cm -1. By analogy we assign this excited state in NbCH as A <D2, v = 0. The energy of this level is found to shift to the blue by 59.1 cm upon deuteration, indicating that the bending frequency in the excited state is considerably lower than that of the ground state. Immediately to the blue of the A - X (0,0) band in both isotopomers is a cluster of parallel-polarized bands. Comparing the frequencies of the most intense of these bands in 175 N b C H N b C D A (040) _ A (001)" A (020) P .2 "2 -2 .2 1 A (010) AJ<D (000) f B A, (000) <j I Figure 5.2.5 Vibrational levels of NbCH and NbCD belonging to the A3<J>2 and B3Al excited electronic states. The levels of the B state are shattered by interactions with lower-lying states. 176 NbCH and NbCD shows that there is a blue shift of approximately 60 cm -1. It would appear that this is a second electronic state that has been shattered into several components by a lower-lying dark state. We assign this state as B 3Ai. Since the levels of the B state are split into multiple components, it is difficult to assign the vibrational levels of this excited state. It appears that the A state is not influenced by either the B state or the dark state that perturbs it. As a result, we have been able to assign a few of its vibrational levels. In NbCD we have observed an isolated level with P = 2 at an energy of 16552.4 cm -1. We have assigned this as being the bending overtone level of the A state of NbCD because it has the same P-value as the v = 0 level, and it emits strongly to the bending overtone level of the ground state in the dispersed fluorescence spectrum. This establishes the upper state bending frequency as approximately 221 cm -1. Looking to the red by this amount we find the level at 16326.7 cm - 1 that emits strongly to the non-totally symmetric bending levels of the ground state. We have tentatively assigned this level as the bending fundamental of the A state. We have also identified the levels at 16868.7 cm - 1 and 16965.4 cm - 1 as being the Nb-C stretching fundamental and the 4v2 bending overtone level, respectively, because they are both found to have P = 2 and both emit most strongly to the totally symmetric levels of the ground state. In NbCH we have assigned the levels at 16323.0 cm - 1 and 16589.9 cm - 1 as the bending fundamental and overtone levels of the A state, respectively, based on similar reasoning. No further conclusive assignments have been made. 177 We have been able to record medium resolution spectra, of the type shown in Figure 5.2.1, for most of the excitation bands we have observed. Since the hyperfine structure is not resolved in any of these spectra, we fitted the rotational transition frequencies to the simple energy expression of Equation [5.2.10], while keeping the ground state constants fixed, to obtain the rotational constants and term values for most of the excited vibrational states. A summary of these results is given in Table 5.2.5. Table 5.2.5 Rotational constants for some of the observed upper state levels of N b C H and N b C D N b C H N b C D Level T v B v Level T v B v A v = 0 16050.843(38) 0.38607(44) A v = 0 16109.974(24) 0.34237(16) B v = 0 16162.723(34) 0.38090(52) B v = 0 16197.386(74) 0.3132(12) B v = 0 16201.767(34) 0.37971(65) B v = 0 16234.695(20) 0.32452(42) B v = 0 16242.567(24) 0.37206(41) B v = 0 16267.597(78) 0.3234(15) A v 2 16323.010(56) 0.3756(38) A v 2 16326.74(19) 0.3344(14) 16423.843(38) 0.38559(65) A 2 v 2 16552.408(37) 0.33773(23) A 2 v 2 16437.151(28) 16543.397(68) 16589.875(35) 0.39349(23) 0.37826(57) 0.38733(33) A v 3 16744.011(36) 16769.99(16) 16868.689(80) 0.32854(36) 0.3321(17) 0.33577(38) 16909.404(68) 0.3853(14) A 4 v 2 16965.398(37) 0.30930(31) 16928.825(42) 16941.05(17) 16966.569(38) 17032.938(44) 17079.729(25) 17331.927(63) 18258.373(29) 0.38016(72) 0.3677(55) 0.3668(11) 0.38927(53) 0.3754(37) 0.3817(11) 0.3812(11) All values given in cm" . Values in parentheses are 3 standard deviations in units of the last significant figure quoted. There are multiple components of the B, v = 0 level as a result of perturbations (see text). 178 Although we did record the A3<J>2 - X 3 A i (0,0) band for both NbCH and NbCD at high resolution, there are no data available for the other spin components of the A 3 ® excited state. In order to perform a rotational and hyperfine analysis similar to the one we did on the ground state we require at least a good estimate of the spin-orbit coupling constant. Since this information is not available we must be satisfied with the effective rotational constant for the 3<I>2 state obtained from the medium resolution spectrum. We can estimate the diagonal magnetic hyperfine parameter, h, for the v = 0 level of the A state by fitting the upper state hyperfine combination differences from the R(l) line of our high resolution spectrum to Equation [5.2.5]; the result gives h = 0.0284(2) cm -1. e) Discussion This work reports the first observation of the niobium methylidyne molecule. At least 28 bands of NbCH and 15 of NbCD have been identified in the visible region. A number of weaker features also appear in this region but the carrier of these bands cannot be conclusively determined to be NbCH or NbCD. High resolution spectra have given the rotational and hyperfine constants for the X 3 A i ground state for both isotopomers and allowed the determination of an ro structure (see Table 5.2.3). Two excited electronic states have been identified, the A 3 0 2 and B 3Ai states, both of which show signs of perturbations. The vibrational levels of the A state commonly show 179 splittings in some of the rotational levels, but the vibrational structure seems unaffected. The vibrational levels of the B state, in addition to showing signs of similar rotational perturbations, appear to be split into several components by interactions with lower-lying dark states. The nature of the perturbing states and the mechanism of the interactions are not fully understood at this time. NbCH appears to have similarities to the isoelectronic molecule NbN and the isovalent VCH. All three molecules have a 3A ground state and a 3<E> excited state at similar energies. A 3 A excited state has been observed in VCH, but the separation between the 3 0 and 3A states is larger than that observed here in NbCH. The bond lengths of NbCH and VCH are also quite similar: the metal-carbon bond in NbCH is about 5% longer than that in VCH (1.779 A and 1.702 A (6)) while the carbon-hydrogen bond lengths are almost identical (1.083 A and 1.080 A (6)). For comparison, the metal-nitrogen bond in NbN is 1.662 A (17). The ground state hyperfine structure in NbCH and NbN is also very similar. As discussed in Section 5.2.C(ii), both molecules show a reversal in the hyperfine structure as a result of spin-uncoupling. The hyperfine constants themselves are similar in magnitude: the diagonal hyperfine constant and Fermi contact parameters for the X 3 Ai component of NbN are h = -0.06157 cm""1 and b = 0.0881 cm"1, while they are found to be h = -0.04404 cm"1 and b = 0.071 cm"1 in NbCH. The similarities arise because the states in both molecules are derived from the same electron configuration, (5sa)1(4d8)1. With an unpaired electron in the (5so~) orbital the Fermi contact interaction will dominate the hyperfine structure. Since this 180 orbital is mainly niobium in character there should be little change in the hyperfine parameters upon changing between ligands with the same number of electrons. 5.3 Rotational and Hyperfine analysis of TaCH a) Background The characterization of tantalum methylidyne, TaCH, is part of the ongoing study of transition metal methylidynes in our laboratory. The vibrational analyses of the ground and excited electronic states of TaCH had been completed prior to my joining the group. As a background, a summary of these unpublished results will be presented here. Twenty-seven bands of TaCH and eighteen bands of TaCD were observed in the visible region. These have been assigned to two electronic transitions: Al( 1IIi)-X0+( 1I+) and B0 +( 3n 0 +)-X0 +( 1Z +). A series of dispersed fluorescence (DF) spectra provided a detailed picture of the vibrational structure of the ground electronic state; the observed levels of TaCH and TaCD are shown schematically in Figure 5.3.1. The dispersed fluorescence spectra also revealed the presence of the al(3Ai) low-lying excited electronic state at 3620 cm"1. The observed levels of the al(3Ai) state are also given in Figure 5.3.1. 181 ( V P V 2> V 3 ) (0,0,5) (0,0,4) (0,1,3) (0,0,3) (0,1,2) (0,0,2) (0,1,1) (0,2,0) (0,0,1) (0,1,0) (0,0,0) X 0 + ( (0,3,1) TaCH ( TaCD ) (0,2,1) (0,0,2) (0,1,1) 4709 (0,2,0) (0,0,1) (0,1,0) 3786 3471 (0,0,0) 2850 (2720) 2537 1905 (1820) 1596 (1402) 1280 (984) 955 (910) 641 (492) 0 (0) 6355 5762 5440 5144 (4969) 4830 (4554) 4546 (4502) 4227 (4087) 3621 (3638) Figure 5.3.1 Observed vibrational levels of the X 0 + and al states of TaCH. The energy, in cm - 1 , is given for each level. The energies of the corresponding TaCD levels are given in parentheses. 182 Many of the bands observed in the excitation spectrum were recorded at a medium resolution of 0.1 cm"1 where much of the rotational structure was resolved. Typical examples of this type of spectrum are shown in Figure 5.3.2. From these spectra, the polarization of the transition and the upper state angular momentum values could be determined, which facilitated the assignment of the excited state vibrational structure. A schematic representation of the observed excited state levels is given in Figure 5.3.3. Tantalum has two stable isotopes with mass numbers 180 and 181. The natural abundance of 1 8 0 Ta is 0.012%, so that it can be ignored. 1 8 1 Ta has I = 7/2. A rotational and hyperfine analysis of TaCH was not performed in the initial study because the intensities of the spectra were very weak using the high resolution techniques available at that time. More recently a pulsed-dye amplifier system became available, allowing us to perform high resolution experiments with significantly higher laser energies. This work will focus on the rotational and hyperfine analysis of the two bands pictured in Figure 5.3.2. b) Experiment These high-resolution LIF experiments were carried out using the methods and apparatus described in detail in Chapter 3. The molecules were produced by reacting laser-ablated tantalum (Goodfellow, Inc.) with a mixture of approximately 8% methane (CH4) or heavy methane (CD4) in helium under supersonic jet-cooled conditions. Approximately five centimeters downstream from the point of ablation the expansion mixture was crossed by the 183 16398.3 cm"1 A 1 Cnj - X 0 + ( ^ (0,0,l)-(0,0,0) Figure 5.3.2 Medium resolution spectra of the A 1 ClTJ - X 0 + (001-000) and B 0 + ( 3 n 0 + ) - X 0 + ( 1E +), (000-000) bands of TaCH. Rotational assignments are given below the tie-lines. P ( = A + E + / ) .2 B, 001 B, 010 A , Oil A , 020 -1 1 :°*o .2 "0" B, 001 B, 010 A , 011,020 .0 1 -o -0 i l 0" B o + ( 3 n w ) , ooo A , 001 B0 + ( 3 IV) , 000 A , 001 A , 010 A , 010 = 0 "2 A i on), ooo A l ( 'n), ooo T a C H T a C D Figure 5.3.3 Vibrational structures o f the excited electronic states of T a C H and TaCD. Angular momentum values ( P ) and vibrational assignments are given where possible. 185 output from a tunable dye laser. The laser system consisted of a three-stage pulsed dye amplifier (Lambda Physik, model FL2003) pumped by a XeCl excimer laser (Lambda Physik, Compex 102) which amplified the output of a tunable ring dye laser (Coherent Inc., model 899-21) pumped by an argon ion laser (Coherent Inc., model Sabre Innova 20TSM). Fluorescence was filtered, recorded and calibrated as described in Section 5.2.A. c) Appearance of the spectra (i) The A l ^ n ^ - X O Y ^ ) , (001-000) band at 16380 cm"1 A medium resolution spectrum of the Al( 1FIi)-X0 +( 1E +), (001-000) band is shown in Figure 5.3.2. At high resolution, the hyperfine structure of the rotational transitions is resolved. At low-J, where the hyperfine width is largest, the observed hyperfine structure is a combination of the magnetic hyperfine structure in the upper state and the electric quadrupole structure of the ground state. The first few lines of the R and Q branches of this band are shown in Figure 5.3.4. The observed patterns can be explained qualitatively by examining the diagonal matrix elements for the magnetic and quadrupole hyperfine interactions. Magnetic hyperfine structure was described in Section 5.2.C(ii) and the matrix element is given by Equation [5.2.2]. It is clear from this equation that there will be a non-186 Figure 5.3.4 Hyperfine structure in the low-J rotational lines of the A l (1n) - X0 + (V), (001-000) band of TaCH. The numbers below the tie lines are the values of F". The labels r, q and p indicate the value of AF. The R and Q lines are plotted to slightly different scales. 187 zero magnetic hyperfine interaction only when the state has a non-zero value of CI. Since the ground state has Q = 0+, only quadrupole hyperfine structure will be present. The diagonal quadrupole matrix element is given by < r\A ; SZ ; JOIF | 7fQ | rjA ; SE ; JQIF > = eQq0 [3Q2 - J(J + 1)]{3R(J)[R(J) +1] - 4J(J +1)1(1 +1)} 3 81(21 -1)J(J +1)(2 J -1)(2J + 3) where R(J) = [ F(F + 1) - 1(1 + 1) - J(J + 1) ]. The characteristic feature of quadrupole structure is that the hyperfine components in a given rotational line reverse upon themselves forming a kind of hyperfine head. Unless the resolution of the experiment is very high, the quadrupole components of a line are usually highly overlapped and are difficult to resolve in the optical region. The J = 0 level of the ground state has only one hyperfine component with F = 7/2. The R(0) line shown in Figure 5.3.4 has only three hyperfine lines, one for each of the three upper state components. As J increases the number of hyperfine transitions rapidly increases to 21, which occurs for the first time at J = 4. The observed hyperfine structure becomes very congested so that only the lowest J lines of each branch have the hyperfine structure completely resolved. For J values higher than 5 the hyperfine structure has collapsed so that only a broad feature with a width of approximately 0.025 cm - 1 and no resolved hyperfine structure is observed. (ii) The B V ^ r i o + h X O Y ^ ) , (OOO-OOO) band at 16398 cm - 1 188 A medium resolution spectrum of the BO+(3ITo+)-XO+(1E+), (000-000) band is shown in Figure 5.3.2. At high resolution the hyperfine structure is resolved. The hyperfine widths of the rotational lines are significantly smaller in this band as compared to the A - X band. The reason is that both states now possess only electric quadrupole structure, which generally produces smaller splittings than magnetic effects. The lowest-J lines of each branch have all of their hyperfine components resolved. The hyperfine components show the typical quadrupole structure in which a "hyperfine head" is formed. For intermediate values of J, where the number of hyperfine components increases, the rotational lines become blended features with three or four intense 'spikes', each of which is composed of a number of overlapping hyperfine components. At higher values of J the rotational lines tend to develop a Lande pattern typical of magnetic hyperfine structure; that is, the hyperfine components seem to follow the structure predicted by Equation [5.2.2]. This is unusual since no magnetic hyperfine effects are expected for Q=0+ states. The B state must be gaining magnetic hyperfine character through interactions with a nearby state. This will be discussed in more detail below. 189 d) Results and Discussion (i) The XOYE 4 ) State To model the ground state rotational and hyperfine structure, combination differences for all of the unblended pairs of lines in the spectra for both isotopomers were fitted to the model E -BJ(J + 1) - DJ*(T + l) 2 - e Q q o3R(J)[R(J) + l]-4J(J + l)I(I + 0 3 V ' V • 4 8I(2I + l)(2J-l)(2J + 3) where R(J) = F(F + 1) - 1(1 + 1) - J(J + l).The results of these fits are given in Table 5.3.1. The rotational constants of the two isotopomers were used to calculate a structure for the molecule by assuming that the C - H bond length does not change upon deuteration. These results are also given in Table 5.3.1. Both the metal-carbon and C - H bond lengths are very similar to those observed in the isovalent NbCH as well as the other transition metal methylidynes observed to date (6-10). This indicates that the bonding in these molecules is quite insensitive to the particular metal involved. The quadrupole coupling constant, eQqo, is unusually large in TaCH. This parameter represents the coupling between the nuclear electric quadrupole moment, Q, and the electric field gradient at the nucleus due to the electrons. The magnitude of eQqo is directly related to the degree of non-spherical charge distribution at the nucleus, giving insight into the orbitals occupied by the valence electrons and, therefore, the bonding in the molecule. Contributions to the magnitude of eQqo are typically attributed to the ionicity of the molecular bond as well 190 Table 5.3.1 Derived constants for the ground state of TaCH and TaCD. TaCH TaCD B 0.393482(9) 0.33524(4) 107D 3.2(3) 2.8(16) eQq0 -0.2436(10) structure ro(Ta-C) 1.7713(2) r0(C-H) 1.080(1) The bond lengths are given in A, all other values given in cm - 1. The values in parentheses are 3 a in the units of the last significant figure quoted. as the degree of hybridization of the valence molecular orbitals. Highly ionic bonds are generally associated with the transfer of an electron from one atom to another where both atoms are left with a filled shell. In this case, the average charge distribution around the nucleus will be spherical and a small quadrupole coupling constant can be expected. Covalent bonds, on the other hand, involve the buildup of electron density between the two atoms. This generally involves the hybridization of the s, p and d atomic orbtals in order to maximize the overlap of the atomic wavefunctions. A larger degree of hybridization will result in a highly asymmetric charge distribution at the nucleus and a larger value of eQqo is expected. In the case of TaCH, the large value of eQqo suggests that the Ta-C bond has little ionic character, which is consistent with a triple bond between these atoms. It also supports our proposed electron configuration of (Ta 6sa)2(Ta 5d7i;CH it)4. The effects of any non-191 spherical charge distribution in TaCH are magnified by the fact that 1 B 1 Ta has a particularly large nuclear electric quadrupole moment of 3 28x 10 - 3 0 m 2. (ii) The Al^FTi) and B0 + ( 3 IV) excited electronic states Both of the upper states studied in this work have rotational perturbations at low values of J. As a result, rigorous fits of the transition energies were not possible. In addition, the B0 + state seems to be picking up magnetic hyperfine character through interactions with an Q > 0 state. Since the two upper state levels studied here are separated by less than 20 cm - 1 , we assumed that the hyperfine perturbations may be due to a mixing of these two states. To test this assumption we chose to determine the relative contributions of the quadrupole and magnetic hyperfine interactions as a function of J in each upper state. For the B0 + state the quadrupole contribution would be given by the last term of Equation [5.3.2]. In the A l state, the diagonal quadrupole contribution can be determined from Equation [5.3.1]. There is also a parity dependent contribution to the quadrupole structure given by < riA±2 ; SZ ; JQ+2 IF | KQ | -nA ; S I ; JQIF > = eQq2 V[J(J +1) - ± 1)] P(J +1) - (n ± 1)(Q ± 2)] v 3R(J)[R(J) +1] - 4J(J +1)1(1 + 1) 161(21 - 1)J(J +1)(2J -1)(2J + 3) 192 For both states, the contribution due to magnetic hyperfine effects can be modeled to Equation [5.2.2]. The final model used was simplified to the form Thf(J) = T r o t + Q(J) Y(J) + M(J) [5.3.4] In this equation T r ot is the rotational term energy, the coefficients Q(J) and M(J) represent the J-dependent contributions due to the quadrupole and magnetic hyperfine interactions, respectively; the function Y(J) is given by = 3R(J)[R(J) + 1]-4J(J +1)1(1 + 1) 81(21 -1)J(J +1)(2 J -1)(2 J + 3) and R(J) is defined above. The hyperfine transitions for each individual rotational line observed in the two high resolution spectra were fitted to the model of Equation [5.3.4]. The rotational lines involving the f-parity component of the A l state collapsed rapidly with J until no resolved hyperfine structure was observed. For these lines, the Q(J) and M(J) coefficients could not be evaluated. These lines were sufficiently narrow that the rotational energy for the upper state f-levels could be estimated; an uncertainty equal to the FWHM of the blended line was assigned to each of these rotational energy measurements. Figure 5.3.5 shows the reduced rotational energy plots for both the A l and B0+ states. In these plots the rotational energies were taken from the results of the fits described above. The J-dependence was removed by subtracting off the quantity BJ(J +1), where B was estimated from the first few unperturbed levels of each state. In the A l state there is an avoided crossing at J = 6. The perturbing state is clearly a degenerate state with a rotational 193 a UH O a m CD o 0.4 - a) A l I I i * I f parity 0.2 -I • 0.0 --0.2 -• • • A A • e parity -0.4 -0 20 40 60 80 100 120 140 160 J(J+ 1) 180 200 Figure 5.3.5 Reduced rotational energy plots for the a) A l and b) B0 + states of TaCH. The quantities a) 16376.1655 + (0.3543)7(7+ 1) andb) 16391.8558+ (.3725) 7(7+ 1) were subtracted from the rotational energy level positions. 194 constant that is larger than that of the A state. In the B 0 + state the perturbations seem to be more random where individual rotational levels are shifted out of position. No obvious conclusions can be drawn about the perturbing state or states. To determine the extent of the magnetic hyperfine mixing between the A l and B 0 + states the coefficients M(J) were plotted as a function of J(J+1) in Figure 5.3.6. Since S = 0 in both states, the coefficient M(J) represents the effective value of ' aAQ' as a function of J(J+1). There is an equal but opposite change of the magnetic hyperfine contribution in the two states. Clearly the A l state is donating magnetic hyperfine character to the B 0 + state. This effect can be explained by examining the matrix elements of the magnetic hyperfine Hamiltonian that are off-diagonal in Q. Let us take the hyperfine Hamiltonian for this interaction as # M H F = aI-L+-b F I-S [5.3.6] and evaluate the matrix elements in a case (cp) basis. The dipolar term has been omitted from Equation [5.3.6] to keep the initial model as simple as possible. We can use Equation [2.39] to write the matrix element for the Fermi contact term of Equation [5.3.6] as < (LS)'J a '0';J'Q' IF | b F T^I) • T^S) I (LS)J aO;JOIF > = ( - 1 ) J + I + F | ^ j jj < III T\l) || I >< (LS)'Ja'Q';J'a' || T'fS) || (LS)J aQ;JO > [5.3.7] where < I || T\T) || I > = ^1(1 + 1)(2I +1) from Equation [2.29]. Equation [2.44] can then be used to project the reduced matrix element of T*(S) into molecule-fixed axes, giving 195 o o O »n o o o m o o CN in in o o o o o 1—I © i-H © o CN o Cd H «4H O .2 3 o cd 1-<S CD -*-» CD GO •B ^ cd , — . , -4-> ^—i 1 / 1 2 o CD O cd cd cd ^ a < _cd t+i O CD cd > CD CD a CD CD c cd o to oo CD £ o o X ! 4-* C+H o VO cd 1 0 + o T _ U I 0 / .UVB, 3 A T P 3 J J H 196 < (LS)'Ja'0';J'0' || T^S) II (LS)J aO;JO > = D < J ' Q ' || ® . ( q i r || J O >< (LS)'Ja'O' | T ^ S ) I (LS)JaQ >. [5.3.8] In this equation, the reduced matrix element of <D^*is given by Equation [2.35], while the Wigner-Eckart theorem can be used on the matrix element of T q ( S ) . Equation [5.3.8] can be recast in the form < (LS)'J a 'Q';J'Q' II T ! ( S ) || (LS)J aQ;JQ > = X(-1)J'"QV(2J + 1)(2J' + 1) f v J 1 J Q' q £1 (-l)Ja_Q K 1 Ja V O' q O x(-l)L+S+j;+1V(2Ja+l)(2j;+l)JS' J§a ^kS 'HT^ I IS ) , [5.3.9] where Equation [2.41] was used. We do not know S' and S with total confidence in the A l and B 0 + states of TaCH, so we cannot simplify the reduced matrix element of T^S) any further. The expression for the Fermi contact matrix element in a case (cp) basis becomes < (LS)'Ja'0';J'0' IF | b F T^I) • T^S) | (LS)J aO;JOIF > ( _ 1 ) J + I + F | F i r , + 1 ) ( 2 I + 1 } ^ ( _ 1 } , _ Q - ^ ( 2 J + 1 ) ( 2 J , + 1 } , ^ i j , [ 5 3 1 0 ] j ' I J ( - i ) ] ' - Q ' J a 1 Ja O' q n i ( 1 ) L + s + j k + i ^ ( 2 J a + 1 ) ( 2 J , + 1 ) i s ' i: L l < S ' | | T i ( s ) n s > The matrix element for the nuclear spin-electron orbit interaction can be derived in the same way as the Fermi contact matrix element. Combining the two results we obtain the matrix element for the magnetic hyperfine Hamiltonian of Equation [5.3.6]: 197 < (LS)'Ja'D';J'0' I F l a l - L + bpI-Sl (LS)JaO;JQIF > ( _ 1 ) J + I + F | F I f ^ l ( l + 1 ) ( 2 I + 1 } £ ^ ( 2 J +1)(2J' +1) f r 1 n Cl' q Cly (-1) / T ' . 1 J a -Cl' q Cl V(2Ja+l)(2J'a+l) (1) L+S+J;+I S' J'a L J, S 1 <S'||T 1(S)||S>b F+(l)L' + s + J a + 1|^' £ ^ k L ' H T ^ I I D a [5.3.11] The last two lines of Equation [5.3.11] depend on the electron configuration and can be absorbed into a configuration-dependent parameter. Since the hyperfine mixing observed in TaCH appears to be diagonal in J, we can substitute for the 3-j and 6-j symbols (20) on the first line of Equation [5.3.11]. After simplification, we obtain the desired result < (LS)'Ja' Q+1;J Q+l IF | a I • L + bF I • S | (LS)JaQ;JfiIF > = -JLx R ( J ) xJj(J + l )-Q(Q + l) V2 2J(J + 1) V [5.3.12] where p is the configuration-dependent parameter mentioned above. From this equation we can see that the coefficient of 'R(J) / 2J(J+1)' is proportional to ^ ( J + ^ - ^ O + l ) , so that the energy correction resulting from this hyperfine mixing will be proportional to J(J+1). This seems to describe the observed behavior of Figure 5.3.6 quite well. TaCH appears to be a beautiful example of two states being coupled through the magnetic hyperfine interaction; a mechanism that is not often encountered. In future work we hope to fit the hyperfine level positions of the A l and B0+ states using the above model. 198 Since the first few J levels of the A l state are unperturbed, they were used to estimate the rotational and hyperfine constants. The observed hyperfine transitions for J' = 1 to 4 were fitted to a rotational energy model including the diagonal and parity-dependent quadrupole interactions given by Equations [5.3.1] and [5.3.3], and the magnetic hyperfine interaction given by Equation [5.2.2]. The results of this fit are given in Table 5.3.2. For the B0+ state, the effects of the magnetic hyperfine contamination prevented us from estimating the quadrupole constant of this state from even the lowest J levels. The term energy and rotational constant were estimated by fitting the rotational energies, taken from the modeling to Equation [5.3.4], to E = T v + BJ(J + 1). These results are also given in Table 5.3.2. Table 5.3.2 Derived constants for the upper states of TaCH. Ai( xni), ooi Bo+(3n0 +), ooo T v 16376.1655(6) 16391.8558(1) B 0.3543(7) 0.37250(5) 103 q -2.3(3) eQqo -0.148(12) eQq2 -0.100(12) a 0.0499(4) All values given in cm . The values in parentheses are 3o in the units of the last significant figure quoted. The magnitude of eQqo in the A l state has dropped by forty percent compared to the ground state. This suggests that the electronic transition has promoted one electron into an orbital that is more spherically symmetric around the Ta nucleus. This is consistent with the 199 upper state electron configuration being (Ta 6sa)2(Ta 5d7t;CH 7t)3(Ta 5dS)\ The 5 orbital is essentially completely Ta in character and would have a more spherical distribution around the Ta nucleus than the 7t-type bonding orbital. This electron configuration should also give rise to the B 0 + state. Bibliography 200 References for Chapter 2 1. M. Born and JR. Oppenheimer, Ann. Physik. 84, 457 (1927). 2. AR. Edmonds, "Angular Momentum in Quantum Mechanics", Princeton University Press, Princeton, 1974. 3. R.N. Zare, "Angular Momentum", Wiley-Interscience, New York, 1988. 4. G. Racah, Phys. Rev. 62, 431 (1942). 5. Ch. Jungen and A.J. Merer, Mol. Phys. 40, 1 (1980). 6. H.C. Longuet-Higgins. Adv. Spectrosc. 2, 429 (1961). 7. E B . Wilson, Jr., J.C. Decius, and PC. Cross. "Molecular Vibrations." Dover, New York (1980). 8. L. Pauling and E.B. Wilson, "Introduction to Quantum Mechanics". McGraw-Hill, New York, 1935. 9. P.A.M. Dirac, "The Principles of Quantum Mechanics", 4th ed. Clarendon Press, Oxford 1958. 10. L. Eyges, "The Classical Electromagnetic Field', Addison-Wesley, London, 1972. 11. L H . Thomas,Nature 107, 514 (1926). 12. J.H. Van Vleck, Rev. Mod. Phys. 23, 213 (1951). 13. RS. Henderson, Phys. Rev. 100, 723 (1955). 14. R.A. Frosch and H.M. Foley, Phys. Rev. 88, 1337 (1952). 15. G.C. Dousmanis, Phys. Rev. 97, 967 (1955). 201 16. E.U. Condon and G.H. Shortley, "Theory of Atomic Spectra", Cambridge University Press, Cambridge (1970). 17. N.F. Ramsey, "Nuclear Moments", Wiley-Interscience, New York (1955). 18. P.A. Tipler, "Modern Physics", Worth Publishers Inc., New York (1978). 19. F. Hund, Z. Phys. 42, 93 (1927); 63, 719 (1930); Handb. D. Phys. 24,1, 561 (1933). 20. J.M. Brown andBJ. Howard, Molec. Phys. 31, 1517 (1976). 21. R.S. Mulliken, Rev. Mod. Phys. 2, 60 (1930). 22. A. Carrington, P.N. Dyer, and D H . Levy, J. Chem. Phys. 47, 1756 (1967). 23. H.P. Benz, A. Bauder and Hs.H. Gunthard, J. Mol. Spectrosc. 21, 156 (1966). 24. H. Lefebvre-Brion and R.W. Field, "Perturbations in the Spectra of Diatomic Molecules", Academic Press, New York (1986). 25. M. Larsson, Physica Scripta 23, 835 (1981). 26. J.M. Brown, J.T. Hougen, K.-P. Huber, J.W.C. Johns, J. Kopp, H. Lefebvre-Brion, AJ. Merer, D A . Ramsay, J. Rostas, and R.N. Zare, J. Mol. Spectrosc. 55, 500 (1975). 27. T.A. Miller, Mol. Phys. 16, 105 (1969). 28. J.M. Brown and A.J. Merer, J. Mol. Spectrosc. 74, 488 (1979). References for Chapter 3 1. L M . Ziurys, AJ . Apponi, T G . Phillips, Astrophys. J. 433, 729 (1994). 2. M. Guelin, J. Cernicharo, C. Kahane, J. Gomez-Gonzalez, Astron. Astrophys. 157, L17 (1986). 202 3. K. Kawaguchi, E. Kagi, T. Hirano, S. Takano, S. Saito, Astrophys. J. 406, L39 (1993). 4. B E . Turner, T.C. Steimle, L. Meerts, Astrophys. J. 426, L97 (1994). 5. Z.K. Ismail, R H . Hauge, and J.L. Margrave, J. Chem. Phys. 57, 5137 (1972). 6. JJ. van Vaals, W.L. Meerts, and A. Dymanus, Chem. Phys. 82, 385 (1983). 7. E. Clementi, H. Kistenmacher, and H. Popkie, J. Chem. Phys. 58, 2460 (1973). 8. A.I. Boldyrev, et al. Russ. J. Inorg. Chem. 24, 341 (1979). 9. L T . Redmon, G.D. Purvis III, and R.J. Bartlett, J. Chem. Phys. 72, 986 (1980). 10. R. Essers, J. Tennyson, and P.E.S. Wormer, Chem. Phys. Lett. 89, 223 (1982). 11. L. Adamowicz and C.I. Frum, Chem. Phys. Lett. 157, 496 (1989). 12. A. Dorigo, P V R . Schleyer, and P. Hobza, J. Comput. Phys. 15, 322 (1994). 13. M.L. Klein, J.D. Goddard, and D.G. Bounds, J. Chem. Phys. 75, 3909 (1981). 14. C.J. Marsden, J. Chem. Phys. 76, 6451 (1982). 15. J.J. van Vaals, W.L. Meerts, and A. Dymanus, J. Chem. Phys. 11, 5245 (1982). 16. J.J. van Vaals, W.L. Meerts, and A. Dymanus, Chem. Phys. 86, 147 (1984). 17. P.E.S. Wormer and J. Tennyson, J. Chem. Phys. 75, 1245 (1981). 18. P. Kuijpers, T. Torring, and A. Dymanus, Chem. Phys. Lett. 42, 423 (1976). 19. T. Torring, et al., J. Chem. Phys. 73, 4875 (1980). 20. J.J. van Vaals, W.L. Meerts, and A. Dymanus, J. Mol. Spectrosc. 106, 280 (1984). 21. E. vanLeuken, G. Brocks, and P.E.S. Wormer, Chem. Phys. 110, 365 (1986). 22. C.W. Bauschlicher, Jr., S.R. Langhoff, and H. Partridge, Chem. Phys. Lett. 115, 124 (1985). 203 23. K. Ishi, T. Hirano, U. Nagashima, B. Weis, K. Yamashita, Astrophys. J. 410, L43 (1993) . 24. CJ. Whitham, B. Soep, J.-P. Visticot, and K. Keller, J. Chem. Phys. 93, 991 (1980). 25. M. Douay and P.F. Bernath, Chem. Phys. Lett. 174, 230 (1990) 26. T.C. Steimle, D.A. Fletcher, K.Y. Jung, and CT. Scurlock, J. Chem. Phys. 97, 2909 (1992). 27. C T . Scurlock, T.C. Steimle, T D . Suenram, and F.J. Lovas, J. Chem. Phys. 100, 3497 (1994) . 28. B. Ma, Y. Yamaguchi, andH.F. Schaefer III, Mol. Phys. 86, 1331 (1995). 29. S. Petrie, Mon. Not. R. Astron. Soc. 282, 807 (1996). 30. S. Petrie, J. Phys. Chem. 100, 11581 (1996). 31. D V . Lanzisera and L. Andrews, J. Phys. Chem. A 101, 9660 (1997). 32. M. Fukushima, Chem. Phys. Lett. 283, 337 (1998). 33. J.S. Robinson, A.J. Apponi, and L M . Ziurys, Chem. Phys. Lett. 278, 1 (1997). 34. K.A. Walker and M.C.L. Gerry, Chem. Phys. Lett. 278, 9 (1997), ibid. 301, 200 (1999). 35. I. Gerasimov, X. Yang, and P.J. Dagdigian, J. Chem. Phys. 110, 220 (1999). 36. K.A. Gingerich, Naturwissenschaften 24, 646 (1967). 37. G. Meloni and K.A. Gingerich, J. Chem. Phys. 111, 969 (1999). 38. S A Klopcic, V.D. Moravec, and C C Jarrold, J. Chem. Phys. 110, 8986 (1999). 39. V.D. Moravec and C C Jarrold, J. Chem. Phys. 113, 1035 (2000). 40. A.I. Boldyrev, X. Li, and L.-S. Wang, J. Chem. Phys. 112, 3627 (2000). 41. J. Lie, and P.J. Dagdigian, J. Chem. Phys. 114, 2137 (2001). 204 42. C.W. Bauschlicher, Jr., Surf. Sci. 154, 70 (1985). 43. X.-Y. Zhou, D.-H. Shi, and P.-L. Cao, Surf. Sci. 223, 393 (1989). 44. M. Barnes, M.M. Fraser, P.G. Hajigeorgiou, A.J. Merer and S.D. Rosner, J. Molec. Spectrosc. 170, 449 (1995). 45. B A . Palmer, RA. Keller, and R. Engleman, Jr., "An Atlas of Uranium Emission Intensities in a Hollow Cathode Discharge," Unpublished Report LA-8251-MS, Los Alamos Scientific Laboratory, 1980. 46. A.G. Adam, A.J. Merer, D.M. Stuenenberg, M.C.L. Gerry, and I. Ozier, Rev. Sci. Instrum. 60, 1003 (1989). 47. A. Chedin, J. Molec. Spectrosc. 76, 430 (1979). 48. T.E. Sharp and H M . Rosenstock, J. Chem. Phys. 41, 3453 (1964). 49. W.L. Smith, Proc. Phys. Soc. 89, 1021 (1966). 50. C. Dufour, I. Hikmet, and B. Pinchemel, J. Molec. Spectrosc. 165, 398 (1994). 51. A. Bouddou, C. Dufour, and B. Pinchemel, J. Molec. Spectrosc. 168, 477 (1994) 52. C. Dufour, and B. Pinchemel, J. Molec. Spectrosc. 173, 70 (1995). 53. T. Hirao, C. Dufour, B. Pinchemel, and P.F. Bernath, J. Molec. Spectrosc. 202, 53 (2000) 54. A. Poclet, Y. Krouti, T. Hirao, B. Pinchemel, and P.F. Bernath, J. Molec. Spectrosc. 204, 125 (2000). 55. Y. Krouti, A. Poclett, T. Hirao, B. Pinchemel, and P.F. Bernath, 56th Ohio State University International Symposium on Molecular Spectroscopy, presentation FC02 (2001). 205 56. S.A. Kadavathu, R.Scullman, J.A. Gray, M. Li, and R.W. Field, J. Molec. Spectrosc. 140, 126 (1990). 57. J.A. Gray, M. Li, T. Nelis, and R.W. Field, J. Chem. Phys. 95, 7164 (1991). 58. C.E. Moore, Atomic Energy Levels, Volume II, Circular of the National Bureau of Standards 467(1952). 59. G. Herzberg, Molecular Spectra and Molecular Structure. I. Spectra of Diatomic Molecules, 2nd ed. (Van Nostrand, Princeton, 1950). 60. H. Lefebvre-Brion and R.W. Field, Perturbations in the Spectra of Diatomic Molecules (Academic, New York, 1986). 61. S.A. Kadavathu, R.Scullman, J.A. Gray, M. Li, and R.W. Field, J. Molec. Spectrosc. 147, 448 (1991). 62. A.G. Adam, K. Athanassenas, DA. Gillett, C T . Kingston, A.J. Merer, J.R.D. Peers and S.J. Rixon, J. Molec. Spectrosc. 196, 45 (1999). 63. R. Renner, Z. Phys. 92, 172 (1934). 64. Ch. Jungen and A.J. Merer, Mol. Phys. 40, 1 (1980) 65. G. Herzberg, Molecular Spectra and Molecular Structure. III. Electronic Spectra and Electronic Structure of Polyatomic Molecules, 2nd ed. (Van Nostrand, Princeton, 1966). References for Chapter 4 1. V.R. Rao, Indian J. Phys. 24, 35-49 (1950). 2. V.R. Rao and D. Premaswarup, Indian J. Phys. 27, 399-405 (1953). 206 3. K.S. Rao, Nature (London), 170, 670 (1952); 173, 1240 (1954). 4. U. Uhler, Ark.. Fys. 8, 265-279 (1954). 5. J.M. Brom, C H . Durham and W. Weltner, J. Chem. Phys. 61, 970-981 (1974). 6. JL. Femenias, G. Cheval, A.J. Merer and U. Sassenberg, J. Mol. Spectrosc. 124, 348-368 (1987). 7. G. Cheval, JL. Femenias, AJ. Merer and U. Sassenberg, J. Mol. Spectrosc. 131, 113- 126(1988). 8. A G . Adam, Y. Azuma, J.A. Barry, A.J. Merer, U. Sassenberg, J. O. Schroder, G. Cheval and J.L. Femenias, J. Chem. Phys. 100, 6240-6262 (1994). 9. M. Vala, R.D. Brittain and D. Powell, Chem. Phys. 93, 147-155 (1985). 10. O. Launila, B. Schimmelpfennig, H. Fagerli, O. Gropen, A G . Taklif and U. Wahlgren, J. Mol. Spectrosc. 186, 131-143 (1997). 11. D .N. Davis and P.C. Keenan, Pub. Astron. Soc. Pacific, 81, 230-237 (1969). 12. A.J. Sauval, Astron. Astrophys. 62, 295-298 (1978). 13. B.A. Palmer, R. A. Keller, and R. Engleman, Jr., "An Atlas of Uranium Emission Intensities in a Hollow Cathode Discharge," Unpublished Report LA-8251-MS, Los Alamos Scientific Laboratory, 1980. 14. A.G. Adam, A.J. Merer, D M . Steunenberg, M.C.L. Gerry and I. Ozier, Rev. Sci. Instrum. 60, 1003-1007 (1989). 15. R.D. Suenram, G T . Fraser, F.J. Lovas and C.W. Gillies, J. Mol. Spectrosc. 148, 114- 122(1991). 207 16. M.S. Sorem and A.L. Schawlow, Opt. Commun. 5, 148-151 (1972). 17. AJ. Merer, U. Sassenberg, J.L. Femenias and G. Cheval, J. Chem. Phys. 86, 1219-1224 (1987). 18. RA. Frosch and H M . Foley, Phys.Rev. 88, 1337-1349 (1952). References for Chapter 5 1. J.C. Weisshaar, Acc. Chem. Res. 26, 213 (1993). 2. W.A. Nugent and J.M. Mayer, "Metal Ligand Multiple Bonds," Wiley-Interscience, New York 1998. 3. E O . Fischer, G. Kreis, C.G. Kreiter, J. Miiller, G. Hutner and H. Lorenz, Angew. Chem. 85, 618 (1912); Angew. Chem. Int. Ed. Engl. 12, 564 (1973). 4. J. Manna, S.J. Geib, and M D . Hopkins, Angew. Chem. Int. Ed. Engl. 32, 858 (1993). 5. J. Manna, R.J. Kuk, RF. Dallinger and M D . Hopkins, J. Am. Chem. Soc. 116, 9793 (1994). 6. M. Barnes, P.G. Hajigeorgiou, R. Kasrai, A.J. Merer, and G.F. Metha, J. Am. Chem. Soc. 117, 2096 (1995). 7. M. Barnes, D A . Gillett, AJ. Merer and G.F. Metha, Chem. Phys. 105, 6168 (1996). 8. M. Barnes, A.J. Merer and G.F. Metha, J. Mol. Spectrosc. 181, 168 (1997). 9. M. Barnes, A.J. Merer and G.F. Metha, unpublished results. 10. A.J. Merer, J.R.D. Peers and S.J. Rixon, 53rd Ohio State University International Symposium on Molecular Spectroscopy, 1998, presentation TG03. 208 11. B.A. Palmer, R.A. Keller, and R. Engleman, Jr., "An Atlas of Uranium Emission Intensities in a Hollow Cathode Discharge," Unpublished Report LA-8251-MS, Los Alamos Scientific Laboratory, 1980. 12. A G . Adam, A.J. Merer, D.M. Stuenenberg, M.C.L. Gerry, and I. Ozier,Rev. Sci. Instrum. 60, 1003 (1989). 13. B. Simard, P.I. Presunka, H.P. Loock, A. Berces, and O. Launila, J. Chem. Phys. 107, 307 (1997). 14. A G . Adam, Y. Azuma, J.A. Barry, A.J. Merer, U. Sassenberg, J.O. Schroder, G. Cheval, and J.L. Femenias, J. Chem. Phys. 100, 6240 (1994). 15. C T . Kingston, C.-K.D. Liao, A.J. Merer, and S.J. Tang, J. Mol. Spectrosc. 207, 104 (2001). 16. Y. Azuma, G. Huang, M.P.J. Lyne, A.J. Merer, and V.I. Srdanov, J. Chem. Phys. 100, 4138 (1994). 17. Y. Azuma, J.A. Barry, M.P.J. Lyne, A.J. Merer, and J.O. Schroder, and J.L. Femenias, J. Chem. Phys. 91, 1 (1989). 18. R.A. Frosch and H.M. Foley, Phys. Rev. 86, 1337 (1952). 19. G. Herzberg, "Spectra of Diatomic Molecules," Van Nostrand, Princeton (1950). 20. R.N. Zare, "Angular Momentum," Wiley-Interscience, New York (1988). Appendix 1 2 0 9 Rotational Line Frequencies for the Bands of NiCN The lines are sorted into tables by band, branch, J and nickel isotope. The following symbols are used in this appendix: * a blended or otherwise poor quality line p a perturbed line (also indicated by multiple measurements for a given J) e/f indicates the upper state parity 210 Table 1 Table of assigned lines of the N i C N A-X, 222, 1=2 band ' N i C N 6 U N i C N R Q P J - % R Q P 4 16465.4363* 63.9985 . 4 16465.6979* 64.2721* 5 65.5314* 63.8305 62.3927 5 65.7897* 64.1069 62.6845 6 65.5926* 63.6319 61.9333 6 65.8526* 63.9099* 62.2277 7 65.6235* 63.4021 61.4428 7 65.8834* 63.6826 61.7415 8 65.6235* 63.1407* 60.9220 8 65.8834* 63.4254 61.2252 9 65.5926* 62.8520* 60.3695 9 65.8526* 63.1475* 60.6786 10 65.5314* 62.5312 59.7885 10 65.7953* 62.8195 60.1028 11 65.4439* 62.1785 59.1752 11 65.7054* 65.4713 59.4964 12 65.3235 61.7957 58.5312 12 65.5926* 62.0931 58.8580* 13 65.1726 61.3838 57.8566 13 65.4439* 61.6848 58.1909 14 64.9780p 60.9409 57.1533 14 65.2569 61.2436 57.4952* .9846p 15 65.0462 60.7759 56.7649 .9960p 16 64.7943p 56.0077 15 64.7784 60.4717 56.4180 .0862p 16 64.5351 59.9642 55.6408p 17 64.5351* 55.2202 .6576p 18 64.2348 54.4048p 17 64.2615* 59.4278 54.8564 19 63.9034* 53.5505 18 58.8580* 54.0331 20 63.5451 52.6756 19 63.6216 53.1747 21 51.7640 20 63.2588 22 62.7324* 21 51.3708* ' 22 62.4480* 23 61.9875 Table 2 Table of assigned lines of the N i C N A-Xi 2\, P=l 12-112 band 5 8 N i C N 6 0 N i C N J-Vz R Q P J-V2 R Q P 3 16536.4377* 35.2683 3 16535.5017 4 36.5598 35.1327 33.9606 4 35.3684 5 36.6510 34.9637 33.5360 5 36.8454 35.1933 33.6713* 6 36.7092* 34.7658 33.0773 6 36.8966 33.2157* 7 36.7391* 34.5327 32.5878 7 36.9308* 32.7254* 8 36.7391* 34.2721 32.0658 8 36.9308* 32.2048* 9 36.7092* 33.9811 31.5149 9 36.8871 31.6531* 10 36.6452 33.6595 30.9319 10 36.8363 31.0639p 11 36.5487 33.3049 30.3203 .0720p 12 36.4300p 32.9202 29.6782 .1383p .4377p .1599p 13 36.2135p 29.0007 11 30.4579p 211 'NiCN NiCN Table 2 Continued J-V2 R Q P J-Vz R Q P 13 16536.2370p 16530.5285p .2909p .5597p .3037p 12 29.8147p 14 36.0530p 28.3015p .9354p .063 9p .0397p 13 36.4081 29.1415 15 35.8530 27.5057p 14 36.2370*p 28.4372 .5244p 15 36.0326p 27.7019 .5833p 16 35.7875*p 27.0362p .5938p 26.9378p 16 35.6087 26.7656p 17 35.5127p 26.1420p .7745p .2577p 17 35.3311 25.9838 18 35.2064p 25.3149p 18 35.0220 25.1590 .4366p 19 34.6849 24.3015 19 35.2064p 24.4565p 20 34.3137 23.4124 .5877p 21 33.9134 22.4941 20 34.5018*p 23.5727p 22 33.4831 21.5432 .7083p 23 33.0242 20.5625 21 34.1047p 22.6531p 24 32.5227p 19.5528 .6632p .5323p .7959p 25 32.0053 18.5140 22 33.6713*p 21.7081p 26 31.4580 17.4355p .8553p .4436p 23 33.2157* 20.7308p 27 30.8682p 16.3341 .8800p .8780p 24 32.7254* 19.7238p 28 30.2605 15.2071 .8775p 29 29.6177 14.0368p 25 32.2048* 18.8438 .0478p 26 31.6531* 17.7781 30 28.9481 12.8507 27 16.6832 31 28.2481 11.6289 28 15.5571 32 27.5057 10.3770 29 14.4005 33 09.1010 30 13.2130 34 07.7966 31 11.9966 35 06.4616 36 05.1204 Table 3 Table of assigned lines of the NiCN A-Xi 2\, P=3/2-3/2 band 5 8 NiCN 6 0 NiCN J - % R Q P J-V2 R Q P 1 16544.4123 43.7660 1 16543.9734 2 44.5948 43.6873 43.0404 2 43.8958 43.2604 3 44.7412 43.5780 42.6714 3 43.7867 42.8897 4 44.8588 43.4340 42.2721 4 45.0567 43.6468 42.4929 212 'NiCN ""NiCN Table 3 Continued J - Vi R Q P J - Vi R Q P 5 16544.9435 43.2604 41.8379 5 16545.1416 43.4747 42.0647 6 44.9977 43.0574* 41.3745 6 45.1951 43.2721* 7 45.0206 42.8224 40.8797 7 45.2174 8 45.0135 42.5531 40.3538 8 45.2101 42.7732 9 44.9718 42.2447* 39.7962 9 45.1694 42.4611* 40.0416 10 44.8995 41.9235 39.2074 10 45.0984 42.1509 39.4583 11 44.7957 41.5624 38.5846 11 44.9977* 41.7968 38.8430 12 44.6611 41.1669 37.9332 12 44.8588* 41.3988 38.1975 13 44.4955 40.7420 37.2483 13 44.6986 40.9797 37.5211 14 44.2970 36.5342 14 44.4955* 36.8117 15 44.0706 35.7875 15 44.2777 36.0723* 16 43.8078 35.0085 16 44.0201 35.3044 17 43.5090* 34.2027 17 43.7316 34.5018* 18 e 43.1906 33.3590 18 43.4118 33.6713* f .1961 19 43.0574 32.8080 19 e 42.8355 32.4787 20 42.6847 31.9131 f .8439 .4916 21 42.2447 31.0697 20 e 42.4511 31.5809 22 41.8168 30.0370 f .4611 .5892 23 e 41.3424 29.0396 21 e 42.0342 30.6470 f .3571 .0504 f .0433 .6552 24 e 40.8368 28.0212 22 e 41.5879 29.6922 f .8519 .0340 f .6052 25 e 40.2993 26.9708 23 e 41.1045 28.6843 f .3167 .9859 f .1192 .6940 26 e 40.7329 25.8924 24 e 40.5945 27.6624 f .7520 .9068 f .6099 .6747 27 e 39.1333 24.7818 25 e 40.0416 26.5950 f .1544 .7983 f .0661 .6145 28 e 38.5029 23.6375 26 e 39.4744 25.5003 f .5265 .6580 f .5009 .5212 29 e 37.8437 22.4668 27 e 38.8742 24.3806 f .8699 .4934* f .8975 .3979 30 e 37.1537 21.2636 28 e 38.2438 23.2266 f .1790 .2870 f .2629 .2542 31 e 20.0284 29 e 37.5730 22.0461 f .0551 f .5993 .0702 32 e 18.7643 30 e 36.8744* 20.8363 f .7922 f .9041* .8540 33 e 34.8956 17.4684 31 e 36.1277 19.5880 f .9289 .4955 f .1564 .6128 34 e 34.0837 16.1445 32 e 35.3559* 18.2993 f .1203 .1761 f 18.3355 35 e 33.2386 14.7868 33 e 34.5808 16.9850 f .2771 .8228 f .6190 17.0103 36 e 32.3307 13.3999 34 e 33.7613 15.6460* f .3517 .4371 f .8007 37 e 33.9966* 213 NiCN ""NiCN Table 3 Continued J-V2 R Q P J-V2 R Q P 35 e 16532.9202* 14.2798 38 e 16510.5342 f .9525 .3160 f .5830 36 e 32.0255 12.8802 39 e 09.0554 f .0658* .9200 40 e 07.5492 37 e 31.1133 11.4498 f 07.5991 f .1599* .4908 41 e 05.9395 38 e 30.1657 09.9865 f 06.0049 f .2202 10.0324 39 e 29.1913 08.4926 f .2452 .5406 40 e 28.1833 06.9687 f 07.0216 41 e 27.1462 05.4131 f .2057 .4709 Table 4 Table of assigned lines of the NiCN A - X i (0,0) band 5 8 NiCN 6 0 NiCN JM/z R Q P J-Vz R Q P 2 16608.0147 7.1126 2 16608.1377p 7.2419 3 8.1536p 7.0023 6.1017 .1437p .1640p 3 8.2844* 7.1363p 6.2414 .1799p .1427p 4 8.2844 6.8538p 5.7009* 4 8.3948 6.9783* 5.8476*p .8650p 5 8.4895 5.4269 .8802p 6 8.5438p 6.6296* 4.9699p 5 8.3680 6.6943 5.2657p 5491p .9779p ' .2758p 7 8.5685* 6.3988p 4.4834 .2914p .4040p 6 8.4243 6.4905 4.8174 8 8.5685* 6.1366 3.9664p 7 8.4498 6.2578 4.3244 .9720 8 8.4425 5.9947 3.8028 9 8.5278 5.8476* 3.4192 9 8.4075 5.7009* 3.2506 10 8.4620 2.8423 10 8.3357 5.3748 2.6660 11 8.3495*p 2.2337 11 8.2361 5.0138 2.0529 .3609p 12 8.0889p 4.6248* 1.4032 12 8.2361* 1.5956 .0987p 13 8.0644p 600.9217p .1045p .072 lp .9287p .1107p 14 7.8815 600.2224 13 7.9336p 4.1988p 600.7258 15 7.6593 599.4822p .9427p .2024p 15 99.4894p .2055p 16 7.4074 98.7281 .2130p 17 7.1264 97.9325 14 7.7465p 3.7457p 600.0032p 18 6.8121 97.1094 .7537p .7538p .0117p 19 6.4688 96.2569 214 58 'NiCN 60 NiCN Table 4 Continued J-Vz R Q P J-Vz R Q P 14 16600.0176p 20 16606.0794 16595.3690 .0235p 21 5.2371 94.4534 15 16607.5254 3.2698p 599.2684p 22 93.5074 .2774p .2782p 23 92.5374 16 7.2707 2.7600 98.5040p 16 98.5113p 17 6.9588p 2.2170 97.7057 .9702p .9942p 7.0023p 18 6.6607 96.8734 19 6.3140p 95.9844p .3186p .9958p 96.0198p .0283p 20 5.9341 95.1093 21 5.5260 94.1849p .1902p 22 5.0867 93.2279 23 4.6248* 92.2423 24 4.0888 91.2271 25 3.5615p 90.1847 .5719p 26 2.9999p 3.0067p 27 2.3995p .4104p 28 1.7872 29 1.1318 30 600.4227 31 599.7167p .7248p 32 98.9695 Table 5 Table of assigned lines of the NiCN B - X i (0,0) band 5 8 NiCN 6 0 NiCN j-y2 R Q P J-Vz R Q P 2 16686.8585* 85.9357 85.2808 2 16687.0456 86.1324* 85.4866 3 87.0234 85.8446* 84.9251 3 87.2127 86.0433 85.1365 4 87.1652* 85.7237 84.5434 4 87.3558* 85.9267 84.7572 5 87.2834 85.5774 84.1358* 5 87.4819* 85.7816 84.3571* 6 87.3723 85.4053* 83.6997 6 87.5584 85.6102 83.9207 7 87.4350 85.2065* 83.2389 7 87.6210 85.4053* 83.4628* 8 87.4695* 84.9807 82.7507 8 87.6553 85.1878 82.9811 9 87.4819* 84.7283 82.2363 9 87.6646 84.9389 82.4703 215 'NiCN b UNiCN Table 5 Continued J - Vz R Q P J - Vz R Q P 10 16687.4637* 84.4595 81.6955* 10 16687.6456 84.6621 61.9332 11 e 87.4193* 84.1405* 81.1279 11 e 87.6013 84.3561* 81.3727 f .4248 .1451 f .6078 12 e 87.3480 83.8090* 80.5305* 12 e 87.5314 84.0272 80.7787 f .3558 .8136* .5354* f .5391 .0319 .7856 13 e 87.2503 83.4487 79.9101* 13 e 86.4350* 83.6688 80.1636 f .2603 .4564 .9151* f .6771 .1708 14 e 87.1263 83.0626 79.2619* 14 e 87.3112 83.2861 79.5214 f .1387 .0721 .2693* f .3234 .2971 .5290 15 e 86.9761 82.6492 78.5858 15 e 87.1594 82.8764 78.8530 f .9908 .6614 .5962 f .1744 .8885 .8631 16 e 86.7982 82.2092 77.8842 16 e 86.9839 82.4401 78.1562 f .8161 .2251 .8962 f 87.0010 .4551 .1701 17 e 86.5928 81.7430 77.1561* 17 e 86.7795 81.9755 77.4335 f .6133 .7611 .1699* f .8033 .9957 .4486 18 e 86.3618 81.2502 18 e 86.5500 81.4874 f .3866 .2715 76.4188 f .5760 .5091 19 e 86.1027 80.7300 75.6194 19 e 86.2944 80.9723 f .1324* .7552 .6396 f .3230 .9969 20 e 85.8176 80.1823 74.8093 20 e 86.0092 80.4294 f .8513* .2119 f .0443* .4552 21 e 85.5046 79.6096 73.9739 21 e 85.6997 79.8601 f .5445 .6419* 74.0039 f .7356 .8945 22 e 85.1655 79.0079 73.1119 22 e 85.3618 79.2619 f .0473 .1439* f .4053* .3019 23 e 84.7989 78.3798 23 e 84.9996 78.6416 f .8491 .4251 f .6843 24 e 84.4068 77.7244 24 e 84.6083 77.9945 f .4619* .7759 f 78.0403 25 e 83.9864 77.0443 25 e 84.1909 77.3154 f 84.0513 .1001 f .2527 .3699 26 e 83.5403 76.3351 26 e 83.7463 76.6127 f .6083 .3983 f .8120* .6734 27 e 75.6008 27 e 83.2779 75.8832 f 83.1412 .6681 f .3519 .9513 28 e 82.5647 74.8356 28 e 82.7786 75.1272 f .9119 f .8597 .2029 29 e 82.0346 74.0478 29 e 82.2532 74.3427 f .1308 .1341 f .3479 .4294 30 e 81.4857* 73.2314 30 e 81.7043* f .5839 .3264 f .8038 31 e 80.8981 72.3875 f 81.0111 .4905 32 e 80.2870 71.5173 f .4294 .6293 33 e 79.6501* 70.6178 f .7865 .7431 34 e 78.9870 69.6935 2 1 6 NiCN b"NiCN Table 5 Continued J-Vz R Q P J-Vz R Q P 34 f 16679.1344 69.8280 35 e 78.2967 68.7419 f .4530 .8873 36 e 77.5793 68.7623* f .7495 .9214* Table 6 Table of assigned lines of the NiCN A-Xi 2\ band 5 8 NiCN 6 0 NiCN J-Vz R Q P J-Vz R Q P 2 16788.2415 87.3329 86.6858 2 16788.3523 86.8159 3 88.3922 87.2294 86.3220 3 88.5040 87.3510 86.4530 4 88.5164 87.0922 85.9282 4 88.6269* 87.2174 86.0632 5 88.6095 86.9271 85.5035 5 88.7077* 87.0531 85.6304* 6 88.6731 86.7321 85.0490 6 88.7821 86.8594 85.1934 7 88.7077* 86.5066 84.5655 7 88.8187* 86.6371 84.7143 8 88.7077* 86.2514 84.0521 8 88.8187* 86.3837 84.2047 9 88.6823 85.9559p 83.5083 9 88.7936 86.1020 83.6674 .9679p 10 88.7369 85.7889 83.0992 10 88.6269 85.6502 82.9225p 11 88.6538 85.4480 82.5001 .9350p 12 88.5388* 85.0764 81.8722 11 88.5388 85.3051 82.3292 13 88.3924* 84.6768 81.2141 12 88.4223 84.9295 81.6948 14 88.2163 84.2438 80.5298 13 88.2751 84.5243 81.0316 15 88.0125 83.7851 79.8122 14 88.1000 84.0895 80.3364 16 87.7796 83.2937 79.0643 15 87.8951 83.6240 79.6122 17 87.5132 82.7738 78.2881 16 87.6577 83.1299 78.8590 .5204 17 87.3850 82.6039 78.0776 18 87.2014 82.2270 77.4829 .3950 .2174 .2372 18 87.0922* 82.0410 77.2616 19 86.8987* 81.6444* 76.6396 .0520 .9061* .6473 19 86.7639 81.4605 76.4100 20 86.5551 81.0316* 75.7807 .7727 .4673 .4211 21 86.1708 81.3975 20 86.4118 80.8443 75.5424 .1899 .4050 .4197 .5487 22 79.7270 21 86.0245 80.2016 74.6386 .7372 .0353 .2117 22 85.6116 79.5265 73.7093 .5393 23 85.1613 78.8266 82.7344 .1810 .7436 24 84.7027 78.1062 25 84.1787 77.3386 .1946 26 83.6565* 76.5277 217 Table 7 Table of assigned lines of the NiCN B - X i l\ band 5 8 NiCN 6 0 NiCN J-Vz R Q P J - Vz R Q P 2 16856.9341 56.0085 2 16857.0702 56.1544 3 57.1122 55.9233 54.9982 3 57.2507 56.0682 55.1498* 4 57.2667 55.8125 54.6238 4 57.3967* 55.9613* 54.7812 5 57.3967 55.6784 54.2244 5 57.5275 55.8261* 54.3860 6 57.5019 55.5190 53.8006 6 55.6629 53.9662 7 57.5831 55.3356 53.3520 7 57.7114 53.5222 8 57.6374 55.1272 52.8805 8 57.7659 53.0544 9 57.6726* 54.8938 52.3825 9 57.7994* 52.5606 10 57.6726* 54.6375 51.8613 10 57.7994* 52.0432 11 57.6598 54.3549 51.3153 11 57.7849 51.5031 12 57.6168 54.0499* 50.7442 12 57.7428 50.9375 13 57.5495 53.7174 50.1491 13 50.3465 14 57.4585 53.3520 49.5304 14 57.5831* 49.7330 15 57.3420 52.9809 48.8855 15 57.4686* 49.0936 16 57.2024 52.5773 48.2164 16 57.3297* 48.4300 17 57.0360 47.5232 17 57.1631 47.7421 18 56.8462 46.8048 18 56.9750 47.0302 19 56.6322 46.0626 19 56.7614 46.2949 20 56.3928 45.2948 20 56.5215* 45.5349 21 56.1287 44.5017 21 56.2590* 44.7479 22 55.8422 43.6868 22 55.9732* 43.9378 23 55.5265 42.8456 23 43.1046 24 55.1894 41.9799 24 42.2450 25 54.8234 41.0907 25 41.3627* 26 54.4357 40.1739 26 40.4563 27 54.0236 39.2324 28 53.5858 38.2682 29 53.1247 37.2799 30 52.6367 31 52.1231 32 51.5870 33 51.0254 34 50.4371 35 49.8262 36 49.1897 37 48.5255 38 47.8394 39 47.1273 40 46.3910 218 Table 8 Table of assigned lines of the NiCN A-Xi 2 3 l 5 P=7/2 band 'NiCN J-Vz R Q P J-Vz R Q P 3 16860.8562 21 16859.9989 16848.4926 4 62.1655 60.7262 59.5502 22 59.6121 47.5847 5 62.2681 60.5675 59.1299 23 59.1970 46.6474 6 63.3424 60.3807 58.6814 24 58.7537 45.6812 7 60.1646 58.2030 25 58.2830 44.6857 8 62.4029 59.9198 57.6955 26 43.6614 9 59.6434 57.1617 27 57.2511 42.6097 10 62.3490 59.3388 56.5982 28 56.6942 41.5304 11 62.2792 59.0108 56.0044 29 56.1093 40.4213 12 62.1811 58.6513 55.3823 30 55.4923 13 62.0533 58.2618 54.7316 31 54.8503 14 61.8967 57.8454 54.0525 32 54.1767 15 61.7113 57.3987 53.3451 34 52.7461 16 61.4987 52.6079 35 51.9857 17 61.2560 51.8424 36 51.2005 18 60.9837 51.0474 19 60.6857 50.2252 20 60.3563 49.3734 Table 9 Table of assigned lines of the NiCN A - X i 22„ band 5 8 NiCN 6 0 NiCN J-Vz R Q P J-Vz R Q P 2 16945.1756* 44.2601* 2 16944.9357* 44.0276* 3 45.3326* 44.1591 43.2488* 3 45.0895* 43.9271 43.0250 4 45.4616* 44.0276* 42.8590 4 45.2181* 43.7979 42.6425* 5 45.5622* 43.8707 42.4398 5 45.3188* 43.6404 42.2247 6 45.6345* 43.6829 41.9927 6 45.3889* 43.4561* 41.7818 7 45.6780* 43.4667 41.5170 7 45.4320* 43.2430* 41.3099 8 45.6919* 43.2219 41.0111 8 45.4469* 42.9992 40.8091 9 45.6780* 42.9475 40.4776 9 45.4320* 42.7272 40.2806 10 45.6345* 42.6425* 39.9149 10 45.3889* 42.4282* 39.7231 11 45.5622* 42.3132 39.3234 11 45.3188* 42.0987 39.1380 12 45.4616* 41.9536 38.7034 12 45.2181* 41.7421 38.5240 13 45.3326* 41.5650* 38.0545 13 45.0895* 37.8813 14 45.1756* 41.1469 37.3767 14 44.9357* 37.2096 15 44.9907 36.6705 15 44.7519 36.5105 16 44.7750 40.2266 35.9350 16 44.5193* 35.7820 17 44.5322* 35.1716 17 44.2966 35.0257 18 44.2601 34.3781 18 44.0276* 34.2399 19 43.9576 38.6291 33.5568 19 43.7278 33.4261 20 43.6274 38.0393* 32.7084 20 43.4019 32.5849 219 'NiCN NiCN Table 9 Continued J - % R Q P J-Vi R Q P 21 16943.2688 31.8287 21 16943.0464 31.7146 22 42.8812 36.7705 30.9215 22 42.6620 30.8168 23 42.4650 29.9852 23 42.2507 29.8896 24 42.0206 29.0205 24 41.8088 28.9345 25 41.5480 28.0289 25 41.3409 27.9516 26 41.0458 27.0066 26 40.8437 26.9399 27 40.5163 25.9557 27 40.3195 25.8988 28 39.9578 24.8787 28 39.7667 24.8311 29 39.3717 23.7707* 29 39.1864* 23.7349 30 38.7595 22.6359 30 38.5746 22.6084 31 38.1114 21.4741 31 37.9363 21.4562 32 37.4448 20.2812* 33 36.7501 19.0958* 34 36.0336 17.8182 35 16.5456 36 34.5763* Table 10 Table of assigned lines of the 5 8 NiCN A-Xi 21 13*0 bands P=7/2-7/2 P=3/2-3/2 J-Vz R Q P J-V2 R Q P 3 16980.9632 79.8008 1 16988.4379* 87.7939 4 81.0782 79.6595 78.4768 2 88.6190* 87.7063* 87.0688 5 81.1715 79.4816 78.0598 3 88.7640* 87.6002 86.7000 6 81.2267* 79.2832 77.5957 4 88.8762* 87.4600* 86.2947 7 81.2431 79.0372* 77.1049 5 88.9555* 87.2759* 85.8592 8 81.2311* 78.7785 76.5787 6 89.0051* 87.0575* 85.3920 9 81.1956 78.4768 76.0192 7 89.0210 86.8260 84.8921 10 81.1182 78.1461 75.4255 8 89.0051* 86.5538 84.3606 11 81.0075 77.7800* 74.8052 9 88.9555* 86.2458* 83.7971 12 80.8761 77.3790 74.1508 10 88.9762* 85.9083 83.2003 13 80.7048 76.9608 73.4597 11 88.7640* 85.5346 82.5696 .7221 12 88.6190* 85.1338 81.9068 .7403 13 88.4379* 84.6981 81.2169* 14 80.5245 76.5114 72.7496 14 88.2289 80.4909* 15 80.2856 76.0192* 71.9989 15 87.9883 79.7297 72.0128 16 e 87.7127 78.9400 .0332* f .7195 16 80.0270 75.4956 71.2344 17 e 87.4063 78.1188 .0400 f .4154 .1237 17 79.7297* 74.9541* 70.4155 18 e 77.2602 18 79.3952 74.3574 69.5773 f 87.0606 .2702 .5883 19 e 76.3768 19 79.0372 73.7554* 68.6993 f 86.7118 .3842 20 78.6635 67.7849 20 e 86.2947* 75.4578 220 p= =7/2-7/2 P= =3/2-3/2 Table 10 Continued J - % R Q p J - Vz R Q P 21 16978.2362 16966.8438 20 f 16986.3129 16975.4715 22 77.7847 65.8895 21 e 85.8592* 74.5096 23 77.3701 64.8900 f .8822 .5206 24 76.7985 22 e 85.3920* 73.5256 25 76.2566 f .4184 .5415 26 75.6769 23 e 84.8921* 72.4861 27 75.0753 f .9201 .5063 28 74.4289 24 e 84.3606* 71.4634 29 73.7686 f .3957 .4881 30 73.0673 25 e 83.7971* 70.3853 31 72.3163 f .8370 .4080* 32 71.5660 26 e 83.2003* 69.2777 33 70.7728 f .2464 .3054 27 e 82.5696* 68.1332 f .6235 .1660 28 e 66.9615 f 81.9689 .9985 Table 11 Table of assigned lines of the NiCN A-Xi 3*0 band (This band is heavily perturbed) 'NiCN NiCN J-Vz R Q P J-Vz R Q P 2 17040.9646 40.0759 2 17039.2102 38.3310 41.0350 .0869 .2265 .3433 3 41.1852 39.9532 39.0647 3 39.3430 38.2083* 37.3215 40.0235 .0765 .3742 .3395 4 41.2492 39.8701 38.6519 .4127 .3067* .8841 .7247 4 39.4908 38.0543 37.9233 5 41.4059 39.6603* 38.2808 .0846 .9360 .7197 .2955 .1264* 6 41.4405* 37.7830 5 39.5633 37.9143* 37.4826 .8428 .5777 .5112 7 41.4797* 37.3631 .6023* .5530 8 41.4405* 36.8581 6 37.7044 36.0569 .4797* .8677 .7212 9 38.6939* 36.2409 .7409 .7401* .2411 7 39.6603 37.4554 35.5590 10 41.3646* 38.3618 35.6612 .4783 .5726 .3941* .3854 .6612 .4921 .5891 .4405* .4104 8 39.6447* 37.2309* 35.0254 11 41.2891 38.0440 35.0422* .0422 .3067* .0725 .0619* .0619 .1264 .0884 9 39.6185* 34.5141* 12 41.2203 34.4322 10 39.5304 36.6080 33.9253* 221 'NiCN 6 0 NiCN Table 11 Continued J-Vz R Q P J-Vz R Q P 12 17034.4624 10 17039.5398* .5141* 11 33.3222 13 17041.0411 33.7783 12 39.3098 32.6666 .1233 .7963 .3249 .6726 14 40.9088 33.1325 13 39.1491 32.0151 .9349 .1672 .9646 14 38.9541 31.2975 15 40.8064 32.3773 .9664 .3167 15 40.8206 32.4587 15 38.7094 30.5666 16 40.4927 31.6671 .7405 .5865 .5079 .6918 .7511 .5917 .7235 .7686 17 40.2556 30.9874 16 38.5049 29.8001 .3414 31.0017 .8122 .4210 17 38.2083 28.9875 18 40.1394* 30.0954 .2359 29.0261 .1114 .0160 .1953 .0481 19 39.8488* 29.2821 18 37.9005 28.2071 .8701* .3672 .9081 .4468 19 37.5328 27.3371 20 28.5885* .5569 .3669 21 27.7215* .5677 .7416* .5806 22 26.6674* 20 37.1675 26.4585 .7037* .2078 .4659 .7195* 21 36.7585* 25.5196 .7577* .5445 23 25.8303* .5544 24 24.8469* .5670 .9111* 22 36.3321 24.5786 .9417* .5855 25 24.0268* .6239 .0392* .0764* 222 Table 12 Table of assigned lines of the NiCN A-Xi 21031<, band 'NiCN ""NiCN J - Vi R Q P J-Vz R Q P 2 17232.2624 31.3588 30.7135 2 16229.7942 29.1507 3 32.4116 31.2500 30.3471 3 30.8386 29.6836 28.7887 4 32.5319 31.1123 29.9512* 4 29.5472 5 32.6217 30.9429 29.5230 5 31.0386 29.3797 27.9738* 6 32.6785 60.7425 29.0656 6 31.1021* 29.1812 27.5183 7 32.7039* 30.5113 28.5766 7 31.1230* 28.9519 27.0432* 8 32.7039* 30.2500 28.0561 8 31.1230* 28.6940 26.5502* 9 32.6667 29.9569* 27.5059 9 31.0886* 28.4004* 25.9751 10 e 32.5972 29.6334 26.9250 10 31.0252 28.0859 25.4006 f .6032 11 30.9311* 27.7355 24.7947 11 e 32.5065 29.2783 26.3111 12 30.8047 27.3545* 24.1616 f .2852 13 26.9444 23.4916 12 e 32.3806 28.8928 25.6643 14 30.4651* 26.5152* f .8969 .6729 15 26.0282* 13 e 32.2179 28.4810 24.9940 16 e 25.5236 21.3098* f .2309 .9979 f .5339 14 e 32.0310 28.0307 24.2923 18 24.4363* f .0446 19 e 23.8357* 15 e 31.8088 27.5516 23.5526 f .8470* f .8178 .5566 .5652 16 e 31.5611 27.0370 22.7841* f .5679 .0500 .7916* 17 e 31.2826 26.5151* 21.9884 f .2904 .9979 18 e 30.9705 25.9354 21.1595 f .9807 .9483 .1724 19 e 30.6246 25.3360 f .6398 .3493 20.3132 20 e 24.7058 f 30.2681 .7211 19.4313 21 e 29.8505 24.0448 18.4968 f .8693 .0593 .5123 22 e 29.4161 23.3518 17.5435 f .4372 .3721 .5616 23 e 22.6293 16.5668 f 28.9804 .6522 .5882 24 e 28.4551 21.8724 15.5550 f .9023* .5782 25 e 21.0947 f 27.9634 .1233 26 e 27.3731 f .4176* 27 e 26.7884 f .8284 223 Table 13 Table of assigned lines of the NiCN A-Xi 22<&\ band 'NiCN b"NiCN J-Vz R Q P J-Vz R Q P 2 17390.1079 89.2028 2 17387.8819 86.9902 3 90.2642 89.0967 88.1924 3 88.0277p 86.8659p 85.9878 4 90.3858 88.9638 87.7967 .0415p .8796p 5 90.4794 88.7971 87.3756 4 88.1571 86.7403*p 85.5791p 6 90.5429 88.6021 86.9198 .7532*p .5921p 7 90.5734 88.3762 86.4347 5 88.2493 86.5839 85.1672p 8 90.5829 88.1176 85.9210 .1805p 9 90.5527 87.8390 85.3728 6 88.3085 86.3908*p 84.7247p 10 90.4954 87.5200 84.8062 7 86.1633p 84.2437p 11 90.4077 87.1733 54.1983 8 88.3488* 85.9210* 83.7306 12 90.2907 86.7973 83.5629 9 88.3231 85.6321 83.1962 13 90.1442 86.3908 82.8980 10 88.2664 85.3196 82.6280 14 89.9679 85.9560 82.2040 11 88.1801 84.9639p 82.0297 15 89.7609 85.4910 81.4799 .9760p 16 89.5231 84.9952 80.7257 12 88.0652 84.6044 81.4001*p 17 89.2531 84.4696 79.9414 4117*p 18 88.9582 83.9101 79.1265 13 87.9178 84.1983* 80.7420 19 88.6321 83.3285 78.2797 14 87.7448 83.7703 80.0557 20 88.2757 82.7128 77.4069 15 87.5390 83.3097 79.3357 21 87.8891 82.0672 76.5037 16 87.3070 82.8200 78.5902 22 87.4744 81.4001* 75.5684 17 87.0445* 77.8133 23 87.0246p 80.6883 74.6054 18 86.7471 77.0084 .0332p 19 86.4260 76.1746 24 86.5491 73.6141 20 86.0716 85.3056 25 86.0427 72.5876p 21 85.6915 74.4120 .5964p 22 85.2787 73.4858 26 85.5091 71.5351 23 84.8359 72.5346 27 84.9429 70.4529 24 84.3651 71.5506 28 84.3480 69.3419 25 83.8586 70.5362 29 83.7404 26 69.4941 30 83.0699 224 Table 14 Table of assigned lines of the NiCN A-Xi 3 2 0 band (This band is heavily perturbed) 5 8 NiCN 6 QNiCN J-Vz R Q P J-Vz R Q P 2 17475.5314 74.5501 2 17471.9063 70.9906 .5446 .5842 .9414 71.0056 3 74.5202 73.5391 3 72.0297* 70.9049 69.9903 .5337 .5730 .0528 .9383 70.0045 4 74.3254 73.2203 .0740* .3725 .2350 .0949* .4085 4 72.1551* 70.7410 69.6166 .4649* .1801 .7875 .6511 5 74.1972 72.7358 .2007 .7943 .7842 5 72.2416 70.5819* 69.1678 .8209* .2572 .6094* .1930 .8766 .2734* .6274* .2125 6 75.8151 73.8289 72.3204* .2336* .8513 6 72.2734* 70.3849 68.7210 .9844 .2911* .3990 .7478* .9979 .3010* .4157 .7682* 7 75.8803* • 73.6494 71.6665 7 70.1302 68.2374 .8912* .6844 .2515 .8182 .2667 .8312 8 72.3404* 69.8348 67.6962 8 75.8577* 73.4297 71.1941 8 72.3725* 69.8619 .9452 .4368* .3919* .8789 9 75.7852 73.1158 70.6843 .4349* .8577* .2012 .6918 9 69.5531* 67.1174 10 72.7461 70.0823* .5922 .1407 .8209* .1679 .6295* .1618 11 75.6635* 69.4276* .6511* .4996 10 72.1610 69.2336 66.5542 12 75.5641 68.7478* .2120 .2991* .5886 .6386 .7682* .6128 .8021* .6580 13 75.3891 68.1523 11 72.0297* 68.8724 65.9411* .3971 .0653 .9203* 66.0144* .4143 .0949* .4342 12 71.9214 68.4534 65.2956 .4478 .9489 .4874 .3464 14 75.1815 67.4774 .5229* .2570 .5499 13 71.7017 68.0613 64.5922 15 74.9677 66.7260 .7154 .6265 .9845 .7314* .7290 .6556 75.0195 .7498 .7450 .0324 .7692 14 71.5506 67.5971* 63.9115 .7815 .9382 16 74.6652* 65.9411* 15 71.3004 63.1181 225 58 NiCN 60 NiCN Table 14 Continued J - V z R Q J -Vz R Q 16 17 18 19 20 21 22 23 24 25 26 27 28 29 17474.7472 .7785 74.4464* .4649* 74.1137 .1403 73.8040 73.3963 .4368 .4461 73.0018 .0230 .0488 .0736 72.5655 .5744 .5916 .6011 .6173 .6531 72.1197 .1375 71.6426 71.1342 70.5819* .6094* .6274* 70.0161 69.4276* 68.8021* 17466.0144* 65.1484 .1654 .1994 .2127 64.2677 .3515 .3819 63.4716 .4793 62.5636 .5889 61.6745 60.6897 .7320 .7404 59.7181 .7406 .7675 .7922 57.7054 .7131 .7335 .7429 .7570 .7900 57.7006 .7254 56.6289 55.5433 54.4071 .4281 .4489 53.2704 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 17471.3148 .3352 .3525 71.0529 .0643 70.7548 .7692 70.4323 .4406 70.0823* 69.6722 .6967* .7090 69.2654* .2991* 68.8180 .8368 68.3345 .3459 67.7949 .8175 .8316 .8501 67.2862 66.7136* 66.1146 65.4737 .4923 64.8164 64.1286 63.3842 62.6442 .6749 17463.1321 .1451 .1665 62.3973 61.5771 .5881 .6122 .6415 60.7557 .7651 59.8852 .8995 58.9901 .9978 58.0685 57.0893 .1153 .1244 56.1101 .1418* 55.0846 .0942 54.0352 .0464 52.9306 .9482 .9625 .9798 51.8458 50.6982 226 Table 15 Table of assigned lines of the NiCN C-Xi (0,0) band 'NiCN ""NiCN J - V z R Q P J - V z R Q P 2 17812.6196* 2 17812.8402 3 12.7718* 11.6080 3 12.9902* 11.8386 4 12.8931* 11.4710 10.3092* 4 13.1116* 11.7081* 5 12.9840* 11.3036 9.8832* 5 13.2019* 11.5386 6 13.0455* 11.1063 9.4274* 6 13.2619* 11.3425 809.6784* 7 13.0757* 10.8785 8.9410* 7 13.2923* 11.1161 9.1963* 8 13.0757* 10.6202 8.4234* 8 13.2923* 10.8619 9 13.0455* 10.3314 7.8764* 9 13.2619* 10.5744 8.1411* 10 12.9840* 10.0124 7.2983* 10 13.2019* 10.2577 7.5692* 11 12.8931* 9.6630 6.6904* 11 13.1116* 9.9114 6.9671 12 12.7718* 9.2828 6.0536 12 12.9902* 9.5347 6.3348 13 . 12.6196* 8.8724 5.3835 13 12.8402* 9.5347 6.3348 14 12.4377 8.4323 4.6847 14 12.6578 8.6911* 4.9805* 15 12.2248 7.9607 3.9548 15 12.4472 8.2244 4.2567 16 11.9820 7.4594 3.1951 16 12.2059 7.7274 3.5042 17 11.7081 6.9281 2.4055 17 11.9349 7.1997 2.7212 18 11.4049 6.3656 1.5850 18 11.6333 6.6427 1.9091* 19 11.0702 5.7731 800.7335 19 6.0536* 1.0660* 20 10.7052 5.1498 799.8527 20 10.9392 5.4386 800.1916* 21 10.3092* 4.4960 98.9408 21 10.5476* 4.7897 99.2870 22 9.8832* 3.8123 97.9990 22 10.1259* 4.1119* 23 9.4274* 3.0986 97.0262 23 9.6721* 3.4044 24 8.9410* 2.3532 96.0242 24 9.1899* 2.6660 25 8.4234* 1.5783 94.9902 25 1.8990 26 7.8764* 800.7725 93.9278 26 800.0999 27 7.2983* 799.9367 92.8333 27 800.2696 28 6.6904* 99.0708 29 98.1740 30 97.2460 31 96.2893 32 95.3011 33 94.2828 34 93.2348 227 Table 16 Table of assigned lines of the NiCN D-Xi (0,0) band 'NiCN J-Vz R P 7 Head: 19128.349 19124.248 8 123.747 9 123.190 10 122.611 11 122.018 12 121.371 13 120.694 14 120.018 15 119.293 16 118.539 17 117.692 18 116.896 19 116.071 20 115.146 21 114.251 22 113.322 23 112.318 24 111.328 25 110.294 Table 17 Table of assigned lines of the NiC 1 5 N A-% (0,0) band 5 8 NiC 1 5 N 6 0 NiC 1 5 N J-Vz R Q P J-Vz R Q P 2 16608.8973 608.0303 2 16609.0405* 608.1800 3 9.0405* 7.9272 607.0600 3 9.1817 8.0777 607.2187*. 4 9.1570 7.7943 6.6797 4 9.2966* 7.9470 6.8424 5 9.2425 7.6317 6.2688 5 9.3802 7.7851* 6.4366 6 9.2966* 7.4403 5.8299 6 9.4361 7.5954 6.0007 7 9.3237* 7.2817* 5.3615 7 9.4591* 7.3759 5.5363 8 9.3237* 6.9690 4.8615 8 9.4591* 7.1279 5.0436 9 9.2912* 6.6897 4.3344 9 9.4248 6.8486 4.5196 10 9.2329 6.3798 3.7783 10 9.3634 6.5427 3.9678 11 9.1405 6.0441 3.1922 11 9.2730 6.2071 3.3858 .1453 12 9.1570* 2.7754 12 9.0405* 5.6777* 2.5789 13 9.0035 2.1361 13 8.8260* 1.9326 14 8.8266 1.4663 .8350* .9369 15 8.6162 600.7681 .8510* 16 8.3790 600.0401 14 8.6822 1.2773 17 8.1119 599.2833 .6742 18 7.8171 89.4975 .6833 19 7.4929 97.6829 228 'NiC 1 5N 6 0 NiC 1 5 N Table 17 Continued JM/2 R Q P J-Vz R Q P 15 16608.4678 16600.5114* 20 16607.1400 16596.8380 .5181* 21 6.7654 95.9660 .5352* 22 6.3389 95.0633 16 8.2244 599.7920 23 5.8981 .2414 .8034 24 5.4282 93.1659 .8126 25 4.9286 92.1761 17 7.9572 99.0430 26 4.3990 91.1588 .9710 27 3.8413 90.1101 18 7.6613 98.2459 28 3.2532 89.0327 .2629 29 2.6373 87.9251 19 7.3327 97.4019 30 1.9909 86.7903 .4243 31 1.3168 85.6261 .4376 32 600.6129 20 6.9782* 96.5742 33 599.8785 21 6.5924 95.6915 34 99.1168 22 6.1766 94.7744 .7814 .7848 23 5.7319 93.8430 24 5.2588 92.8730 25 4.7535 91.8736 26 4.2198 90.8471 27 3.6572 89.7880 28 3.0659 88.7020 29 2.4406 87.5857 30 1.7912 86.4403 31 1.1145 32 600.4077 33 599.6739 229 Table 18 Table of assigned lines of the NiC 1 5 N A-Xi 3% band (This band is heavily perturbed) Lines are listed by UPPER state J 5 8 NiC 1 5 N 6 0 NiC 1 5 N J'-Vz R Q P J' -Vz R Q 2 17035.5181 34.5462* 2 17032.7695 35.5536 34.5839* 17033.7314 32.7725 35.5668 34.5967 33.7830* 32.8211 3 17036.3948 35.4247 34.1770 3 17034.5462* 32.3476 36.4062* 35.4363 34.1885 34.6497* 33.6899 32.4510* 36.4470 35.4763 34.2293 4 34.8196* 33.5831 32.0718 4 36.5548 35.3078* 33.7830* 5 34.8356 31.5409 36.5711 35.3237 33.7988 34.8534 31.5588 36.6298 35.3826 33.8575 6 34.9537 33.1713 31.1141 5 36.5978 35.0715 33.2712 34.9587 33 1756 31.1185 36.6631 35.1380 33.3357 7 no lines found 36.6931 33.3643 8 35.07* 30.1270 36.7023* 33.3764 35.1091 30.1676 36.7389 35.2138 33.4121 35.1560 30.2133 36.7800 35.2561 33.4536 9 35.1202 29.6285 6 36.8267 35.0225* 32.9445 10 35.0822 29.0421 36.8674 35.0653* 32.9849 11 35.0346 28.4446 7 36.8477 34.7701* 32.4128 35.0549 28.4680 36.8863 34.8066 32.4509 12 34.9911 27.2545 8 36.9172 34.5607 31.9272 34.9990 27.8607 36.9271 34.5722* 31.9378 13 34.8620* 27.1765 36.9422* 34.5839 31.9536 34.9048 27.2189 36.9636* 31.9727 34.9307 27.2448 36.9819 31.9925 34.9749 27.2902 9 36.9369 34.3018 31.3915 14 34.7554 26.5219 36.9927 34.3582 31.4477 34.7919 26.5570 10 35.9913 29.8889 15 34.6193 25.8359 36.0683 29.9702 34.6376 25.8539 37.0197 30.9221 34.6497* 25.8663 37.1554 31.0561* 16 34.4412 25.1073 11 36.1436 29.4896 34.4584 25.1238 36.1624* 29.5113 17 34.1131? 24.2335 36.1777* 29.5260 34.2514 24.3703 36.9927* 30.3385 18 33.9061 23.4747 37.0610 30.4079 19 33.5658 22.5841 12 36.0956 28.8916 33.5831 22.6034 36.1624* 28.9568 33.5991* 22.6227 13 36.2378 28.4767 20 33.2321 21.7028 36.2948 28.5331 33.2852 21.7589 36.3627 r 28.6006 33.3101 21.7839 14 no lines found 21 20.6753 15 35.9116 27.0412 20.7139 35.9807 27.1098 20.8010 230 5 8 NiC 1 5 N 6 0 NiC 1 5 N Table 18 Continued J ' -Vz R Q P J - V z R Q 15 17036.0183 17027.1478 16 35.7538 26.3297 35.7939 26.3676 35.8092 26.3841 35.8560 26.4298 35.8703 26.4449 35.8852 26.4598 17 25.5816 35.5783 25.5988 35.6401 25.6611 35.6939 25.7152 18 35.3080 24.7765 35.3304 24.7978 35.3639 24.8310 35.3995 24.8677 19 35.0346 23.9430 35.0469 23.9606 35.0909 24.0031 35.1038 24.0158 20 34.7480 23.1077 34.7701 23.1291 21 34.4010 22.2061 34.4242 22.2284 22 34.0073 21.2590 34.0309 21.2815 23 33.5991 20.2955 33.6202 20.3178 24 33.1551 19.2984 33.1627 19.3052 33.1980 19.3418 25 32.6630 18.2520 32.6762 18.2657 32.6916 18.2810 26 32.1789 17.2162 32.1971 17.2313 27 31.6485 16.1301 31.6574 16.1395 28 31.0561* 14.9842 31.0776 15.0052 29 30.4544 13.8278 30.4590 13.8327 30.4985 13.8730 21 17020.8325 22 17031.4125 19.7810 19.8314 19.8389 23 31.9536* 18.7982 31.9727* 18.8103 24 31.5700 17.8480 31.5964 17.8747 Appendix 2 231 Hyperfine Line Frequencies for the Bands of NbO The lines are sorted into tables by sub-band, branch, J" and F". The branch labels used in this appendix are given by the letters R, Q, and P to indicate the value of AJ, followed by two numbers to indicate the upper and lower state spin components (e.g. R32(J) = SR32(J), etc.); the N-form superscript labels are not used in this appendix. The labels r, q and p are used to indicate the value of AF. ? 2 3 2 CN + II PH CN + PH CN IT) + PH CN cn + PH CN + H-, II PH CN H4 II PH CN cn HA, II PH CN HA, II PH CN i H-l II PH CN as HA, II PH CD < rH vo CNJ rH 00 rH o o CN] •5J 1 CNJ cn 00 i> LO i> CTi o LO CTl 00 O rH VO LO 00 CNJ rH CNJ CNJ r - o rH vo i> o LO i> CNJ CN] rH CNJ LT) oo 00 cn rH o VO cn rH 00 vo LO vo LO 00 00 o rH CNJ rH r~ r - 00 cn cn O r~ [— oo 00 00 LO CTl cn vo l> •^ r •=r 00 ro 00 rH rH ro rH rH rH rH rH rH rH LO LO rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH r-~ r - l> l> r - r - l> l> l> r - r - r - r-~ [— r - l> l> [-• r~ r - r - r -co CNJ OO cn cn VD CTl 00 rH VO ro LO r-~ o rH co vo l> o ro CTl LO cn CTl l> 00 cn LO CTl CNJ uo LO o r - LO rH i> oo LO rH LO oo o rH ro ro r - 00 o rH r - oo VD vo CNJ LO o oo o r - ro i> CD o rH rH ro LO LO ro vo 00 CN] M< 00 LO vo LO r -CTl cn o rH rH rH CNJ 00 cn cn LO LO cn cn cn 00 00 vo vo vo o o r~ l> [-- ro ro ro ro CNJ CNJ CN] rH rH rH rH rH rH rH rH rH LO LO rH rH rH LO rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH r - r - r - r - l> r - r - r - r - r - r - r - [-- r - [-- l> r - r~ r - [-• [— r~ o r~- r - l> l> rH CTi 00 o CNl 00 o CTl l> o ro LO CD o oo oo cn cn rH CTl o CTl 00 LO M< CNJ LT) VO rH LO cn rH rH CN] o CNJ CNJ o vo Ol cn rH rH rH o r - OO CTl LO rH oo O rH •a* O LO r - oo r - 00 cn O CN] oo rH CN] ro LO l> 00 cn oo CTl o rH ro o rH rH CNJ 00 00 00 00 o rH LO LO LO O o o CTl cn r - r - r-~ O o r - r - 00 CNj ^ C N ] rvj ^ CNJ H H H H rH rH rH rH rH rH r ~ i > r - - r ~ i> i> o i> o i> LO LO LO LO LO • ^ ^ r ^ o j C N j C N j ' ^ i ' ^ r r H r - r - r~ o r -LO LO r~ r - r -LO LO LO i—It—I i—I rH rH rH rH rH [— r - r - r - r -rH O r~- VO O 00 ro CT1 cn ro o CNJ O VD VD CO oo CNJ CTl rH CO rH CNJ ro cn LO rH CTi rH rH 00 LO 00 CM 00 00 rH VD CN] i> o CTl rH CNJ CNJ LO LO VD [--CNJ CNJ ro ^ CNJ CN] vo o rH CTl 00 00 CD rH 00 LO M< •^ f «3< CN] CN] CNJ CNJ CNJ CNJ •sT rH rH rH LO rH LO rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH l> r~ r~ t— r - l> l> r - r - r - l> [-• r~ t~ l> LO LO LO LO LO LO LO LO rH rH rH rH rH rH rH rH CNJ cn CNJ rH r~ o LO r-~ CNJ ro •5T CTl r - o CTl 00 LO LO •q" CNJ LO rH r- CD CTl o M< LO r~ CTl VD i> l> CO o rH VD o rH rH o CO 00 rH rH 00 00 LO LO •q" CNJ CNJ LO rH rH LO LO rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH r~ r- r— r— r- r- r~ r - r~ r - r - r- r -LO LO LO LO LO rH rH rH rH rH 00 CNJ VD OO VD oo o LO LO CNl 00 LO LO CNJ oo CD O CO 00 CNJ CTl o rH rH rH rH cn rH CTl CTi cn VD LO LO CNJ rH LO rH rH rH LO rH rH rH rH rH rH rH rH rH rH rH rH r- r - r~ [-- r~ r - r - r - r - r -LO LO LO LO LO LO LO LO rH rH rH rH rH rH rH rH LO o LO cn LO MtrftMD'ftMD'ftMD'o, M t r a n t r a n t r M t r a M t r M f f f t H t r n t j 1 ^ r-{ T-\ ^-i C N J C N J C N J C N J 00 rH PC 00 rH cn rH rH CH ro rH 05 ro rH CH •a1 05 CH 00 00 rH 05 00 oo rH CH ro ro PC CH 233 CN O N II fe CN + fe CN fe CN CN + fe CN + >—> II fe CN II fe. CN CO I H-» II fe CN •/-> II fe CN r -i-I, II fe CN ON 1 >—> II fe CD ON r - ON LO 0 00 r - r H KO CNJ 03 0 CNJ 0 0 r H O r H 03 0 0 ON r H CNJ 0 ON 00 ON r - r - r H KO KO CNJ KO KO 00 O l > 00 l > CNI r o KD 00 KD 0 03 00 ON ON 0 KO KO 00 t — 00 LO KD ON O 0 0 LO r o ^ ON ON ON 0 0 ON r H r H LO LO CNJ CNJ r~- ON 0 LO co r H LO LO r H r H LO O O LO LO r H r H KO O 0 KD V D O VD 0 KO 0 r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H [— [-- r~ r~ l > O l > l > t-- r - r - r~ r~ r - r - r~ l > r~ r - O r - r~ OD 0 03 00 0 0 ON ON LO P^ r H LO ON r - r - r H r H 00 r - O ON KO r - CNI r -CXJ r H ON ON ON r - CNJ O l > r - 00 CNJ 0 0 r H 00 CNJ KO •q* CNI t — 00 0\J O r H LO ON CTl r H r H 00 ON 0 CNJ r H CNJ r o CNJ r o O 00 ON 0 CTl 0 r H [> 00 O O r H CNI O KD KD KD LO r o LO LO LO O O O 0 ON ON r H r H r H LO LO KD KD CNJ CNJ 00 0O 0O ON r H LO 0 0 CO CNJ r H LO LO r H r H r H KD r H r H r H LO LO r H r H r H KO O O 0 KO KD O O O KD O VD O O r -r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r - l > r - [— r > O r - l > l > r - l > l > i > O r - r - r - r - r > r~ r~ r~ r - l > r - r - r - r -LO LO r H r H 0 O KD O LO CNJ •^r VD VO KD r - 00 O0 0 0 0 0 0 CN1 CNJ ON O r - LO r - KD CM 0 0 m KD LO O 0 0 0 CNJ r H CNJ ON r H 0 0 0 0 0 KO r - 00 r H LO O LO ON 00 ON 03 CNJ 0 0 LO LO KD r - LO LO r H r H r o r H r\ j 00 ON O CNJ CNJ 00 CNI r - r - l > KO LT) LO LO LO 0 0 O 0 ON ON CNI CNJ LO KD KD KD CNJ 00 00 00 00 r H LO r o r o CNJ r H 1 0 r H r H r H KD r H r H r H LO LO r H r H KD O O O KD VD O 0 O O VD 0 0 r -r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r~ i > r~ O r > r - r - r - r~ r - r - r - r - r~ O r~ l > l > r— r~ O r~ LO LO LO LO LO LO r H r H r H r H r H r H OO 0 0 0 0 00 LO LO r H r H 03 CNl r o CO LO ON r H r H ON 03 r - r H r H 0 0 r o KD r - CNJ r H 0 0 KD r H 00 ON KO 00 r - LO KD 03 03 ON 0 r - CNI r o LO 1 0 00 CO r~ •q* LO LO L0 O 0 0 r H ON CNJ CNJ KD KD KO 0 0 00 r H r o ONI r H LO r H r H r H KD r H r H r H LO r H r H O O O 0 0 O 0 r~ r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r - r - r~ r~ O O r - O r-- r - r - [— r~ r~ r~ [— r~ r - r~ LO LO r H r H V D ON 0 0 00 KD 00 O ON O ON 0 0 r o CNJ 0 0 LO CNJ r -LT) LO 0 LO LO 00 r H r~ 03 CNJ LO -=r r H VD VD ON CNJ CM 0 ON ON O r H CNJ CNJ P^ LO LO KD r~ LO LO ON 03 LO V D LO LO r H r H r H r H CNJ CNJ CNJ KO KO 03 r H r o CNJ r H LO r H r H r H r H r H r H r H r H O 0 O O 0 r~ r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H l > r > l > r - r - r - r - r - r - l > O r - l > r~ r - r - r~ LO LO r H r H CNJ r H r \ i KD CNJ LO ON r H ON r o r H C\J ON 00 OO r - KO 00 LO ON O 0 0 r H ON LO ON 00 LO O r H CNJ 0 0 KD KD r~ 00 ON KD r H 0 03 LO KD KD r H r H r H CNJ CNJ CNJ KO KO 00 KD CNI r H r H r H KD r H r H r H r H r H O 0 O KO 0 r~ r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H [-~ l > r-~ r - r - r - [-- r~ r - r - [~- r - r~ r - r > LO LO LO LO LO LO r H r H r H r H r H r H 00 l > 0 0 03 ON CNJ 0 0 0 0 0 3 LO r - r H r H 00 0 0 LO r H r~ r - CNJ 00 r o r - 0 0 0 0 O r H LO KD VD KO r H c\j CNJ CNJ r~ -=r r H r H r H r H K0 r H r H r H O 0 r H r H r H r H r H r H r H r H r H r H r - r - r - r - r~ r - [~ r~ l > LO l O LO LO LO r H r H r H r H r H CNJ 00 ON l > r H 00 •q* 00 r -LO r - ON 0 3 KD r H r H CNI 0 0 r H KD r H r H 0 r H r H r H r H r H l > r - O l > L -^LO LO LO r H r H r H 0 0 0 0 03 OO LO r H r o L0 KO O 0 0 KD r H r o r o r o r H KD r H r H r H r H r H r H r H r H i > O 0 r— r~ LO LO LO LO r H r H r H r H ON 00 O 0 0 0 0 r H 0 r H r H r - r -ft U SH CT Pu SH S-J ft SH tr H tr ft H H ft H SH ft SH t r H SH M 00 LO LO LO LO KD V D KO KD l > l > 00 0 0 r o r o M< CO 00 00 r o r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H OI CC d CC cn OH cu DH Of CC 0 1 Pf, CU CC cu PC; 234 CN ON ,+ fe CN + fe CN in + fe CN m .+ fe CN fe CN fe'i CN CN II fe CN IT) l-k II fe CN II fe CN 1 II fe CD .SP < C D ^P CNJ m CTl o o LO ^p ON ON r- TP r- co KO 0 0 ON KO ON KO r H O r H r H ^ P O [ — 0 0 KO 0 0 LO O 0 0 ON KD ON r H O r- r-LO LO KD r H KO co LO ON r-LO tr M tr M r> 0 0 0 0 ON ON LO CO o LO ro 0 0 KO 0 0 r-r H ro ro ro r H r H r H r H cn ix cy vc M o r H ro 0 0 TP r H O KO r H 0 0 LO r~ r> r H r H r- O ON ON 0 0 l> LO r H KO r H LO ON ON CN] 0 0 KO TP CN] r- C~ r- r-r H r H r H r H r- r- r- r-LO r- 0 0 KO ON r H CM LO TP 0 0 O 0 O OO KO TP CN] r- r- r- r-r H r H r H r H r- l> r-~ LO r H CNJ 0 TP CN] 0 0 r- r- ON KO TP r H i> i> l> r H r H r H r- [--r- LO r-CNJ r- LO KO LO i> KO TP r H r- r-~ i H r H r H O 1— l> r- r~- L O r H TP CN] 1 0 TP KO KO TP r H r- i> r-r H r H r H r~ r- r-CNI LO LO 0 0 TP 0 'IP 0 0 LO KO TP r H r- i> r-r H r H r H r- r- r-0 0 CNJ LO KO 0 0 0 0 CNJ ro KO TP r H r- r- r-r H r H r H r- r- l> ON ON 0 0 r~ LO KO CNI r H CM KO TP r H r- r- r-r H r H r H r- r- r-u M M M r H CO TP LO r H r H r H r H ^P TP TP TP r H r H r H r H Pf, Pf, PL, P , 235 cn Os + PH CN + H i PH C N .+ PH cn PH cn PH cn PH CN CO cn H!» II PH C N Pp H1> II PH cn OS H i II PH cu a op \< rH CD CN rH CD LO LO 00 O o rH o 00 CTi 00 CM 00 VD o oo <Tl LO LO CTi O 00 00 oo CTl 00 CTl 00 CM rH 00 <NJ r - VD LO r -O r - VD CTi 00 LO 00 CTi r - oo [-- oo LO ^p 00 00 r - VD o ro r~ CTl 00 00 00 LO CTl CTi 00 rH rH LO LO l > o o r - CNJ CO LO LO CTi VD VD rH VD VD ^p oo oo r - ^p CD CO VD ^p «=P ^p LO LO LO ^p ^p ^p LO •=p •=p LO vo LO ro LO CM LO T oo CTi CN CTi VD 'S) r-t O O CD VD VD VD 3^* **P o o VD VD O VD o ro oo oo LO 00 CM rH VD •a* M< VD 00 o [-- cn rH o 00 cn ^p LO rH O rH CM o ro oo ^p 00 o CNJ LO VD VD CM CTl CNJ CM VD cn 00 00 rH LO LO LO VD 00 LO VO o r - CNJ VD ^P CM CM CM rH CTl r - o o VD LO rH 00 r - VD rH LO VD LO o CTi CTl rH LO LO LO iS rH rH o CTi 00 00 VO VD VD cn 00 rH rH rH 00 00 VO 00 VD LO LO o VD VD VD rH r~ r - [— 00 00 r - r - r~ ^p 00 00 00 vo 00 ^p LO ^p ^p ^p LO ^p •^ p LO LO ^p <=p LO ^p ^P LO CNI 00 LO 00 o r - o LO vo vo LO oo CM VO VD VD O VO VD VD LO ^p ^p ^p O VD ^P 00 cn r- vo o CN] cn oo ro CNJ o cn co CNJ CNJ rH O LO ro ^ co cn r - rH cn O0 CTl o H u i ro ^p ^p r - r - r -ro co i—it—i CNJ LO o rH rH ro r -•rp LO r - VD LO rH m CTl CM CNJ CNJ CTi r- i> r- LO ^ ^ ^ ^ o . VO ro ro r - r - r -i n in ^ ^ ^P 00 00 00 ^P L/1 i o ^ ^ ^ o vo o vo ro cn ro LO o vo vo LO ro o oo M< o vo ro o o ro LO LO CM CM CN] 00 LO LO •^P rH rH GO LO ^P ^P r-VD CO LO ^P [-- CNJ CO CNJ CTi oo ^P CTl rH 00 CM oo VO cn oo rH r - o rH vo cn cn CN] O oo CTl r - CM LO LO 00 CN] ro •5P 00 oo VD cn o r - CNJ O 00 r - CTl O oo CN] rH 00 •3* oo CM o oo rH CM rH r~ r - 00 CNJ CNJ LO 00 00 CO O oo oo 00 o LO 00 VO VD vo VD r - r - r - oo 00 r - r - r~ LO 00 00 CD LO VD 00 ^ p ^ p •^p ^ p ^ p ^ p LO LO ^ p ^p ^p LO •5P ^p ^p LO ^ p o O o VD VD VD rH rH rH rH rH VD rH O ^p ro rH VD cn ^p c— cn CNJ o CD LO o 00 rH CD CO VD ro CM LO ro r~ r~ cn CM 00 VO CTl CN] rH ^ p ^ p rH cn CO rH vo LO r-~ r-~ cn 00 00 o o cn cn rH 00 ^ p CO r - i— O ro ro ro LO LO oo 00 00 rH ^ p ro co vo 00 o VD VD VD CM r - oo oo r - r - LO CD CD CD VD 00 LO M< ^P LO LO LO •=p -5p LO ^ p LO o O o VD VO vo rH rH rH rH CD 00 oo LO r - vo LO LO 00 o LO CO CNJ CM ro CNJ VO VO rH LO oo 00 rH LO oo CD CNJ r - r - r -LO •^p c - rH CTl oo =^p ro [-- LO LO ^ p r - oo CO CD o o ^ p oo vo cn cn cn rH ^ p VD CT) VD vo CM CN] c - r - ro r - LO oo CO oo VD 00 ^ p LO LO LO LO ^ p ^ LO o o o o vo VO VD VD rH rH rH rH ^p ^p o r - rH cn rH rH CM CN] o VD O rH rH LO 00 ^P r~ 00 CNJ l-~ CM 00 00 CM CM ro co 00 00 CN] o cn cn ro CD rH rH ^ p VD cn CNJ LO ^p r~ cn CNJ CNJ l > r- ro r-- LO CD 00 00 VD CO LO LO •3* •=p LO ^ p LO ^ p •5P LO O O o o o o o o VD VD VD VD VD vo vo VD rH rH rH rH rH rH rH rH CM LO vo LO VD r - [-- CTi ON vo CM rH VD r--^ r - o CNJ r~ oo 00 LO vo LO LO LO o VD VD LO CNJ -JP VO LO SH SH cr a SH SH tr a a SH tr SH C ft ft SH tr >H tr ft a. S-l tr SH tr ft ft SH SH rH rH CM CNJ CM 00 oo 00 •=p ^p LO LO LO VD VD rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH CM CM CM CN] CNJ CNJ CNJ CNJ CNJ CNJ CNJ CNJ CM CM CM CNJ PC a PC o> PL, PC Ol Pu PC a CM PC Oi OJ PC a 236 r H V D 00 o 00 L O TP CM O V D 00 cn r H L O 00 V D CM CO TT TP 00 TP TP r H 00 L O 00 CO TP V D TP r - l> 1— 00 o 00 CM r H CM V D CM CN] L O V D CTl 00 r H o CNl r H 03 o L O L O l> o TP r H TP CM L O L O r~ CTl cn r - CM TP 00 L O OD TP r - CTl TP CTl ON TP O O CTl 00 r H oo 00 o 00 TP T f TP L O TP TP L O TP TP V D V D TP TP V D TP V D L O TP V D L O l> r H 00 o r H L O 00 L O r H r H r H CM 00 CNI V D TP V D LO CTi l> r - cn V D 03 o i> o CM L O 03 r H r H V D V D CM CTl TP CTi L O OD TP 00 o r H CO L O TP cn CM r H O cn CNI V D r H CM L O V D l > OD O r H O o CM o 00 CTl V O V D V D 00 r H r H o L O CM L O 00 V D V D OD o O O CM 00 00 L O TP L O 00 00 TP r> CTl CTl O N TP CTi CTl TP O O CTi TP CM CM O oo 00 o 00 TP TT TP TP L O TP TP TP TP L O TP TP V D V D TP TP V D V D L O TP V D L O TP V D r H l > oo CTl O CM 00 r - O CM CTl r - TP r H r H 00 L O LO 00 CTi L O r - r H cn r H oo o O OO V D ON 00 03 TP 03 00 V D TP 03 TP OO C M r H OD ON 00 co 00 OD CNJ CTi 03 r - r H L O L O ON oo oo TP r - ON o OO CTl r H r H V D 00 [-- r - [-- ON r H r H r H V D 00 00 L O L O L O IT- r H O r H CM C D TP TP L O V D 00 oo TP r - CTl CTi ON TP CTl cn CTl CTl CTl O TP CNJ CM o 00 00 00 CO TP TP TP TP L 0 TP TP TP TP L O L O TP TP TP V O TP V D V D L O TP V D V D TP V D o O O V D V D V D r H r H r H cn L O OD L O V D 00 r - V D 03 V D TP V D CTl TP CNJ r - CM r> TP CN] r H V D o TP r H TP 00 TP V D o L O CTi OO CTi r~ r H TP V D CM TP r H o r - o V D L O T P 00 V D V D L O CTl CM CM LO OD CTl TP LO V D 00 00 00 o CM CM CM TP V D V D V D TP OO O CM r H TP V D V D r -03 oo TP 00 ON cn ON CTi CTi CTi CTi TP o O TP CM oo O CO TP TP TP TP L O TP TP TP L O TP TP TP TP V D L O TP V D V D L O TP V D V D CM r H r H V D r H oo CO r H V D l> TP CM 00 l> 00 V D TP V D r H o L O ON L O CTl r H O L O O TP r - CM V D CM r~ r H r - r - OD CM r H r H r - r H 00 CM CM o CTl cn LO r H CM TP 03 03 o 00 00 00 r - L O r - r - r - ON o o CNJ [ — r - 00 03 00 OO CTl cn CTl TP CTl CTi CTi CTl O o o CM O oo TP TP TP L O T P TP TP TP L O TP TP TP V D L O LO V D L O TP V D O O o o O V D V D V D V D V D r H , H r H r H r H r~ CO CM r~ L O L O r H O CN] r H CM CTl CM r H 03 00 r H V D V D o L O CTl CM r H CM CM r H L O r H 03 CTi o oo CM TP oo r> r - 00 TP r - L O o CM 00 r H 00 r H ON ON r H 00 oo L O r - V O CTl r H TP co TP r H V D CTl C D 03 00 CTl cn CTl CTl TP O o TP CM O TP 00 TP TP TP L O TP TP L O TP TP V D L O TP V D L O TP V D V O o o V D V D r H r H OD r - LO 03 TP r~ TP r - r H oo ON L O 03 00 00 r H r~ CM 00 00 CTi 00 L O CM r H L O V D o o 00 00 oo o L O 00 00 O V D r -O CM CTi V D OD o CM TP 00 L O r - oo CTl L O 00 TP CTl CTl r H O TP CM o 00 00 TP TP LO TP L O TP V D L O TP V D L O V D TP V D O O V D V D r H r H 00 r - oo r - oo r H r - CM V D L O V D L O o 00 ro CTl L O CTi r H V D oo TP L O o V D L O o LO V D V D 00 L O 03 r H TP CO V D r H oo r H CM TP TP V D l > o L O TP CM r - CTl o L O OD CTl cn CTl TP r H TP CM TP oo 00 L O TP L O TP TP L O TP V D TP V D TP V D TP V D O o o O O V D V D V D V D V D r H r H r H r H r H oo oo CM O r H L O V D TP r H 00 00 CTi TP TP CTl 00 L O L O CNI 00 CTi 03 00 00 L O CTl CM 03 r H 00 CM CTl [ — r H L O TP V D CM 00 o 00 TP CTi r H TP CNI O TP oo L O L O TP L O V D TP V D L O TP V D V D o O O V D V D V D r H r H r H l > L O 00 L O CTi r H CN] r H r H r - O L O CTi O 00 l > r - CN] r~ r - CTl 00 L O 00 o oo r - r H LO L O 03 r H CTi 0D CTl r H TP CM 00 L O TP L O l O V D TP V D V D V D tr Pu Pu M M tr a PC H tr M tr Pu Pu M tr SH tr Pu SH tr tr C L . SH tr tr Pu SH V D V D r> r - r - 00 00 00 CTl CTl CTl o o O r H r H r H CM r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H CM CM CM CN] CM CM CM CM CM CM CM CM CM CM CNI CM CM CM O I C M CC cu C U cc C U C M CC cu C M cc cu C M CC cu CM CC 237 3 o O CN tD H C N ON + H I PH CN PH CN I T ) + PH C N co + H i II PH C N s II PH C N II PH C N CO I H i II PH C N m H!> II PH C N Pp H1> II PH C N ON HIJ II PH VD LD O o LD O r H l> r H CNJ 00 CNJ r H VD o r - VD ON o 00 m CM VD 00 ^p VD ^p VD VD r - ^p r-- o O CNJ 00 00 CD CD r o r H O 00 r H ON ^p t H CNJ oo H LO r - LO r - t H CD CD O r H LT) ^ P o oo i n LO r - CD LO LO IT) VD VD VD VD o O O O VO VD VD VD t H r H t H t H VO oo o oo ON r~ t H o [— ON o r H o ON 00 CN] ON CD O CN] 00 if) CNJ r-~ 00 ^p VD VD VD CN] LO o r H LO CTl 00 CNJ ON CM CD cn 00 CM CN] cn 00 ' r H oo 00 IT) CNJ r - 00 ^ P VD ^p VD VD LO r— cn LO c n 00 oo CTi cn VD O ON ID VD LO m VD ON co o ON CM CN] 00 00 VD CM r - r - 00 VD VD VD VD ON CNJ 00 00 VD VD O VD O l> CM 00 r -VD [-- LO ON r~ V0 C~ •SP VD LO VD LO LT> LO CNJ r H *SP 00 VD 00 [--^p VD ^P VD o VD r H 00 CD LO O CN] ^P r H CN] t H VD CO LO 00 VD r~ ^P VD vo O VD t H CN] r~ 00 LO r - vo 00 LO VD c~ VD VD a, U cr a SH CN] oo oo r H r H t H t H t H r H t H r H CNJ CM CNJ CM PH CC P J CC r -•5P oo VD VO CNJ l> LT) CM r - ^p ^p ON ON o ON ON 00 ^p CNJ o oo LO 00 vo oo r - OO •sp VD ^p VD VD o VD oo VD r -o VD VD CD VD •sp 00 VD M u cr a LO o o r H CNJ CM r H r H CN] CNJ CNJ CM CC CC P J 238 CN ON + H i II PH CN + PH CN + PH CN CO PH CN PH CN PH CN CO H-i II PH CN i/"N i H i II PH CN Pp Hi, II PH CN ON H I II PH .2P ON rH VO 00 o CM ON oo r~ o o rH LO OM ON LO ON 00 VO 00 ON o ON ON to r - ON VD LO ON LO ^ p rH ON O •sr VO VD O r~ co o ON ON r- ON o O CTN O ON O o ON VD LO r~ t— VD ON ON O r - [~ VO LO rH 00 00 LO LO 00 00 00 rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH ro 00 00 00 00 00 ro 00 oo oo oo oo oo 00 00 CO 00 00 o ON O ro H H H Ol CM s]< VD 00 CM o ro t CM ON CM CM rH rH 00 t— LO LO LO 00 rH rH rH rH rH oo oo oo ro ro VD CM LO r-LO rH CM 00 ON 00 r - rH 00 00 VD [-- ON oo rH oo r— LO CM [— ro oo CM vo oo oo co CM CM r- VD CO LO LO LO 00 rH 00 rH rH rH rH rH rH rH rH 00 oo oo ro ro oo oo oo VD VD VD rH rH rH VO [ 00 ON r- o in OO O ON [ ^ p LO o 00 00 00 00 00 LO LO LO 00 00 rH rH rH rH rH 00 00 00 00 00 vo rH O VO 00 CO LO rH O LO ON [ LO CM ON ON ON ON LO LO LO 00 <-{ r-{ 00 00 00 00 VD oo r-LO ON oo rH r-CM VD r -t CO oo ro o co r-{ <-\ CD oo oo ro VD VD r~ co o ro ON rM CM 00 LO OO oo oo ^> CM [— LO O CM VO •=P [-- VD CO ON CM t^> ro ON LO rH 00 ro CM VD ro 00 ro VO LO ON ON ON o o r - r - LO LO 00 rH 00 00 CO vo vo rH rH rH rH rH rH rH rH rH rH rH 00 oo 00 ro 00 00 ro ro ro ro ro VD vo VO VD VO VD VD rH rH rH rH rH rH rH o CM r- ro CM oo r-LO ^ ON LO r- r- vo vo o co oo oo ^-t CD CD CD ro ro ro oo vo ro 00 00 00 ON ro LO rM VD LO 00 t— VD rH LO r--rH ON CM o ON ON CO ro ON o ON rH rH O LO vo VD LO ON CD VD VD VD 00 o 00 CO rH rH rH rH rH rH rH o o 00 00 00 00 00 00 00 oo ro VD VD VD VD rH rH rH rH ON LO O oo VO CM r -rH vo LO oo oo VD VD ON VD r-oo uo VD LO o oo rH O oo ro VD VD M t r t t M c r f t n t r a r j 1 M t J T j . n f f a t i ' f t n t r c M t r f t o o vo LO ON ON ro l> VD oo o LO ON ro CM •5J1 oo l> CD rH rH rH LO CO O o o VD vo CO ro CM CM CM rH rH rH rH 00 ro 00 oo oo ro ro 00 LO ON CM ON VD CM o ON 00 rH CM l> o o VO LO •q* oo VO CO CO CM CM CM LO LO LO VD O o o vo VO vo ro ro CM CM CM rH rH rH rH rH 00 ro oo 00 00 00 00 ro ro ON LO LO ^3- oo r- r— ON 00 oo VD r-VD L O r - LO •*f VD 00 ro ro 00 VD vo VD [-- vo o o o VD VD VO 00 ro CM CM CM rH rH rH rH rH ro ro oo oo oo oo oo ro VD CM 00 CM ON r-00 ON ON LO ro o ro •sf 00 CM rH •sr r - C-- t-~ VD o o VD VO VD ro CM CM rH rH rH rH 00 oo 00 ro ro 00 rH rH LO CM CM VO VO ON [-- ON r-rH o o ON CO LO LO 00 [-- r- LO o o VD VD vo ro CM CM rH rH rH rH oo oo oo oo oo ro VD rH VD LO VD ON ro 00 LO LO 00 r- VD VD LO 00 00 ON LO CD CO CO ON o VD VD VD oo ro CM rH rH rH rH rH ro oo ro oo oo co vo VD VO VD rH rH rH rH 00 o ON ON 00 r-00 00 VD VO rH rH 00 oo vo VD rH rH M tr a M tr ft a H oo ro a CM 00 05 CM ro ro 05 ro a ro 0J rM CM CM co ro ro 05 CH Pu ro 05 ro CH rH CM 00 00 PH 05 239 CN ON + fe CN + s~-a II fe CN + fe CN co + fe o 0 3 0 0 r H 0 0 VD LO r H LO VD 0 3 LO 0 0 r H LO 0 0 VD OO r H CM LO VD O LO i > 0 0 0 0 o r H CNJ LO l > r H 0 0 o CM LO T f 0 0 CM co r~ l> r H LO T f 0 0 CNJ CO r H CNJ CO CO 0 0 0 0 VD CM 0 0 r H o VD r H 0 0 r H 0 0 VD VD r H r H T f CM LO r H r H i > r - CM CM LO T f T f O CM 0 0 O o rH r H r - r - oo ON LO 0 0 oo [-- r - 0 0 0 0 T f 0 3 0 3 oo r ~ r H r H o CNI CM r H r H r H O O CNJ CNJ r H r H r H O CNJ r H r H r H o oo 0 0 oo oo 0 0 oo 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ON T f VD LO o 0 0 O 0 0 0 0 ON 0 0 CNJ CNJ 0 0 CO O r H LO VD LO r \ i O r ~ oo CM VD r - r ~ oo O O r H 0 0 r - r H VD r - o 0 0 r H r H LO 0 3 CN] T f CM LO ON VD LO 0 0 0 0 LO r H T f CM 0 0 0 0 ON 0 0 0 3 LO T f 0 0 r H O O LO T f O r H r ~ r - CM LO VD r H T f T f CNJ CNJ 0 3 0 0 0 0 0 0 r H VD L O LO L O rH r H O r - r H r H r - 0 0 0 0 ON LO LO 0 0 0 0 r - r - r - 0 0 OO T f OO 0 3 0 3 oo r -r H o CM CM r H r H r H O o O CNJ CNJ rH r H r H r H O CM r H r H r H r H o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 CO oo 0 0 0 0 0 0 0 0 r o r o 0 0 oo VD VD VD VD r H r H r H r H TT CD T f 0M VD O CNJ 0 3 r H ON 0 3 CNJ Tf LO r H 0 3 CNJ 0 3 0 0 OO VD LO 0 0 LO o oo r H T f r - ON 0 3 r - LO 0 0 0 3 r H LO 0 3 CNJ T f LO r H [-- r — CNJ r -VD r H LO LO Tf oo CM r H r H r - 0 0 VD LO 0 0 CNJ 0 3 r - VD T f VD VD VD r o ON r H oo 0 0 0 0 oo 0 0 oo VD LO O 0 0 oo 0 0 0 0 ON ON ON T f O r - r - CNJ ON r— r H r H r H r - r - r - CO CO ON LO LO L O CO r - r - r - 0 0 0 0 T f Tf co O o CM CM CM r H r H r H r H r H O O o O CM r H r H r H r H O CM CM r H CO oo 0 0 0 0 CO CO CO CO CO CO 0 0 CO CO CO CO 0 0 0 0 0 0 0 0 0 0 0 0 CO CO VD VD r H r H VO O o o LO CO CO r> 0 3 r H r H l > r o r H T f LO ON CM LO r -CM VD CM 0 0 VD oo T f VD 0 0 0 0 CM ON co VD oo T f LO CM CNJ o O 0 3 T f ON 0 0 r H o ON VD 0 3 r - LO o LO T f T f r H O Tf r H VD oo o ON ON T f T f 0 0 ON CNJ CM CNJ T f O o o LO O 0 0 0 0 CO ON r - VD r H l > i > l > 0 0 LO LO LO 0 0 0 3 0 0 0 0 CO 0 0 T f oo r H O o o CM r H r H r H O o O o CNJ r H r H r H r H o CNJ r H oo 0 0 oo oo 0 0 0 0 oo oo 0 0 oo 0 0 oo oo 0 0 oo oo CO oo co 0 0 CN + II fe CN II fe o O LO VD LO 0 3 O 0 0 ON T f LO VD 0 0 O r H oo ON o r H co VD r H VD VD T f O LO LO ON oo O T f ON VD 0 3 T f CM T f CM o ON I"- O CM o ON VD VD CNJ rH O T f o r -CD ON ON o ON T f ON rM CNJ r H T f T f r H r H r H ON ON 0 0 ON VD VD CM r H L— 0 3 L O LO L O 0 0 0 0 0 3 0 3 0 3 L— T f 0 0 O O O CNJ CNJ rH O O o o CM CM r H r H r H O CNJ r H 0 0 0 0 0 0 0 0 0 0 0 0 0 0 r o oo oo oo 0 0 r o r o co r o oo oo VD VD VD VD VD r H rH r H rH r H r - 03 r H 03 T f T f VD CN] r - VD o o ON r H rH CD LO VD O T f T f oo r H CM oo oo CNJ VD ON LO CNJ CN] rH LO VD L O Tf CM r - O VD 03 o LO LO LO 03 r H rH rH LO rH ON ON ON VD CM [— r — r ~ 03 LO LO LO oo 03 [— T f o O CM r H rH r H O O o O CNJ rH O CN] oo 0 0 0 0 0 0 oo oo 0 0 oo oo r o 0 0 oo 0 0 OO CN CO -A II fe CN >TN i I—> II fe o o ON o T f o T f 0 0 VD rH CNJ LO VD VD 03 LO 00 r H 00 r - o ["-oo VD LO LO CNJ O o VD r H r H r ~ LO LO oo 03 r H r H LO CM CM T f ON [— l > oo 00 LO L O 0 0 03 00 r o o r H r H rH o o o CM r H rH r H oo 0 0 0 0 0 0 0 0 0 0 0 0 0 0 oo co r o VD VD VD VD VD VD VD r H r H r H rH rH rH r H [ CNJ ON 0 0 0 0 LO 0 3 OO [ 1 o o OO LO LO o o o ro oo oo VD VD VD L O L O o VD 0 0 CM 0 0 r -oo L O CM CO VD CN fe CO r o VD r o CM 0 0 VD CN ON II fe a CD B c cr cr SH tr a S H t r & S H t r & f t S H t r s H t r a M t? M tr a a t? r o oo oo T f T f T f T f T f T f LO LO LO LO VD VD CM CM CM rH rH rH CM CM CM rH rH rH CM rH rH 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a PJ PH cu Ol OH cu PJ PH CU PM cu PH Oi SH tr SH tr Pu Pu tr r H CNJ 0 0 0 0 Pj CU C N ON + PH LO rH CNJ i— CNJ ON o KO O [— LO 00 r— LO TP rH TP TT o o ro 00 00 KO o KO O CM t— LO t— TP VO TP O ro 00 00 KO oo KO oo TP 00 KO LO 00 CM rH MO LO O 03 rH ro LO t— CNJ o O at LO rH o o TP ro 00 cn CNJ VO r - CM 00 CM TT1 O rH rH rH TP TP lO LO LO rH rH O CN] rH CM rH O 00 rH rH rH rH rH rH rH rH CO ro ro CO ro 00 00 00 00 00 CO oo oo oo oo oo oo C N CN LT) fe CN C O fe C N fe C N fe C N C O -A II fe CN IT) I 1—5 I' fe CN -A II fe CN ON s4> ll fe <D £ < oo 00 TP rH OO 00 O 00 CM i — KO 1— O KO O i— oo co [— oo OO o O ro rH TP o CM rH 00 [— ON rH 00 CNJ ro KO oo ON ON CM rH IT- LO LO CM LO 1— 00 rH TP LO TP r - CM o KO O o ON rH TP KO O 00 CO ON rH O KO KO CM [— 1— 00 t KO ON CM KO [— CN] LO 00 CM 00 O CM rH CM rH ro oo LO LO CM rH rH O CNJ rH o CM rH O 00 rH rH 00 rH rH rH rH rH 00 ro 00 CO oo 00 oo 00 ro 00 00 00 00 00 ro ro 00 oo oo KO KO KO KO LO TP 00 o 00 VD O 03 c— rH LO TP o ON CM KO KD o CM KO oo TP r o rH 03 KD L— CO rH rH [— 00 oo O TP oo ON o CO rH rH ON CM r o CM rH rH rH O O [— ON ON TP ON CM O [— tr- CO KD ON ON oo VD CM TP 03 CM CO O CM rH r \ i rH CN] rH rH rH O rH o CM rH O CO rH rH r o rH 00 00 00 00 00 c o r o 00 00 00 00 00 CO 00 CO VD rH 00 CN] O ON CNJ CM 00 VD CM O ON O 00 O rH LO TP ON oo rH L— LO [— ON O rH v o VO LO LO L— 00 o TP [— O VO CD C— O o ON CM 0\] O ON oo ON ON LO 03 CM rH 00 00 00 KO ON 00 LO CM TP OO CM OO O CM rH CM rH CM rH rH O rH o CM rH o 00 rH rH r o rH 00 00 00 00 oo r o r o oo oo CO 00 00 r o 00 KO rH o LO o VD VD 03 TP ON O LO 00 rH o CM r o TP O CN] [— [— TP tr- LO LO TP [— ON TP t— CM LO c o r o i o i — VD ON 03 03 o LO 03 r o CM vo 03 00 TP LO CM TP cn CNJ oo o CNJ rH rH CM rH O rH O CM rH o r o rH CO rH CO rH 00 00 CO CO CO 00 CO CO CO CO CO CO VD VD rH rH rH CM ON rH CM VD CO TP r— r o 1— TP t— VD TP rH O LO rH rH 00 i — o [— t— ON ON oo LO o CO 03 ON ON c o CNJ 00 rH OO ON 03 rH VD ir- CM VD ON LO KD r o LO CM TP ON CM on CM rH rH rH CM rH o rH o CM rH o rH r o rH rH 00 r o oo oo r o r o CO oo oo c o CO 00 KO KD VD rH rH rH 1— TP rH 00 00 CM 00 O OO VD oo ON VD LO oo ON CM LO rH LO 03 TP LO OO TP 00 00 rH VO [— 00 ON KO LO TP ON CNI 00 CM rH CM o o CNI rH o rH rH 00 00 oo 00 00 oo 00 00 O CM TP O 00 LO t— TP TP TP o 03 CM 00 t— t— [— CM oo O 00 o 00 r o TP 00 t— CM L— TP O VD KD LO TP ON CM CNJ CM rH CNJ o o CM rH rH rH rH 00 CO 00 CO r o 00 00 00 KO KD rH rH TP [— ON LO vo t- TP 1— CM ON TP TP TP LO ON LO TP [— 03 03 03 r— L— CM [— VO O VO LO TP ON CNJ CO CM rH o o CM rH o rH rH 00 CO CO r o 00 CO CO vo VD rH rH TP LO KD LO 00 t— LO ON LO rH 00 [— CM 00 VD LO [— [— CM VD KO LO TP ON 00 CM o O CM O 00 oo 00 00 00 SH SH cr cr SH a, cr SH cr SH SH tt SH SH CT SH L— L— L— I — 00 00 OO ON ON ON o O rH rH CM CM o . O rH rH rH rH rH rH CM CM rH rH rH CM rH rH CNJ rH rH CM rH rH rH rH rH rH rH CM 00 r o CO CO 00 00 00 CO CO CO CO CO CO CO CO CO 00 CO CC Oi PJ a CC 0J cu CC PJ Oi CC DJ CC PJ cc DJ DJ DJ 241 CN O N + PH C N + H i II P H C N + P H CS CO + P H C N £ II P H C N C N CO I H i II P H C N I T ) I— II P H C N II P H C N ON I H i II P H VD M< 0 0 CM ON VD o 0 0 L O ON L O L O CM 0 0 L O o l> r~ VD ON o 0 0 VD L O 0 0 ON ON ON o m VD 0 0 o CM VD CM o VD o L O ON 0 0 VO o 0 0 VD 0 0 o VD 0 0 VD r-~ l> o 0 0 VD ON r- 0 0 oo CM oo 0 0 o o o rH o o o rH r- r~ l> ON o ON ON 0 0 co o O o o rH rH rH 0 0 rH rH rH 0 0 rH rH rH r~ oo rH r- [— CM CM ro 0 0 oo ro oo oo oo CM oo oo oo OJ oo oo oo OJ CM 0 0 OJ OJ oo 0 0 ro 0 0 0 0 ro 0 0 0 0 0 0 0 0 oo oo oo oo oo oo ro oo oo ro oo oo oo oo ON VD VD ON VD VD 0 0 VD ON ro CO VD VD VD l> o ro ON 0 0 o OJ CM 0 0 OJ CD ON o ON r- VD ON [— CM rH o VD CO rH r- r- o 0 0 CD ON rH VD r~ o VD ON CM VD VD r- O oo r- o oo VD oo L O ro VD r- rH L O o rH OJ OJ VD ON o o 0 0 L O rH CM L O L O L O rH rH rH CM rH rH rH CM OJ ro CO 0 0 o o o o CD o o o •sp M< o O o o o o rH rH rH 0 0 rH rH rH CD CD rH rH rH 0 0 oo CD rH rH 0 0 CD CD OJ CM ro 0 0 0 0 ro 0 0 0 0 0 0 ro ro CM ro ro 0 0 CM Ol ro ro ro CM CM CM ro 0 0 CM CM OJ 0 0 0 0 ro oo 0 0 ro oo 0 0 0 0 oo oo ro 0 0 ro ro ro 0 0 0 0 ro ro 0 0 0 0 0 0 ro oo 0 0 oo ro oo 0 0 J VD VD VD L O o VD L O o VD [~- r- L O CTl ON r- VD oo o ON L O ON VD rH ON L O o rH oo VD r- 0 0 VD r- rH o ON CM o o L O r- r- 0 0 o 0 0 ro CM ro r-- ON r- ON oo L O VD 0 0 CM L O VD 0 0 rH L O VD 0 0 oo cn VD VD vo VD VD VD CM CM CM CM ro ro OJ CM CM oo ro 0 0 0 0 oo o oo o o o O o O o o rH rH rH 0 0 0 0 0 0 rH rH 0 0 0 0 0 0 rH rH rH 0 0 rH 0 0 0 0 ro 0 0 0 0 ro 0 0 0 0 ro ro 0 0 CM OJ OJ 0 0 0 0 CM CM CM 0 0 0 0 0 0 CM 0 0 OJ CM 0 0 0 0 0 0 ro 0 0 0 0 ro ro 0 0 ro ro oo oo oo oo 0 0 ro 0 0 0 0 0 0 0 0 0 0 ro 0 0 VD VD rH rH r- r- r- r- r~ r- rH rH r- r- o o 0 0 rH ^ r- VD ro r- OJ 0 0 [— CM 0 0 o CM rH [— VD L O •sr VD L O oo VD 0 0 o CN 0 0 o CM o 0 0 0 0 o rH r- CM o rH CM D-- CM o 0 0 0 0 r~ 0 0 0 0 0 0 0 0 •sr 0 0 0 0 0 0 •sr CTl ON ON rH rH o o O o o o rH 0 0 CO rH rH CD CD rH rH rH CD CD ro oo ro oo 0 0 0 0 0 0 CM CM 0 0 0 0 CM CM oo 0 0 oo CM CM 0 0 0 0 ro 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 VD VD VD VD VD VD VD VD VD rH rH rH rH rH rH rH rH rH L O o L O ON VD 0 0 rH 0 0 r- rH ON 0 0 r- oo ON o rH 0 0 oo oo o CM r- VD VD o ON oo ON L O r - ON r~ ON VD L O r- 0 0 •sr L O 0 0 ro I— 0 0 rH oo oo •sf oo -5f -=r ON ON ON ON rH rH L O rH rH 0 0 0 0 rH CD 0 0 0 0 rH rH rH rH 0 0 0 0 CM oo oo CM CM oo OJ OJ CM oo ro ro ro OJ OJ oo oo 0 0 oo oo oo oo oo oo oo ro ro ro oo oo oo VD VD VD VD VD VD VD VD rH rH rH rH rH rH rH rH ON r- r- rH oo rH VD ON ON m o rH oo •sr oo rH rH rH 0 0 rH o OJ VD r~ •=r L O L O •vf L O L O ON ON rH ob 0 0 rH 0 0 0 0 rH rH ro CM CM oo CM CM oo ro ro oo oo oo oo oo 0 0 ro VD VD VD VD VD VD VD VD rH rH rH rH rH rH rH rH n o* n, w tr a u t r f t H t r a n t j a M t r a M t r a M t r a M t r H t r f t n tr rH rH . CM CM CM CM 0 0 0 0 0 0 0 0 T 0 0 •sr cc "St" CC 0 0 •sr CC ro a CC CH ro CC ro cc CH ro CC 242 -a CD o O CD CN O Y + CN + PH CN + PH CN co + PH CN £ II PH CN II PH CN CO I H i II PH CN I J O I H i II PH CN Fp H i II PH H i II PH rH CO CM co 00 m o m CM m m o VD CM VD CM o rH r— rH 00 VO ON o o 00 o CM 00 00 CM CD LT) VD IT) m OJ o rH r - ON rH o rH •sp ^ p 00 •ST 00 00 00 ON m ON ON OJ ^ rH ON 00 00 r - rH r~ OJ CM r~- CM [> OJ OJ o r - o 00 00 r - 00 VD 00 VD m OJ 00 ro OJ oo OJ 00 ro OJ OJ OJ 00 ro OJ 00 OJ 00 CM OJ 00 00 00 00 00 00 00 ro 00 ro ro ro ro 00 00 00 00 00 00 vo vo VD rH rH rH CD O 00 o vo ON r- oo in •sr •sr ON OJ ON o CO (Tl ON rH CD o m ro vo ON m o r - OJ OO m CO O CD o ON rH CO ro ON o ro OJ CN VD m VD •sp CD CD ro •sp o CD ON ON ON •sr m CM •sp •sp rH ON 00 00 r~ r- OI OJ [> r- OJ CM OJ r- r- r— oo oo r-~ oo VD oo <N OJ ro 00 OJ CM 00 ro CO CM CM CM 00 00 OJ 00 CM 00 ro 00 ro 00 ro ro 00 00 00 00 00 00 00 00 00 00 ro 00 VD o rH rH rH ON ON r - m CM CM CD r - VD VD CD m OJ 00 •sP •sP VD ON O oo r- CM ro oo o 00 m 00 m 00 r - r - m 00 ^ ^ p CD o m ON m CM •sP rH ON 00 r - CM Ol r~ 00 o CM r~ r~ 00 r- ro oo OJ oo ro OJ oo OJ ro CM CM oo CM ro oo ro oo ro oo ro ro ro ro ro oo ro ro oo VD VD vo VD VD VD VD rH rH rH rH rH rH rH ^ p OJ oo r- CO O r- ro vo rH oo o ON CO ON rH m r-o rH VD OJ o CM m oo vo ON ON 00 o VD m •sP ON CO r~ r~ r- ro r- ro ro co oo OJ OJ OJ ro CM ro ro oo ro oo 00 00 ro 00 ro ro 00 ro vo VD VD VD vo rH rH rH rH rH r- ro 00 rH 00 -sP ON ON r - r-CM CM oo oo VO VD o ON in in oo oo oo vo U X T C U U X T U V S X n t r u c r u t r a <sp ^ ^p in in uo uo SH CT SH CT CT o in ON ON oo oo oo o vo o o •oo oo ON 00 00 00 OJ o oo oo VD cr oo ^ p Ol •sP ^ p CC ^ p ^ p Oi oo oo ^sf •sP ^P ^P CC CH CC ^ p •sp CH oo oo -sp •sP "Sf1 "SP OH CH OH SH cr M cr r - r - r - c— oo oo ^  -sP -st1 CH OH Oi PC CH CH 243 CN ON PH C N C N + PH C N C N + PH C N PH C N r - ON CNJ VD •sr r - ON •sr rH VD oo ON ON co CM 00 00 rH ON ON 00 00 o 00 VD VD 00 O O O VD vo [~ ON OD rH o VD VD 00 r~- ro LO r~- 00 00 00 CM LO CNJ 00 00 LO o LO LO LO CM oo rH ON ON ON oo CM rH rH CD CD vo -SP oo VD VD VD M< oo VD VD VD [— •sr ^ 00 CD 00 00 00 00 00 CD 00 00 00 00 00 00 00 00 00 00 00 uo LT> LO LO LO LO LO LO LO LO LO LO LO LO LO m LO LO LO cn rH ON ON VD O VD o 00 o 00 O l oo o r~ o ON rH CM oo o VD rH 00 o ON O rH 00 00 VD CNJ rH r— •sf rH LO o ^ j - LO CM ro LO LO CM LO ON rH oo rH r - oo rH oo LO r~ r~ rH ON VD r - 00 o r - oo ON o LO LO LO VD VD CNJ r - r - r~ LO 00 o o o LO oo oo oo CNJ CM CD CD VD ^ 00 00 VD VD VD 00 CO r- r - r- •SP r - [-- r- M< CO OO CO CD 00 CD 00 00 00 oo 00 00 CD CD oo 00 00 00 00 00 00 00 oo 00 LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO U0 LO LO VD rH VD rH VO rH CNJ CD LO ON CNJ LO o rH LO ON ON CM 00 LO LO rH LO oo LO LO [-- r - CNJ co ON CNJ ON ^p O l> LO ON o r~ CD r~ o o CM rH VO ro CM rH rH 00 ON 00 LT) CD 00 O VD [— LO ON o CNJ LO CM CM LO LO i > 00 CM vo LO VD VD ON oo CD VD VD 00 00 00 00 LO CO ON ON VD VD rH rH rH LO m LO ro 00 CM oo CD VD VD 00 oo VD VD vo ^i" ro 00 r- [— r- CM CM r- r- r -CD 00 00 00 00 00 CD CD 00 00 00 00 00 00 00 00 00 oo oo 00 oo 00 00 00 00 00 00 LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO VD VD VD VD VD rH rH rH rH rH 00 00 VD rH oo rH oo oo oo r - CNJ CM CM LO oo rH VD ON o LO vo rH CM ON rH 00 oo CO 00 ON r-- LO LO ON ON 00 LO ON rH ON rH 00 l> ON VD l> ON ON LO r-~ VD rH CNJ oo ON rH oo ON o rH CM LO 00 rH rH CM r~ ON l> r~ r - ON ON VD O o o r - 00 r - rH CM CM VD VD 00 i O LO 00 oo CD VD VD -SP 00 r-~ [-- r- ^> 00 r - r- r - CM CNJ CM r - r -CD 00 00 00 CD CD oo 00 oo 00 00 CD 00 oo 00 oo 00 oo 00 00 00 00 00 00 LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO CD VO VD VD VD VD VD VD VD VD VD VD VD VD VO VD vo vo rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH CM 00 o ON VD CM 00 rH r - 00 LO vo VD ON vo 00 CM CM CM VD ^ r~ r~ IT- CM CNJ 00 oo CD 00 00 CD LO LO LO LO LO LO VD vo VD VD rH rH rH rH r- oo CM [-- LO 00 CM r~- r~ LO -sp •a 1 CM 00 CD 00 LO LO LO VD VD VD rH rH rH C N m i H i II PH C N m H i , II PH C N • H i P ^ C N ON H!> PH C <U B c ' t o c« 244 fN ON PH fN + II PH CN >TN .+ PH CN fe fN II fe CN i i—i I  fe fN co t-A II fe fN IT) I II fe CN c-^  A , II fe CN ON i •-> II fe CD .SP rH [— TP LO ON VD LO TP IT- 0 0 ON oo rH oo IT- r— oo oo TP ro Tf CM CO CO rH rH oo VD CO CNJ TP rH C— rH CD [— TP ON CN 0 0 rH CNJ CNJ co 1 — ON ON o [— oo [— OO CM TP ON o TP ON TP ON LO CNJ ON ON 0 0 0 0 ON o ON ON TP TP LO LO co TP VD VD ON o r— TT1 [— r— oo oo IT- 0 0 oo oo OD OD co oo 0 0 OD oo 0 0 CD oo 0 0 0 0 0 0 OO 0 0 oo CD 0 0 0 0 OD 0 0 OD 0 0 oo oo oo CD C— CD oo LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO VD LO ro CNJ o ON ON ON o LO rH ON LO [— rH C— LO CM o t— 0 0 CO t— CM rH CM LO rH VD CO TP TP o CN] TP o o 0 0 0 0 TP 0 0 o r - LO 0 0 LO TP VD rH [— VD ON t— 0 0 rH oo LO 0 0 TP o rH rH O rH VD 0 0 CM 0 0 0 0 VD rH CM TT LO CNJ CNJ ON ON ON ON ON o o o o o LO LO LO LO TP TP [— ON rH rH CNJ [— TP TP IT- t- 0 0 0 0 0 0 0 0 0 0 TP TP TP 0 0 0 0 0 0 0 0 CD 0 0 0 0 CD 0 0 0 0 0 0 OD 0 0 0 0 CD 0 0 CD CD 0 0 0 0 CD CD CD CD CD 0 0 0 0 oo oo 0 0 c— 0 0 OD OO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO L O LO LO L O LO LO LO LO VD VD VD VD rH rH rH rH CTl O r- o VD oo CM TP 0 0 VD o 0 0 VD co oo oo ON o co t— t— 0 0 CNJ co oo CM co ON ON [— t— LO ON CM TP LO CM o t— CM CM [— rH CNJ oo Tf CNJ 0 0 VD IT- co TP 0 0 ON o rH LO VD ON L O TT Tf LO VD VD VD o ON o CD o o LO LO VD VD TP TP VD rH Cs] CNJ CM [— IT- IT- 0 0 co 0 0 0 0 TP TP 0 0 oo oo ro OD 0 0 co 0 0 OD 0 0 OD oo CD CD 0 0 0 0 0 0 0 0 0 0 0 0 0 0 oo OD 0 0 oo 0 0 0 D 0 0 LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO L 0 VD VD VD VD VD rH rH rH rH rH CTl VD i— o 0 0 rH [— rH VD VD rH c— 0 0 OO ON O lO O ON ON VD LO 0 0 LO CNJ t- CM LO 0 0 VD VD LO 0 0 r- 0 0 VD VD VD CM r- oo VD t— 0 0 rH O VD [— LO LO LO VD 0 0 o o o o LO LO VD C— o rH rH CM CNJ CM t- TT1 OD TP TP TP 0 0 0 0 oo oo ON CO 0 0 OD 0 0 0 0 0 0 OD OD 0 0 0 0 0 0 0 0 0 0 oo oo 0 0 0 0 OD LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO LO VD VD VD VD VD VD rH rH rH rH rH rH O rH rH rH ON 1 — TP TP 0 0 LO TP ON VD OD [— r— oo CM r— rH L O L O t- rH t— TP rH 0 0 o rH o o ON ON LO ON CNJ 0 0 ON VO VD r- [— rH rH LO LO VD TP O rH rH CM CM c— t— TP TP 0 0 0 0 oo 0 0 ON 0 0 oo 0 0 0 0 0 0 0 0 OD OD OD OD CD 0 0 OO 0 0 0 0 LO LO LO LO LO LO LO LO lO LO LO LO LO VD VD VD VD VD VD VD VD vo CM TP rH PH 0 0 0 0 0 0 VD LO oo [— 0 0 ON o I— oo rH t— ON VD IT- VD VD VD CNJ IT- 0 0 CO OO 0 0 0 0 0 0 0 0 0 0 LO LO LO LO LO VD VD VD VD rH rH rH rH o IT-CD OD LO VD O 00 VD 0 0 0 0 LO CM TP VD 0 0 L O VD o LO VD LO vo M t r f t H t j ' f t L i t j ' v i t j ' a H t r M t r a H t T H t r a CO 00 C O C O T P T P T P T P H tr tr ft M u tr ro rH P H CO rH Oi TP rH TP rH Oi CO r H CC CO rH Oi TP rH CC TP rH cu ro rH cc LO LO LO LO 0 0 0 0 T P T P rH rH rH rH CM Cu CC 0> 245 -o o U i n <u cl H fN 0\ PH C N '5 PH. CN IT) .+ PH CN + PH C N + H i II PH C N i - i II PH C N m ll PH C N in i-i II PH C N Fp 1-1 II PH C N Os H i II PH c B « , 'co co CTl 00 rH CNJ 00 VD r - r - cn CTl o VD cn 00 O LO LO VD rH O 00 ^P 00 CTi ON l> 00 rH 00 rH r~ CNJ LO LO CTi l> o LO rH 00 00 00 CN] CN] CO CNJ VD VD cn 00 00 00 00 00 CD 00 00 LO iO LO LO LO LO LO LO LO iO VD VD rH rH 00 CTi •SP r - 00 VD rH ^P CTi VO O P^ 00 VD LO •=P l> 00 00 LO VD o O ^P LO CNJ CTi rH r - CNJ VD O O O LO rH 00 00 00 CNJ CTi VD VD VO CTi 00 00 00 00 00 l> r - l> 00 m LO m LO LO LO LO LO LO VD VD rH H LO CNJ rH rH •SP VD H o o CNJ VD rH o P^ ID r-~ 00 CNJ CNJ r - O rH r~ CNJ vo O o CNJ oo cn 00 CNJ cn VD ON 00 oo 00 CD 00 l> 00 LO LO LO LO LO LO LO VD H 00 CNJ VD CNJ LO CTi rH 00 00 l> "SP 00 00 CD CTl 00 00 rH rH r~ CNJ o o CNJ 00 00 oo CTl VD CTl OO 00 00 CO [-• 00 LO LO LO CO LO LO VD VD rH rH [-- l> o 00 l> p^ o CT) CNJ CD O CNJ VD r -L O vo o oo CNJ VD VD LO VD O 00 00 00 00 LO ^P 00 00 LO VD CTi r— VD O CTi 00 LO VD SH tr tr a, a . . , , , LO VD VD VD r - r - 00 ^P 00 oo ^P 00 00 00 "SP oo rH rH rH rH rH rH rH rH rH Cd CC CC a OJ PM CC 2 4 6 C N O s + PH CN PH ^r1 LO rH rH uo cn r - o rH U0 VD 00 00 CM vo vo cn r~ oo r~ rH VD r - cn cn r - o ro uo CD CD o 00 cn rH vo VO 00 r - vo r - CM CM rH r~ oo CO VD rH cn t> CTi 00 VO o cn i > cn cn UO t^< cn CM cn 00 00 CM t> r~ r - vo VD CD co 00 uo ^ cn cn r-~ CM CM o o cn cn CD cn ro CM CM CM r~ CM CM CM cn cn CM CM CM tH rH uo uo rH rH CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM 00 oo CM CM CM CM CTl cn cn cn cn CTi CTi cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn VD vo rH rH LO cn LT) r~ CTi ro 00 VD vo cn r- o o 00 •sr r - o r - rH r~ oo CM CD rH CD r~ cn r~- O UO rH •SF 00 i> vo uo o cn uo ^i- CM rH T—i VO rH cn cn cn O cn VD ro rH vo M< CM o o vo uo 00 00 00 i> vo 00 ro VD i> o cn CD UO cn CTi cn uo uo o UO UO uo 00 00 00 vo vo o o o cn H rH rH rH vo uo UO CD cn cn ro CM CM CD ^ " CM CM CM cn cn uo uo uo CM CM CM rH rH uo UO uo CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM 00 oo CM CM CM cn cn cn cn cn CTi cn cn CTi CTi cn cn cn cn cn cn cn cn cn cn cn cn cn cn m cn CN m + PH CM cn 00 o r~ rH cn vo cn o CM CM rH VD o r- r - o cn o o vo •sr r - cn ro CM o vo cn ro cn CM LT) cn VD cn rH CM cn o rH uo rH oo VD o cn cn ro rH VD oo r- vo ro r - cn cn 00 vo rH o o 00 H VD VD VD CM r- r - rH rH rH o o o CM VD VD VD VD CM CM 00 M< CM cn cn UO UO UO CM CM CM rH uo uo uo CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM 00 CM CM CM cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn CN C O + PH 00 o 00 cn VD CM 00 r~ uo oo oo o oo 00 rH uo o oo o UO rH CM o rH r - uo o o 00 uo •sp VD vo cn 00 VD r - o vo o r - rH o cn o oo rH o r~ VD uo 0- vo uo vo r~ VD VD r - CM rH oo oo CM oo r - r - r - rH CD 00 CM CM CM cn cn cn oo r - r - t> vo •sf CM CM CM 00 M< CM cn cn UO uo UO rH rH rH rH uo uo uo CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM oo CM CM CM cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn vo VD vo vo vo VD VD VD vo VD vo VD C N II PH 00 rH CM 00 cn oo vo » CD cn cn oo rH rH r~ 00 rH o CD rH uo r- cn 00 r~- CM rH rH ^p oo 00 CM oo r- r - r - oo oo 00 "SP CD oo 00 00 ^p -=p uo uo U0 rH UO UO uo CM CM CM CM CM CM CM 00 CM CM CM cn cn cn cn cn cn cn cn cn cn cn C N lA II PH CN C O II PH CN >n II PH cn VD uo ro M< ^p VD rH t> rH uo vo VD r - oo rH VD ro ^p o M< cn 00 ro CM •=p 00 r- VD o cn 00 r-•sp 00 CO ro cn ro ro uo CO 00 00 00 ^ oo cn uo uo H uo uo uo CM CM CM CM CM CM CM oo CM CM CM cn cn cn cn cn cn cn cn cn cn cn vo VD vo vo VD VD VD rH rH rH rH rH rH rH vo CM VD VD VD rH ^p o CM rH UO oo o uo cn o UO rH uo 00 CM 00 CM cn cn cn cn VO rH ro CM 00 VD CM o uo cn vo o uo cn o rH uo ro ro CM cn m cn C N o PH ro cn C N O S CM 00 CM VO PH 00 cn 8 1 M n tr&M tro, M u t T ' O i H M t j ' O i H f f M c r a a M c r c ! , M tr M tr a. M tr 00 < CM CM cc cn CM CM CC CM CM CM O rH CM CM CM CU OH CM OH rH rH CM CM CM CM Oi Cu OH CM OH CM CM CM OH 247 C N ON + PH CN + PH CN " J O + PH CN oo + CN II PH C N II P H CN CO I I—s II PH CN wo PH CN c— • I—j II PH CN ON I H i II PH CU op LO o ON r - KO 0 0 r - oo r - CM VD o oo ON 0 0 a t oo TP r H r~ 0 0 ON o c— L O r - KO TP r H r - ON r - TP CM TP r - r - L O oo L O TP TP l O CM L O L O oo [— O r H CN] co CM TP co TP TP CO o r H ON 0 0 TP CM r H CM L O L O ON ON VO O O TP TP TP TP TP 0 0 0 0 0 0 0 0 ON r H r H L O TP TP CNJ CNJ L O LO CN] TP TP VO VD CNJ L O L O VD VD VD VD r H 0 0 0 0 I-- ON at CO CO CNI CNJ CNJ CO CO CNJ CM CNJ CO CO CM CNJ oo oo CNJ 0 0 CO CM 0 0 CO ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON KO KO 0 0 0 0 L O CN] 0 0 r H f - TP o r H 0 0 0 0 ON oo L O VO TP r H CM r - L O L O r H 0 0 TP r - TP O 0 0 O TP L O ON L O TP ON KO TP TP L O CM o oo o KO r— ON 0 0 r— CN] 0 0 0 0 0 0 CM L O 0 0 TP 0 0 o r H ON ON co TP r H r H CM KO KO o o o r H r H L O L O L O L O L O L O ON ON ON CNJ O CM CM vo L O l O CNJ CNJ KO KO vo TP TP VO vo VO CNJ L O L O VD VD VO I — CM 0 0 0 0 [— a t ON CO 0 0 CNJ CM CN] 0 0 0 0 CN] CM CNJ CM 0 0 0 0 CM 0 0 CO CM CNJ oo 0 0 CM 0 0 0 0 ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON a t ON ON ON ON ON ON KO r H TP o 0 0 r H 0 0 O r H CO CM ON O CO o 0 0 ON VO O a t oo TP r - CM r - L O TP KO CNJ ON CNI TP r H r H TP 0 0 r H TP o CNJ L O O O CO 0 0 TP VO vo 0 0 ON TP r H KO [— r - r— KO CM CNJ r H o L O 0 0 TP 0M r H r H TP O o r - 0 0 CM CO 0 0 o r H r - [-- r H r H r H CNJ VD VD VD VD VD VD o O O TP o o oo r H oo oo VD VD VD CNJ OM vo KO KO TP VD VD VD OM L O L O r - [— [— CNJ r - c - t — CM 0 0 0 0 r - ON ON co 0 0 CNI CNJ CN] co CNJ CNJ CNJ CNJ oo 0 0 CM CM CM CNJ 0 0 CO CM CM oo co CM oo 0 0 ON ON a t ON ON ON ON ON ON ON ON ON ON ON ON ON ON at ON ON ON ON ON ON ON VD VO VD r H r H r H TP co 0 0 TP 0 0 co CO TP r H 0 0 TP r - O VD r H r H co VD 0 0 CM o VD TP ON oo VO O CNJ 0 0 f - TP 0 0 0 0 r - ON TP ON r - CNJ VD ON L O CM L~-L O L O L O TP TP o O o ON 0 0 0 0 oo r H CNJ 0 0 0 0 ON TP o r H VD OO CO 0 0 CNI CNJ CNI ON ON oo VD VD vo !"- r - r - O o o TP TP TP r - VD CNJ CNJ KO VD KO CNJ CNJ TP VD VD VD CNJ L O L O c— [— r - [— 0 0 OO IT— ON CO CO CN] CNJ CNJ CNJ CN] oo CNJ CNJ CNJ CNI co co CNJ CO CO CM CO oo CM oo ON a t ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON VD VD KO VO VD VD VD vo r H r H r H r H r H r H r H r H f - oo co O CNJ r - 0 0 r H r - ON L O o VO o c— oo ON 0 0 I—• TP 0 0 co CNJ vo 0 0 TP co r H 0 0 L O L O TP ON L O L O VD 0 0 CM VO ON co co [— [— [— [— r H r H r H TP OO l—• CNI KO TP VO VO VO L O r - [— r - 0 0 L—• ON co CNJ CO CN] CNJ CNJ oo CNJ CNJ oo 0 0 CM oo ON ON ON ON ON ON ON ON ON at ON ON ON VO KO r H r H co CO [— LO ON CNJ o r - ON L O CM L O ON o ON CN] 0 0 r H r H O L O TP ON ON r - TP r H O VD 0 0 r - LO CO ON ON oo TP 0 0 0 0 0 0 CM L O L O 0 0 CNI CNJ vo TP VD VD L O [— L—• 0 0 ON CO CO CNJ CO CNJ CNJ CO 0 0 CM 0 0 CO at ON at ON ON ON a t ON at ON ON KO r H TP L O o KO r H CNJ TP TP o L O ON TP 0 0 CNJ L O L O O o r H CNI r - o VD r-TP L O r H o VD CM a t r - r H TP r - ON o o TP L O 0 0 ON CM TP VD ON r H 0 0 CO 0 0 KO TP KO L O r - CNJ 0 0 r - CM ON co oo CNJ 0 0 CM 0 0 CO CM CO CNJ CM co a t ON a t ON ON ON ON ON ON ON ON ON KO KO VO VD VO r H r H r H r H r H TP KO ON o CM CO VD o co CNJ CNI L O r H TP LO CM VO TP ON L O ON r - TP VD r - 0 0 L O o L O 0 0 ON oo VD VD ON ON co TP VO L O r— r - 0 0 r— ON co CO CM oo oo CNJ oo CNJ co ON ON ON ON ON ON ON ON ON VD VD r H r H CO r H r - L O ON 0 0 o 0 0 TP ON r H r - 0 0 TP o TP CNJ 0 0 r H 0 0 0 0 o CM O r H L O o oo 0 0 r - r~ O CO TP vo r - I — r - 0 0 O 0 0 0 0 0 0 CN] CO CM 0 0 TP ON ON ON ON ON a t ON ON VO VD r H r H r - L O CO r H L O CM ON TP VO O TP L O r - l> TP r H L O TP CNJ 0 0 TP r H KO ON o TP r - o oo TP VD VD r - o o oo 0 0 CNJ oo 0 0 CM TP ON a t ON ON CJN ON ON H tr SH tr tt tr tt SH tr SH tr a tt SH tr SH tr tt tt SH tr tr tt SH tr tr tt SH tr L O L O L O vo VO VD r - r - r - 0 0 0 0 0 0 ON ON ON O r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H CNJ CNJ CNJ CNJ CNJ CM CM CM CNJ CNJ CNJ CM CM CM CM CM vc cu PJ VC Csi DJ vc o> PH vc cu DJ CC cu PJ VC 248 -a CD o U VO CD CN O N + P H CN + H i PH CN i n + PH CN CO + H i I  PH CN + H i I  PH CN ni I  PH CN CO Hi, I  PH-CJ in H i I  PH CN Hi, I  PH CN O N H i I  PH in CN] o UO o O O 00 00 r- 00 00 o C O ON r H m m 00 CD oo r H r H ON C D CD 00 ON r H o 00 i> o o o r H CN] oo oo CN] CN] m CN] CN] CN] CNJ CN] CJN ON ON ON ON ON ON ON ON CD CD CD CD r H r H r H r H CM o CD CD 00 00 C D m oo OO oo o ON oo m CNJ CD r- m C D i> ON o m m o o ON ON C D r H o m oo o ON oo r-o ON m ON ON m m CD o ON o oo ON CD OO C D CNJ ON CD ON CNJ 00 CNJ •sr ON 00 o o o ON r— CN] CD m CN] CSN ON m i> oo 00 o oo C N " 3 1 ON ON l > CN] ON 00 ON m CN] UO 00 ON ON oo CNJ 00 ON oo oo ON m oo oo oo •=3" ON C D CN] m oo ON oo m r— in oo ON CN] CD 00 ON oo oo CNJ CNJ ON ON CD CD CN] CN] ON C D H tr ct, M tr a a, rH CN] oo o o o rH rH rH CNJ CN] CN] rH rH rH rH rH CN] CN] CN] CNJ CN CN] CN] CC CC CC CC PH PH 249 -a 3 o i PQ CD +-< u c2 CO CD _ £ CD Ci S3 CD eu i ? C D a .2P 'co C O r-CD \1 H C N ON" fe C N fe C N J l fe C N CO + fe C N + >—> II fe C N i fe C N m r - i II fe C N CTl r-i II fe C N i I—> II fe C N ON l-i II fe r - r - i oo o m H C D C M O r - r» r -CO CO CD r H r H r H CM CM CM ^ ro H ro CM O CD t- O CD CD LO ro o uo ON dl CTl CTt r- uo ON oo ro oo oo CO CO CO Tf r H r H r H r H CM CM CM CM rH rH CM CM ON LO r - LO o o CM O rH O LO i—I •sP OO 3^* O ON ON LO T 1 -sr H H H CM CM CM r -rH CM CD CM ON -sr CD [— L O CM CD 00 ON LO rH rH rH O O CM CM CM CM CM r - r - c— c— r -C D C D ON 00 ON ON LO ON rH O C D o o o rH o C D 00 C M C M ro ^F •SF C D o 00 C D C M ON C D 00 00 UO C M rH rH [-- I 1 r -00 rH ON IT- LO rH O TF C M rH LO o o r - TF r o C M C M rH o C D 00 C M C M TF TF 00 00 00 CD rH rH 00 00 r o o o C D 00 ON rH OO OO o o U0 UO O ON ON ON C D C D ON H rH rH C D C D 00 rH rH rH rH rH rH rH H rH rH rH rH o C M C M C M rH rH o C M C M C M C M C M C M C M C M C M C M C M C M C M C M C M C M C M C M C M 00 O Ml r - u o ro UO rH r o UO C M TF UO ON 00 OO ON C D ON o o rH C D CO C M C M o C M UO rH 00 C D C D 00 O 00 00 O U0 00 r -00 iO 00 C M rH 00 UO C D C D TF 00 C D TF C D T F r»o 00 TF rH o •SC -sP M< •SF C D LO UO C D ON ON C M C M C M r - TF TF TF ON ON 00 rH 00 00 00 UO UO UO O ON ON C D C D C D ON rH rH rH C D C D 00 rH rH rH rH rH rH rH rH rH rH rH rH rH o C M C M C M rH rH o C M C M C M C M C M C M C M C M C M C M C M C M C M C M C M C M C M C M C M C M 00 LO ro m t— 00 rH U0 ON ON C D [-- 00 00 r o TF r - O O ON C M 00 00 LO U0 r - TF OO OO [— OO LO OO o o TF ON o r o O 00 LO CM CD 00 o C- LO TF LO TF 00 IT- U0 TF C D o o r o r M C M O C M 00 LO LO LO r - C D CD U0 O O O CO 00 o o C D u o u o LO O O [--rH 00 00 00 LO LO LO o O O O C D C D C D ON rH rH rH r - r - 00 rH rH H rH rH rH rH rH C M C M C M rH rH rH O C M r M C M rH rH o C M C M C M C M C M C M C M C M C M C M C M C M C M C M C M C M C M C M C M C M C M 00 C M •=F 00 C - TF rH r o UO ON TF rH 00 U0 r - rH C D ON r o r -C D r o o o C D o o r o 00 00 OD rH 00 TF rH r o C D 00 C M TF r o C M 00 00 C M r- UO 00 UO 00 C M C M •st" ro C M 00 rH o O o ON 00 LO C M C D C D C D r- 0- r~ TF rH rH rH TF TF TF LO C D C D C D rH o o C D rH 00 00 00 UO UO UO o O O O C D C D CD ON rH rH rH r - r - r - 00 rH rH rH rH rH rH rH rH C M C M C M rH rH rH o CM C M C M rH rH rH o C M IT-CM C M CM C M C M C M CM C M C M C M C M C M C M C M C M C M C M C M C M C M C M rH rH C D LO rH IT- C M TF LO r o O C T i 00 C M TF ON T F ^F rH C D ON OO rH OO 00 UO ON C M CD C D TF r - O TF 00 C D rH O ON ON C M o ON r - O ON CD O ON 00 rH 00 l > C D LO ON r - CD C D o o 00 r - o o C M rH rH UO TF TF U0 CD C D C D rH UO 00 OO 00 U0 U0 u o o O O O CD C D C D ON H rH rH r - C D rH rH H rH rH rH rH C M C M C M rH rH rH o C M C M C M rH O C M C M C M C M C M C M C M C M C M C M C M C M C M C M C M C M C M C M C M t— r -H rH C M 00 ON TF rH O r - UO TF 00 r - 00 00 O C D OO O C D •sp ^F OO rH ^F O t— rH UO rH rH 00 TF C M 00 C M TF [— o rH LO •SF C D UO 00 LO TF UO TF o o C D 00 C M C M rH o o [-- r - [-- 00 00 o o C M C M U0 U0 u o ^F r - r - r - C M C M C M LO o o 00 00 UO UO o O O C D C D C D ON rH rH rH r - r - [-- 00 rH rH rH rH rH rH C M C M rH rH rH o C M C M C M rH rH rH o C M CM C M C M C M C M C M C M C M C M C M C M C M C M C M C M C M C M C M r - r - r - r - r — [— r — r — r - r - [— r -rH rH rH rH rH rH rH rH rH rH rH rH O UO UO O r - C M 00 M< O [— 00 C M C M o o 00 r - C M r- UO •SP rH LO LO ^F r - C M C M LO C D C D ON rH r - r - 00 rH rH O C M rH rH o C M C M C M C M C M C M C M t— r - r - r - r -H tr p, ci t r c , u M ON O CM [— M tr a, H tr a H U tr CH H tr ft M M tr ft n tr a M 00 oc 00 CM CM rH 00 00 00 cc a cc 00 a O l ro CH ro CC ro CH CM ro CH ro CC oo CH 250 CN II PH CN PH CN PH CN cn PH CN £ II PH CN r - ON 00 OO ON ON O ON T f L O O ro CD OO r - 00 r H l> 00 ON r H r H r H T f CN T f O ON CO ON CSN ON r H CD ro r -o ON r - CO T f 00 00 l> T f L O O ON CN r H l> 00 CD o 00 r - T f T f CN CN O O CD CD o r H ro CD 00 o CN 00 CM CN I — t> T f T f 00 00 L O 00 r— ON 00 ON o CN ro ro CM CN r H r H CM CM r H r H CN r H CN r H CN CN ro ro oo r H CN CN CN CN CM CN CN CN CN CN CN CM CN CM CN CN Cd rM CN C<0 r-i I  PH CN cr> i H i II PH CN n i II PH CN ON n i I  PH cu £ op < CD O 00 ro o T f ON O 00 rH r - 00 rH rH l> r~ L O o r -r - O ON ON o CD ON Tf UO 00 rH CM oo r - o L O r - rH CD o O r~- CO CO 00 CN 00 r- CD 00 ON 00 rH ON o L O o T f ON ON L O L O L O 00 00 rH rH rH r - O CN T f [-- r - ON rH 00 CN CM l> r~ l> T f T f 00 00 00 L O r~ ON 00 ON ON o CN oo CN CN rH rH rH CM CN rH rH rH CM CM rH CN rH CN 00 ro 00 CN CN CN CM CN CM CN CN CN CN CN CN CN CN CN CN CN CN CN CO 00 00 OO ON T f oo ON L O CD 00 ON i> r~ rH o ON ON CM rH 00 o T f r - oo oo L O o T f L O 00 rH ro ON CN r~ r - CM T f r - C D CD o T f ON 00 CO uo T f CN rH CD L O L O rH CN r- CO ON r- oo oo 00 CD L O CM ON ON C D CD CO T f Tf CN CM CN 00 OO rH 00 T f 00 r- oo O r- CN T f CN CN o r- I— Tf Tf 00 00 00 L O 0O r - ON oo ON ON o rH o CN oo CM CN rH rH rH CN CN rH rH rH CN rH CN rH CM rH CN CM ro CM 00 oo CM CM CN CN CN CN CN CN CN CM CN CN CN CN CN CN CM CM CM CM CN CN CO 00 r- CN L O 00 ON rH T f ro r- CD ON L O T f C— T f ON CO r- L O O oo CD 00 O L O ON CN L O l> 00 CD o O ON o o 00 CN 00 L O r~ CO ro CN CN ON 00 00 CN 00 o T f T f r - L O rH rH 00 CN ON ro o o r-~ r~ r- T f T f oo 00 00 ON CN T f L O oo Tf rH 00 00 T f C D oo oo r- [-- r- T f T f 00 00 L O CO t— ON 00 ON o rH o C N ro Tf CN CN rH rH rH CN CN rH rH CN rH CN rH CN C N CM 00 CN 00 ro oo CN CN CN CN CN CN CN CN CN CN CN CN CN CN CM CN CM CN CN CN CN r- r~ rH rH rH r~ ro rH o rH CD CD L O ro CN rH C— o CN Tf ON CM T f ON CM L O oo rH L O ON L O rH L O o CN 00 CN CD [-- ON L O C D r - rH CD ro ro ON ON oo L O L O O ON ON L O CO rH O 00 o CN [— [— ON CO o rH r- r - r - L O L O T f ro oo ON ON 00 L O CO o ON T f rH 00 L O r~ ro r~ r~ r- Tf Tf 00 00 00 L O oo [-- ON 00 o ON O rH CN oo T f CN rH rH rH CN CN rH rH rH CN rH CN rH CN CN CN CN 00 00 oo oo CN CN CN CN CN CN CM CM CN CN CN CN CN CN CN CN CN CN CN CM CN r- r- r-rH rH rH r-~ O 00 C D oo 00 ON O H oo r - T f O L O ON r - T f 00 rH T f ON L O O L O CN L O r - ON CO r - ON 00 o oo 00 L O T f 00 rH rH CN r- CD ON CO 00 ro 00 L O oo CD rH 00 00 00 CD O O oo L O CO o ON L O CN T f C D r-ro r - r - r - T f CO ON r- ON oo o ON o rH CN oo Tf CM rH rH rH CN CN H CN rH CN CN CN CM 00 00 ro ro CN CN CN CN CN CN CN CN CN CN CN CN CN CN CM rM CN r - r~ l> r - r -rH rH rH rH rH CM OO 00 O r - CO Tf L O rH r - r - r- Tf 00 00 00 ON ON L O ro CD o T f rH ON 00 oo ON CO ON L O r- CN rH L O ON rH 00 CN CM 00 C D T f o o Tf CD r~ CN L O CD 00 00 r - T f 00 CD ON l> ON 00 rH CM ro T f CN rH CN rH CN rH CM rH CN 00 00 oo oo CN CN CN CN CN CN CN CN CN CN CM CN rM l> r -rH rH T f 00 ON ON rH L O 00 CN rH r— T f T f 00 CN CN CO OO rH r~ o rH C D 00 oo 00 CD O O rH CO CD ON ON T f Tf CD T f oo CN r~ rH rH T f CO [-- o C D oo L O r- 00 00 Tf CO ON r- ON 00 o o rH CM oo T f CN CN CN rH CN rH CM oo CN 00 00 00 00 CN CN CN CN CN CN CN CN CN CN CN CN CM 00 O OO OO L O ON ON L O L O CN T f L O Tf r- rH CO 00 T f rH rH CN T f ON 00 00 L O o 00 00 ON rH ON 00 CN l> rH rH L O 00 rH 00 CD r- ON 00 T f CO ON r - 00 o rH CM 00 T f CN CM CN rH CN CN 00 00 00 00 00 CN CN CN CN CN CN CN CN CM CN 0M r-ON 00 rH CN rH ro r~ r- L O r- 00 L O L O o rH CN r- r- rH CO ON 00 o Tf CN CN CM L O 00 rH co L O ON CD r - ro ro r - r - CN 00 L O 00 00 oo l> L O rH rH L O r- 00 rH l> T f C D 00 00 r~ T f 00 CD ON r- ON 00 o O rH CM 00 CN rH CN rH CN rH CN rH ' CM 00 CN 00 00 00 CN CN CN CN CN CN CN CN CN CM CN CN CN CM SH tr M tr (X SH tr SH tr a, SH tr SH tr M tr H tr M tr M SH SH SH L O L O CD C D l> r - 00 00 ON ON o o rH rH CN 00 T f o rH rH rH rH rH rH rH CM rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH 00 00 00 00 00 oo ro ro ro ro oo 00 00 00 00 00 00 00 CC a CC a CC a CC CH cc CH CC CH cc CH CC CC CC OJ C N ON + fe CN + CNJ C CN] 00 CM 00 C N ] i— vo T—I O LO LO LO LO rH rH rH CN] CNJ CN] r-rH VO [— 00 ON rH VO LO Tf lO LO rH rH CM CNI r- r-CN fe CN CO + fe CN II CN i i s II fe CN C O I I—> II fe CN wo •A II fe CN H i II fe <N ON l H ^ II fe H tr a o CNJ CNJ oo Cu 252 CN H i PH CN II PH CN i n PH CN cn + PH CN PH CN i - i II PH CN CO H-i II PH CN i n r - i II PH CN r-i II PH CN ON r - i II PH SH s 'co CO oo oo IT- 00 00 l> CM T f o 00 UO o m 00 o IT- rH CD CM oo t— T f oo uo T f oo m T f 00 ON tH T f CD IT- T f ON r- rH o CD CD ro r- o ro r- o ON rH 00 ON rH oo CD oo ON CM UO rH UO rH oo rH rH CM rH tH CM 00 ON ON 00 ON ON m U0 UO oo 00 ON UO 00 00 T f T f T f T f T f T f ^ f T f •sf T f T f T f m uo U0 rH rH 00 U0 rH H T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f 00 T f T f rM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CO rH m CD rH m T f CM in T f UO 00 CM o O CM rH T f 00 rH r- T f r- CD r-T f l> T f T f r- T f 00 T f rH ON ON CD ON oo CD rH UO CD T f 00 uo 00 CM 00 rH T f r- o T f r- o ON rH oo OO O CM CM T f UO r- ON rH U0 ON rH uo 00 O T f ro oo T f oo 00 T f ON O o ON O O CD CD CD oo 00 ON ON ON CD 00 oo ON ON T f T f T f T f T f ^ f T f m m T f UO UO UO U0 U0 rH rH rH 00 00 UO H H rH 00 T f T f T f T f T f T f T f T f T f T f T f T f •sf T f T f T f T f T f 00 00 T f T f T f T f oo CN CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM r- r- r-rH rH tH CM 00 00 CM ro oo r- CM 00 CD ON CM r- CD 00 CD 00 rH CD r- IT- O r- ON CM UO CM CM CD oo m CD 00 m H ON 00 00 O 00 CD T f 00 oo CD oo CM T f CD UO CM U0 ON rH CM ON rH CD rH T f CD 00 ON o UN ON rH r— ON o m 00 rH 00 ON O 00 00 CD CD CM T f tH UO m L O m m m o O rH rH rH CM o O rH rH tH CM CD CD r- ON o O CD ON ON O T f T f T f T f T f T f m UO in CM CM CM m m m CM CM CM m UO UO rH ON ON UO rH rH ON •Sf T f •sf T f T f T f T f T f T f T f T f ^ f T f T f T f T f T f T f T f T f T f T f oo 00 T f T f T f 00 CNJ CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM [— r- r- r-rH rH H L O ro ON m oo ON r- m 00 00 O ^ f 00 CD 00 CD CD CM T f ON r- O 00 00 00 T f O 00 T f o r- CM T f ON i— 00 H CD r- 00 O CM o rH o O CD CD m o ON m r- ON uo r- oo T f IT- ON uo CD r- T f r- ON 00 T f o 00 rH 00 CD CO CD CD CD CD rH rH rH CM CM CM rH rH rH CM CNI CM r- r- rH rH r- O T f T f •sf T f T f T f m m U0 CM CM CM U l U l U l CM CM CM UN uo ON ON UO ON T f •sf T f •sf T f T f T f T f T f ^ f T f T f T f T f T f T f T f T f T f •sf oo 00 oo CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM r- r— IT- r- r- r- r— r-tH rH rH rH rH rH rH oo UO U0 CM rH ON CD CD r- CM r- UO 00 rH CD o CM O T f CD rH 00 r- ON m CM CM r- r- CM CM ro T f CM T f CD rH rH ro m r- OO UO UO T f CM CM CM 00 00 00 CM oo oo oo r- [— rH r- rH m in m CM CM CM m CM CM CM m U0 ON uo ON T f T f T f T f T f T f T f •sf •sf T f T f T f 00 T f CO CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM r- r- r- r- IT- r- r-tH rH rH rH rH 00 r- CD CM 00 rH T f 00 oo CM CM OO tH UO rH UO CM o 00 00 ON CD r- ON o CM ON CM 00 00 CM 00 00 CM CM r-m CM CM m CM CM ON ON uo T f T f T f T f T f T f oo 00 T f CM CM CM CM CM CM CM CM CM r- I— r- IT- r- r- r- r-rH rH H rH H rH rH r-o CM CM IT-CM UO CM ON OO CM r-ro ro ro ro oo oo T f 05 T f T f 05 CM 00 T f 05 CM 00 T f Oi CM T f T f 05 CM T f "Sf Oi ro ro T f 05 00 T f 00 T f P J T f T f T f T f 05 O l 253 T3 CD 3 o U oo CD C N O N + PH C N + C N I T ) P H C N C O + PH CN + >—> I  P H C N i-i I  P H C N C O I H-> I  P H C N I /O H i I  PH CN r -i H-5 I  P H CN O N I H i I  PH C CD a c o oo CO rH [— oo r— VD 0 0 [— CNJ o VD rH oo LO [— ON VD [— T f VD 0 0 ON rH LO 0 0 ON rH r— O CN] 0 0 CNI o ON VD ON LO CNJ ON LO 0 0 0 0 ON rH ON [— VD T f LO 0 0 ON T f rH rH LO rr- t— [— o ON [— C— CNJ o rH O CNJ 0 0 rH 0 0 rH rH LO LO 0 0 [— 0 0 [— VD VD CNJ rr- rH ON LO rH ON ON LO VD OO VD r— VD VD rH rH ["- VD rH VD VD VD rH VD C— O LO [— O O LO [— 0 0 T f CO T f T f T f T f 0 0 T f T f 0 0 T f T f T f 0 0 T f T f 0 0 T f T f T f 0 0 T f CN] CN] CN] CN- CN] CNI CN] CN] CN] CN] <N CNJ CNJ IN CNJ CNJ CNJ CNJ CNJ CNJ CNJ CNJ CNJ rr- rr- rr- tr- t— rH rH rH rH rH VO VD rH LO LO CN] rH ON T f rH [— T f T f LO VD 0 0 0 0 OO VD VD ON 0 0 O CN] 0 0 cn VD VD ON rH 0 0 I— T f LO VD CNJ LO T f CNI CNJ rH ON rH LO 0 0 rH 0 0 T f rH oo CO ON 0 0 ON o O CNJ T f rH o T f CN] 0 0 rH 0 0 oo ON CN] VD VD ON rH VD 0 0 r- VD t— 0 0 rr- t— CNJ VD rH ON ON LO LO VD OO VD rH rH rr- VD rH r— VD VD VD rH VD VD t— LO t— O O LO LO rr-oo T f T T T f 0 0 T f T f CO CO T f T f T f co CO T f co T f T f T f 0 0 0 0 T f CN] CN] CN] CM CN] CN] CN] CN] CNI CN] CN] CN] CN CNJ CNJ CNJ CNI CN] CNJ CNJ CN] CNJ Pu T f o oo CN] t— LO o T f t— O LO rH o o CN] CO oo LO T f r— rH CN] CM T f CN] c— ON 0 0 co T f ON ON rH ON rH CM 0 0 LO T f VD CN] 0 0 CM LO rr- oo CM LO T f T f T f LO T f o ON ON CM ON rr- rr- rr- CM VD rH ON ON LO LO VD ON [— [— VD rr- VD VD VD rr- LO r— O O LO L O t— co oo 0 0 T f oo T f oo oo T f oo T f T f T f 0 0 0 0 T f CNJ CM CM CM CM CM CM CM CM CM CM CM CNJ CM CM CM [— rr- rr-rH rH rH LO T f O rH CO O ON O 0 0 T f rH LO CO rH VD T f 0 0 [— ON rr- O o CO ON T f 0 0 LO rH rH CM rH CM O O L O rr- LO o LO T f rr- LO VD VO r— VD rH t— ON ON ON 0 0 0 0 CM VO rH ON ON LO LO VD ON rH [— [— [— VD VD rr- LO r - O O LO LO rr-0 0 T f 0 0 0 0 oo oo oo T f 0 0 T f T f T f co co T f CN] CM CN] CNJ CM CM CM CM CN] CM CM CM CM CM CM I— r— rr- rr- t— r- t— rr- rH rH rH rH rH rH rH rH rH 0 0 0 0 rH rH CM LO LO 0 0 O ON T f VD ON VD VD VO r— rH ON CM VO vo VD ON rr- r— LO LO r— 0 0 0 0 T f 0 0 0 0 T f CN] CM CM CNI CN] CM rr-rH T f rH CNJ T f T f LO LO O O lO LO o 0 0 r— 0 0 0 0 CM CM VD vo VO ON rr- LO LO rr-0 0 T f 0 0 CO T f CM CM CM CM CM [— 0 0 ON VD o lO rH T f VD ON 0 0 ON LO ON rH ON ON ON ON O ON CM VD VD VD 0 0 VD r— LO LO t— oo CO T f oo CO T f CM CM CM CM CM CM 0 0 o LO oo CM r— L O L O L O L O T f OT oo CO T f T f T f oo oo oo T f T f T f CO co oo T f T f T f 0 0 T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f CL- Del cu DJ DH cu DJ cc cu DJ CC cu DJ CC CU DJ cc CU DJ CC 254 o O 00 CU v l H CN O N + CN + fe CN V N .+ fe CN cn + CN + H i I  fe CN -A I  fe CN cn i H i I  fe CN un i H i II fe CN fe CN O N I - I . II fe s c 'lo L/> < r H T f LO LO co VD CM L O o VO r~ LO r- CO LO oo o CM r H 00 ON T f T f CM CM 00 00 O O I— CO VD I- r H T f r H [— r- T f r H VD T f ON VD oo VO r H O CM oo T f 00 T f 00 LO LO 00 LO T f CM ON O 00 ON ON oo [— ON t — CM T f LO O o T f [— o T f [- 00 i — ON CM 00 r H 00 r- r- vo co T f T f co T f T f CO T f CO T f 00 00 T f 00 T f oo oo oo CO CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM r- r- l> 1— r- r~ [— r H r H r H r H r H r H r H co VD r H LO 00 CO T f CO vo VD o r- T f 00 [— VD r- LO 00 r H r H r H 03 ON LO VD CM LO I"- r H CO r- r H L O LO 00 00 LO CM o ON r- CM LO o O T f T f r- T f co CM r H [— 00 TT" T f 00 CO T f co CO 00 00 oo 00 CM CM CM CM CM CM CM CM CM CM CM CD CM CM 00 r H CM 00 r- 00 oo r-CM ON LO T f L O o oo LO o co r H O O I— 00 co [— 00 CM T f VD ON VD VD 00 oo LO CM o ON r- CM T f O O T f T f r- T f CO CM r H r~ oo T f T f 00 CO T f CO CO 00 00 CO 00 CM CM CM CM CM CM CM CM 0M CM CM r- r-r H r H OO LO CM O CM r H vo 00 LO 00 LO CM r H ON LO T f ON co ON r H r H CM ON ON T f OO ON LO o r~ VD VD 00 CO LO CM o CM T f T f O O T f T f r- T f co c~ VD oo T f T f 00 co T f CO co co oo oo CM CM CM CM CM CM CM CM CM CM r- r- 1 — r- r-r H r H r H r H r H OO C"- r- VD T f ON r~ 00 ON o T f LO CM r H CM T f T f CO CM r-co co CM r-r-co CM oo o oo CM r-oo CM c— oo o r-oo VD co CM T f CM VD oo VO oo CM I— 00 oo CM co L O CM T f CM 00 CM r-tr a, tr Pu SH tr PL, SH Pu SH tr Pu SH Pu SH tr tr tr tr tr r-- [— l> r- r- 00 00 00 00 00 ON ON CM CM CM 00 vo r-r H r H r H r H r H r H 00 CO T f T f T f 00 oo T f T f T f 00 00 CO 00 T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f cn PH A Cd PL, PC PJ CJ cu Pj PH Pj PH CU cu cu CU cu 255 CN ON + fe CN + fe CN </"N + fe CN m + fe CN II fe CN H i II fe CN m H ) II fe CN ir> H i II fe CN i H i fe CN ON H i II fe r- 00 00 00 00 00 ON o CO r H r H co r- LD 00 r- CO o KO [ — r- 00 r H T f r H LO r- r- T f KO oo LO LO 00 KD r H rH T f LD ON LO r- r H r- KO 00 ON LO r- LO 00 o r H r H r H r H CNJ 00 00 00 r H ON r- r- r H ON o ON ON r H co o CM <M o 00 CNJ CN] o 00 CNJ CNJ o I — CO ON ON oo oo o LO LO LO T f LO LO LO T f LO LO LO T f LO T f T f T f LO LO T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f r- T f T f T f r H KO CNJ ON 00 ON CO 00 00 LO ON 00 LO KO ON CM ON KD r H 00 LO CNJ o CO O ON CM T f co r~ LO ON o KO CM ON 00 CNJ LO T f ON CNJ r H C\J o r H T f KO LO T f KO r~ T f r H KO r- 00 CNJ 00 KO f - 00 LO 00 oo r- f -00 00 o CNI LO LO LO r H 00 00 00 CNJ o o r H r H r H o r H CNJ 00 o CM CNJ ON ON CNJ CM CM ON ON CN] CNJ o 00 00 00 00 00 o 00 00 oo o LO LO T f T f LO LO LO T f T f LO LO LO T f T f LO LO LO LO T f T f LO LO T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f r- r- r- r- r-r H r H r H r H r H O ["- KO T f r H co CD r- T f o KD 00 r H VD ON ON r H CNJ KD ON ON LO KO KO CNI t— [ — T f KO LO KD T f r H r H ON r- ON T f T f r H r- ON O 00 o r H CNJ T f LO KO LO ON T f LO LO T f ON CO CNJ CNJ T f T f in KD t — L—• r- ON ON ON r H r H CNJ CNJ CNJ r H CNJ oo T f r H CM CM CNJ O CNJ CNI CNJ CNJ CNJ CNJ 00 00 00 CO CO o 00 00 oo o LO LO LO LO LO LO LO LO LO LO T f T f LO LO LO LO T f T f LO LO T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f r— r-,—1 r-.—1 r— ,—1 r H o LO 00 CNJ T f KO KO LO CNJ CNJ T f r H 00 o o T f ON CNI [ — T f r H LO r— T f T f LO CM LO KO 00 00 ON T f oo o T f CNJ CNJ r- r H r H ON LO O r H CM f - ON o CNJ 00 T f T f KD r H CM oo r H LO [ — o ON r H KD KO KO KO KO t — r- LO 00 oo 00 KD LO o o o CNJ CNJ CNJ CO oo T f T f r H CNJ CNJ CNJ o o ON CNJ CNJ CNJ o ON CO CO CO 00 00 00 oo CD 00 oo o LO LO LO LO LO T f LO LO LO LO T f LO LO LO T f T f T f LO T f T f LO LO T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f T f r- r- r- i — r~ r- r- r- r- r- I-— r- r- [ — r- r- r- I — r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H CNJ o co o r H co [ — KD CNJ KO o o oo co LO CNJ 00 CO 00 o T f LO LO LO T f T f T f T f r- r- r-r H rH rH o ON r -L O oo LO 256 CN O N II PH CN + PH CN m + PH CN co + PH t - UO LO r - rH 00 00 00 tH [— CM vo CM oo rH rH 00 00 uo r - tH VD ON 00 TP tH ON ON O 00 O rH r— TP tH CN] U0 U0 CD 00 VO I— vo t— tH r- I— CN] 00 tH VD TP CD 00 oo ON ON IT- oo ON TP ON TP TP TP TP LO LO TP TP TP LO TP LO TP UO UO UO TP TP TP TP TP TP TP TP TP TP TP TP TP I— rH CNI CTi ON 00 rH CM ON CM [— VO o ON [— U0 00 TP [— TP 00 CNJ rH rH tH uo 00 00 VD ON o UO r— 00 ro VO TP LO 00 LO 00 rH r— UO LO CD 00 00 t - 00 oo O l [— IT- [-- IT- rH 00 r— CM 00 00 00 tH VD TP VO VO 00 CO ON ON r— 00 ON TP ON ON ON TP TP TP TT TP LO UO TP TP TP uo TP UO TP TP TP uo LO UO TT TP TP TP TP TP TP TP TP TP TP TP TP TP TP TP r - r— I— r- r- r -rH tH tH tH tH rH T f rH VO CN] CO LO 00 r- CD VO 00 rH cn rH ON o TP TP O CNJ ON OD CM 00 LO o rH O O IT— C— CN] CM 00 00 TP c— t— OO ON IT- [— oo ON ON TP TP LO TP TP TP uo TP TP T f TP TP TP TP TP TP TP TP r - [— I— rH tH rH CN] oo r- TP LO tH 00 tH 00 oo oo rH 00 IT- oo 00 CO r- 00 L O r- CO oo 00 O o 00 00 CM CM 00 TP I— r- 00 ON r- l— 00 ON TP TP uo TP TP TP LO TP TT -5P TP TP TP TP TP TP CN H PH ON VO oo U0 TP r-oo ON t - t— tH CM 00 00 r- t— TP TP TP TP r- ir-CN PH CN CO I I—» II PH CN c n II PH CN t> H-i II P H T 3 IU •g O O O N cu CN O N PH (U B c , .SP "co < tf CH M XT M oo oo oo oo TP TP tH rH tH PH CC Ol TP tH P J M M M D 1 D , M M TP TP TP TP U0 U0 00 00 TP TP 00 TP tH tH tH tH tH tH Pi CH Pi CH CC CC 00 tH CC 257 CN ON + II PH CN + PH CN WO + PH CN co + PH CN + H i II PH CN i H i II PH CN CO I H i II PH CN </o • H I II PH CN • H i II PH CN ON ni II PH 'to CO CNJ r- 00 o r- ON TP oo 00 CD TP 00 00 L O CNJ o o CO ON [ — ON m r H TP CO r H TJ 1 CNJ [ — L O 00 o CD r— CNJ r H o 00 o 00 r H CNJ CO oo CNJ CO TP CD r H O ON o CN] r H L O CD 00 00 CD r - ON CNJ [ — CNJ CNJ oo CD CD CD TP TP 00 TP ON ON oo 00 oo oo CNJ CNJ [ — CO r- uo LO ON L O L O o CO CO CNJ CNJ CD CD 00 00 r- [ — L O L O f - CD ON ON CJN ON ON ON o ON ON O o ON ON o o ON ON o o ON O r— t— c— [ — [ — [ — CD [ — [ — O O oo r- r- 00 00 r- r- CD 00 r- 00 ON CNJ rH 00 00 CD 1— 00 TP CN] oo t— 00 o ON H uo TP L O CD ON [~- ON U0 ON [— O oo U0 UO CNJ CD O CNJ O CD TP CD TP CN] TP UO oo TP TP l> o rH oo CO L O ON CD 00 ON CNJ o ON CN] U0 oo CN] rH CNJ TP 00 CNJ CD t— ON oo 00 1~- ON CNJ ON TP TP TP TP O o ON O U0 UO UO L O L O o o o CTl ON TP TP TP oo 00 [— r- L O UO UO ON CD CD UO ' rH CD CD CO CNJ CNJ r- r- r- 00 op [— [— [-- L O [— CD ON ON ON ON ON ON ON ON O ON ON ON o o ON ON ON o o ON ON ON o ON o r- [— [— t— r- [— [— r— 00 D— r- [-- 00 00 r- r- r- t— oo CD [-- [-- r~ 00 r- 00 L O oo ON ON t— [— o 00 r- r- r- 00 00 oo tH o ON tH ON [— oo oo UO 00 co 00 CNJ CNJ U0 ON CNJ rH CD CNJ r - CNJ 00 CO [— TP UO CO ON ON UO CN] L O ON ON ON rH rH rH 00 L O CNJ 00 tH o •00 TP TP 00 CNJ CNJ oo CN] rH CD t— 00 r- CO CO t- CN] rH CD UO UO CD rH rH rH rH rH co CO CO CD rH rH H o o L O L O U0 TP ON CD CD L O U0 UO ON CD CD CD H rH CD CD CD CNJ r— [— I T - TP TP r- [~- [— L O [-- CO ON ON ON ON ON ON ON ON O O oo oo ON o ON ON ON o o ON ON ON o ON o [— r - [— f- r- r- t— r- 00 00 f- t— r— 00 r- t - r - 00 00 r- [•"- 00 r- 00 CN] 00 oo rH r - 00 rH CM oo CM LO [— CM t— CNJ 00 00 oo CO o o CD TP LO CO rH CO ON TP rH ON TP 00 00 ON CD CM TP [— 00 00 tH CD r - oo 00 CN] ON l> CN] CN] rH o oo oo CM tH o rH rH o ON LO LO LO TP LO U0 o CNJ CD CD r- C~- CNJ CM tH CM t r- r- f- CM CM tH rH CD CO CO LO o ON 00 UO LO ON ON CO CD CD tH CD CD CD CM r - [— [— TP [— [— [— UO 00 CD ON ON ON ON ON ON ON ON o ON ON ON o ON ON ON o ON ON ON o ON o [— I T - r— r - r - [-- [— [— 00 r - [-- oo [— r - 00 [— [— r~ oo r— 00 n n tr o, 00 oo O CD UO TP 00 00 rH ON tH TP CM CD o 00 r- U0 U0 U0 rH CM CD TP CD o TP 00 oo uo o r - CD U0 rH ON 00 C— ON r- t— CD oo 00 00 00 CM CM CM 00 r- i — [~- [— CM CM CM CM CD ON ON CD CD CD rH CO CO CD CM l — r- r- TP UO CD ON ON ON ON O ON ON ON O ON ON ON o O o [— [— r- r- 00 r- [— [~- 00 r- [— [— 00 O O CD r~ [— tH tH 00 TP o 00 TP O TP 00 00 t H 00 oo t H TP CO CD o t H CO t H ON 00 00 CM ON CM CO CM o CM CO CM t H [- TP CM uo CM CM rH o r— O 00 LO oo 00 00 00 00 00 00 oo oo 00 oo r- r- t H o ON CO CO t H CO CD CM f- r- 0- TP [— uo 00 r -ON ON ON o ON ON o ON ON ON o ON o ON o [— r~ [— 00 [— [— 00 r- 1— r~ oo c~- 00 r- 00 o oo t H oo CM r - 00 oo 00 CM [— 00 ON o CM CO r— rH CM [-- CD o r- CD L O LO rH TP 00 00 ON oo oo 00 r- rH t H CO CD CM [-- r - TP uo ["-o ON CTl o ON ON o o o 00 l > r - 00 I — r - oo 00 00 r - l > r -t H t H t H CD 00 tH 00 UO ON TP 00 t H CD O ON 00 [— r - r -uo CO TP ON CM O 00 r-ON CM o 00 00 ON CM o TP 00 ON oo o 00 CM o oo TP o 00 CM LO TP TP o 00 UO o oo UO o 00 CO CM U0 o CD CO ON CO 00 LO o 00 M tr M tr ft u tr M tr ft oo oo u tr M tr ft H tr H tr ft u tr tr CD CD tH tH tH tH rH rH rH rH tH tH rH rH rH CM CM CM CM CM CM CM CM CM CM CM CM CM OC Ol OC a OC CD CC Ol CC a oc o> CC 258 CN H i PH C N t— + PH CN + PH CN cn + PH CN II PH CN i H i II PH CN cn H i II PH CN un • H i II PH CN • H i II PH CN H i II PH CM CTi T f o O CO CM T f O CTl o CM 00 o VD CTl CO LO ro t— 00 CO ON CO VO r H CTl T f r H [— CO ON VO 00 [— 00 CTl 00 O OO O CTl o CTl O ON r H ON OO r - 00 [— 00 t— 00 t— T f T f o r H [— CM o O LO r H CM r H t— ON 00 r— CO LO CO VO 00 r H ON CM c— CM o L0 CM 00 T f o VD 00 00 00 CTl OO O ON o CTl o CTl O ON r H ON 00 c- 00 r - 00 [— 00 r -oo 00 cn t— r H O OO CTl T f T f CM ON VD r H CM ro CM T f r - ON 00 00 ro r H VD CO OO LO 00 oo 00 CTl 00 O o CTi o CTl o CTl r H 00 IT- 00 I— 00 I— 00 o ID r— LO T f [— 00 ON VD ON o VD 00 LO 00 o r H O r H r H VD t— VD 00 CTi T f CM t — T f CTl VD r H VD 00 00 OO CTl 00 o ON O CTi o CTl o CTl r H CTl 00 r— 00 IT- 00 r— 00 t— [— [— r H r H LO CO 00 LO o T f VD CM ON o co LO 00 00 CO T f T f T f CM c— LO O [— CM 00 00 CTi ON o ON o CTl o ON r H ON 00 t- 00 r - 00 r— CTl 00 T f 00 00 LO ro L0 r H 00 CM 00 ro LO T f o r H o LO oo OO VD oo 00 00 00 00 CTi o ON CTl o CTl o r H ON r- 00 IT- oo OO IT-IT-r H IT- vo r H CM CM CO CO vo r H T f vo LO 00 r H IT- LO c— VD LO T f ID r H 00 oo 00 00 ON ON o CTl CTl o O ON r H ON c— 00 00 t - 00 I— t— r H t— VO 00 VO VD o VD CM CO VD CM [— CM O ro r H VD T f t — CM ON T f 00 00 ON ON o ON CTi o O CTl r H ON t— 00 OO C— 00 [— t— r H CM VO r H VO r H CM T f LO T f ON VD r H r— 00 LO VO LO r— ON T f OO 00 ON O CTl CTi o O r H CTl r— 00 00 00 C— t— t— r H r H o CM T f LO r H CM O LO CTi LO r H r H VO LO O 00 00 00 CTl CTl CTl o CTl O r - 00 t - 00 tr tr H tr H tr SH tr r - t— 00 00 CTl ON O O r H r H r H r H r H r H r H r H r H r H CM CM CM (TM CM CM CM CM CC cu cc CU CC a CC CU vo ON LO T f ON ON t — r -t r -SH tr o CM CM CC 259 <+H O a a i x> 3 u •tf PQ CD cn CD CD C *E CD OH - a CD C .bp (75 < CD CN O N + H i II PH CN + PH CN + PH CN cn + PH CN + H i II PH CN i •—> II PH CN cn •A II PH CN i - i II PH CN II PH CN O N I H i II PH CD a c 00 I—• O LO co CM O ON ON oo 00 CM ON L O o VO VD T P ON O ON L O 00 L O CM O T P r H r - L O CO vo r H O 00 LO T P ON r - LO 00 00 00 00 I— r H 00 L O ON CNJ L O CO r H o r- rr- LO ON r- T P 00 L O 00 ON 00 t VD CM r H r H r H r H rr- rr- [— ON oo CM CM LO LO r - r— CM CM r H rH OO OO O O o OO 00 r H r H r H 00 00 co CO ON ON T P T P O o VO VD o O r H r H r H O O r H r H r H o o r H r H o o r H r H rH r H r H rH r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H rH rH r H rH rH r H CO O L O 00 o CNJ r— 00 VO f - ON T P T P VD 00 T P vo ON o o VO 00 ON l O t— ON 00 O ON CNJ ON o CO co O IT— CNJ CNJ VD CM r H r— VD r— T P T P r H L O CM rH CM VO T P T P r H r - CNJ T P ON ON rr- VO VD 00 O 00 r— VO CM O 00 LO T P r~ L O T P ON 00 00 r- VD T P co T P co CNJ 00 00 OO O o O 00 co CO r- r- VO 00 00 00 00 CO CM CM ON ON ON O o 00 00 00 r H r H r H ON ON ON CO co CO ON ON ON T P T P o O O VD VO o O O r H r H O o O r H r H r H O O O r H r H r H O O o r H r H r H rH r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H rH rH r H rH rH r H r H r H 00 00 T P CO 00 T P ON 00 r - L O T P CM ON VD CM T P r - r H O L O 00 ON ON T P 00 co VD oo ON T P co ON CNJ CNJ LO r H r- [ — r H CO O r H r - r - o LO L O vo VD CO O r - ON o ON ON CM o oo ON ON o 00 r- LO CNJ O 00 [— VD r H ON oo T P 00 CM L O T P 00 rr— VD r— LO T P L O L O T P T P CO o ON ON r H r H r H T P T P T P 00 IT- [ — ON ON ON T P T P T P 00 00 o O o O o o 00 00 CNJ r H r H ON ON ON 00 00 CO ON ON ON T P T P T P o O o VD VD r H r H r H r H r H r H O o r H r H r H o O O r H r H r H o o o r H r H r H r H rH r H rH rH r H r H r H r H r H r H r H r H 00 r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H rH rH r H r H rH rH r H r H T P CNJ r H CO L O r H O ON r - L O r H O 00 00 00 VD 00 00 T P r H T P VO CM O T P rr- T P L O T P ON r H 00 T P ON 00 L O O ON r H O r H r - O f - O CM LO VD CM L O rH r H oo r H ON t — L O O 00 VD L O CNJ O r - VD L O T P 00 rr- L O CM r H o rH L O T P T P 00 CM VD L O LO L O LO O O o CNJ CNJ r H L O L O L O 00 00 00 O O o L O T P T P r H r H r H O O O 00 00 CN] CN] CN] ON ON ON CO CO CO ON ON ON L O LO LO O VD VD r H r H r H r H r H r H o o r H r H r H O O O r H r H r H o o o r H r H r H rH rH rH rH r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H rH r H r H r H 00 00 00 OO 00 r H r H r H r H r H ON r H T P r H ON CNJ CO 00 CO LO VD o r H 00 00 rH 00 L O 00 T P CM LO CM L O T P LO VD O ON T P LO 00 LO o ON T P VD O r - r - ON LO O 00 oo r— T P ro CNJ r - VD CO CM r H o T P 00 r H 00 IT- r - 00 r - VO rH rH O ON 00 r H r H r H CNJ CN] CM VD VD VD ON ON ON O O o LO L O L O L O L O CM r H r H CM CM CM ON ON ON rH rH rH O O O 00 00 00 ON ON ON rH rH rH O O O L O L O L O O O O V D V D r H r H oo 00 LO rH oo vo oo ON O O ON OO 00 VO rH T P O r— r— 00 O L O CM L O CM L O ON 00 rr- rr- T P ON V D OO r H T P vo rH 00 00 t rH ON t - VD L O 00 c— VD 00 CM CO CM CM L O T P T P rH rH rH 00 CM VO VD VD ON ON ON rH rH VO V D VD CM CM CM CM CM CM ON ON oo oo 00 ON ON ON L O LO O O O r H r H r H rH rH rH O O rH r H r H O o o rH rH r H rH r H rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH r H rH rH rH rH r H OO 00 00 00 00 00 rH rH rH rH rH rH T P CO T P T P 00 CM T P T P VD LO CM rH 00 CO ON L O LO rH L O rr- CM VD O LO o o r H o I — t— r— vo VD ON ON 00 r— [— O o r H r H VO vo VD CM CM CM CO CO o o LO LO O o O rH rH rH r H r H r H r H r H r H r H r H r H r H r H r H r H r H rH rH r H r H r H r H r H r H rH r H 00 00 00 00 00 00 00 r H r H r H r H r H r H rH co 00 CM LO 00 ON CO rH T P ON T P r H CO o ON CM CM CM o t — V D 00 00 CO o O O r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H 00 00 00 00 00 00 r H r H r H rH r H r H CM ON VO 00 M c r a M t y a n D* B, M cr a u tr cu u v cu n tr a H tr a n tr u tr a r-{ ^ C M C M 0 0 0 0 T P T P L O L O 00 PH 00 CU 00 PH 00 a oo oo a oo PH 00 00 oo CU o OO 00 [— •-a-1 CM o CM [-- [— ON 00 o Ol CD L O CD rH CO L O •--r1 T P CTl O [— I— rH rH OO CM rH rH rH rH rH rH rH rH rH rH rH rH CM 00 CTi 00 00 CTi CTi CTi O o CTi CM 00 O CM iO lO O 00 O CM rH 00 CM CM rH CM rH CM rH rH rH rH rH T P L O 00 L O L O O [— CD r - CTi L O rH 00 CM CM o CM L O L O o T P L O 00 00 CTi CM CM o o o rH rH rH rH rH 00 rH CD TP oo CTi CD 00 LO TP 00 o CM CM CTi o rH O r - oo LO oo tr- CTl 00 O CTl TP [— O 00 CD CD r - CD ["- LO CM CTl rH oo ee CD LO m LO rH O O 00 rH r— 00 CM rH 00 o CD CM CD CD LO LO LO O rH rH rH 00 CD CD o CTi iO rH 00 00 CTi [— r - rH rH rH CTl CM CM CM o CM. H 00 CM 00 Tp LO 00 OO rH rH rH rH rH rH rH rH rH CM rH CM rH CM rH CM CM O O rH rH rH rH rH rH rH rH rH H rH . H rH rH rH rH rH rH rH CM [— [— o CM oo T P oo 00 rH 00 00 L O CD CTl CD I— o CTl rH 00 rH T P 00 o 00 L O CD L O T P L O CM t— r— T P T P 00 T P cn 00 00 CD OO L O CD O cn rH t— [-- CD CD CD rH rH rH rH T P CD r- rH o L O CM r - r - rH rH rH OO CM CM CM o CM rH 00 OO oo T P rH rH rH rH rH rH rH rH rH CM rH CM rH CM rH CM rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH CTi T P CD CTi rH T P T P OO T P T P CD T P CD 00 00 CM O L O rH 00 [— T P L O 00 00 O IT- 00 00 r - T P CM L O T P CM rH O rH CD L O L O T P CD CM 00 r - 00 LT) 00 oo r— t— r - CM CM CM CM L O [— 00 CM o CM T P [— [— rH rH rH CTi CM CM CM O CM rH 00 00 T P UO rH rH rH rH rH rH rH rH rH CM rH CM rH CM CM CM rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH OO rH O CTl T P T P 00 rH o T P CD L O rH o r- CD 00 L O CTl T P r - CM CTl Ol oo [— CD CO T P 00 00 CM rH O 00 r - [— [— CM CM rH O 00 CTi O T P L O CTl CTi [— t— r— CM 00 00 00 CD 00 00 00 rH 00 r - f- rH rH rH cn CM CM CM O CM rH oo oo T P rH rH rH rH rH rH rH rH rH CM rH CM rH CM CM rH rH rH rH H rH rH rH rH rH rH rH rH rH O L O T P T P rH L O 00 CTi IT- 00 L O CD CM CD r— 00 CM CD [— rH [— T P CTi L O T P O T P rH T P T P CM CM [— CD 00 00 00 00 r - f - CD CTi L O CD O cn rH 00 CTi CTl 00 00 00 00 00 00 CD 00 cn 00 CM ["- T P U0 r - t— rH rH CTl CM CM CM O CM rH oo 00 oo T P U0 rH rH rH rH rH rH H rH CM rH CM rH CM rH CM CM rH rH rH rH rH H H rH rH rH rH rH rH rH rH rH O CD rH 00 rH O L O CM 00 rH rH CM 00 00 00 T P CD T P CTi L O CD rH CD L O CTi cn o 00 rH rH 00 00 CM CM rH T P o rH L O T P [— oo o O 00 T P T P T P [-- CTi o T P CM oo T P CD 00 00 CTi CM CM CM o CM CM 00 00 00 T P L O rH rH rH rH rH rH CM rH CM rH CM rH CM CM rH rH rH rH rH rH rH rH rH rH rH rH T—\ rH 00 00 00 rH rH rH 00 L O O CTl 00 CD T P r— rH CD L O 00 00 00 CD rH [— 00 00 CTl CM L O T P rH 00 00 o rH L O CM rH rH CM CD CD 00 L O CD O cn CM cn o CTi CTl CTi T P T P [— OO O T P 00 00 L O CD 00 rH rH rH CTi CM o CM CM oo oo 00 T P UO rH rH rH rH rH rH CM rH CM rH CM rH CM CM rH rH rH rH rH rH rH rH rH rH rH rH rH rH 00 00 00 00 rH rH rH rH 00 00 rH CM 00 r- O l CD T P [— t— CM CD 00 T P T P CM rH O OO 00 CD O CTl CM CTl O L O T P 00 o T P L O [— O O L O 00 CTI t— 00 OO CM O 00 CM 00 00 00 uo rH <H rH CM rH CM rH CM r—i CM rH rH rH rH rH rH rH H rH rH 00 00 00 rH rH rH CD O L O O CD 00 CD o rH O CD CTl CTi O rH CTi 00 L O CM 00 00 rH T P 00 O rH 00 r -00 CTi O 00 CM 00 L O rH rH CM rH CM CM CM rH rH rH rH rH rH rH H H tr a M M tr M tr M tr U tr M H CD CD r - r - 00 00 cm CTi o o rH CM rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH oo 00 oo oo 00 00 00 00 00 00 OO 00 OH CM OH Oi OH a 0H a CC Ol CC CC o CM CM 00 O J 261 CN Os. + fe C N F^ + fe C N m + fe cs co + fe C N + i—> ! f e CN rH CM CM rH CM CM O CD O CM o CM LO T P CM UO CM CM T P UO O T P ON rH ON O rH ON O CO ON ON 0 0 ON oo CD CM ON 0 0 O CM rH 0 0 rH T P ON 0 0 rH UO 0 0 rH U 0 CM T P CO CM LO CM T P 0 0 ON rH CD 0 0 r> T P [— CD rH CO t— r- CO r— !— T P T P T P LO LO T P T P O O rH 0 0 0 0 O 0 0 0 0 CD rH CO CO CO CO CD CD t— i — E— T P T P t— [— 0 0 0 0 OO T P T P 0 0 T P T P 0 0 T P oo 0 0 0 0 0 0 0 0 0 0 0 0 OO oo 0 0 oo oo oo oo 0 0 0 0 0 0 0 0 oo 0 0 0 0 0 0 CO rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH uo [— rH LO [— CM o 0 0 0 0 T P CM CM 0 0 ON oo o CM o [— rH ON rH LO CM 0 0 CM CM O rH ON ON rH CO ON rH CD T P UO CM 0 0 U 0 r- O O r- T P rH 0 0 0 0 CD ON 0 0 CD CD ON O T P 0 0 UO T P r-0 0 CM T P 0 0 CM •-3-" CM T P CD ON 0 0 CO CM T P uo ON oo CD T P LO CD O CM T P CM ON rH 0 0 O co [— 0 0 ON ON 0 0 ON ON UO U 0 UO U 0 CD CO LO LO LO LO CO CO rH rH rH T P T P T P rH 0 0 T P T P r- H rH CO CO CO CO CD CD [— [— [— T P "vp T P t— I— t— T P T P T P 0 0 0 0 0 0 T P T P T P 0 0 T P T P T P 0 0 T P T P 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 oo oo 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 oo 0 0 oo rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH H rH ON 0 0 T P ON 0 0 •--r' 0 0 0 0 0 0 CM O O rH 0 0 oo rH ON 0 0 0 0 0 0 0 0 UO 0 0 ON O T P U 0 oo CM ON ON ON CO [— ON CD r— rH 0 0 oo 0 0 CD rH 1— oo 0 0 ON ON CD LO I— O CD oo LO 0 0 0 0 oo 0 0 CM 0 0 CD LO 0 0 O L O 0 0 o rH CM T P O 0 0 CO O CM oo ON CM LO ON o CM CO 0 0 O OO LO [— oo T P O i—1 O o rH O o rH CD CD CD [— t— r- CD CO CD CD f- r- rH CM CM T P T P U 0 rH T P T P T P [— CM CM [— 1— r- f- f- r- [— [— r- T P T P T P l> r- [-- T P T P T P 0 0 0 0 0 0 T P T P T P 0 0 T P T P T P 0 0 T P T P 0 0 0 0 oo 0 0 oo oo 0 0 oo oo oo oo oo 0 0 oo oo 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 CO 0 0 0 0 0 0 0 0 0 0 0 0 oo rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH <H rH rH rH rH rH OO 0 0 rH rH CN rH U 0 CM rH UO ON 0 0 CD rH rH rH CD T P ON 0 0 LO CM ON rH CM ON CM ON LO CO UO CO CM LO CD CM CD H oo T P O rH LO r- [— oo 0 0 0 0 0 0 0 0 O LO 0 0 0 0 O o ON rH OO ON rH 0 0 0 0 O rH OO T P 0 0 ON o 0 0 oo T P CM 0 0 LO 0 0 o CM 0 0 T P UO rH CM CM rH CM CM CD t— r— r— OO CD CD [— r— 0 0 CM UO U 0 LO CM U 0 LO uo CM CM C N C O I - i II fe C N n o n i II fe C N Pp l - i II fe C N O N I I — » II fe [-• [--[—[— [— [— oo oo oo oo oo oo oo oo oo oo oo oo [— r- r- T P oo oo oo oo T P r r T P oo oo oo oo oo T P oo r— oo T P [ t T P CD 0 0 O 0 0 0 0 ON T P T P T P oo oo oo CM 0 0 rH O O CD CD 0 0 ON 0 0 0 0 0 0 T P T P T P oo oo oo 0 0 oo CO UO T P T P T P 0 0 T P T P T P oo oo oo oo oo oo oo CD oo CD L O T P oo 0 0 ON rH CD O T P 0 0 0 0 ON ON ON co in co r-UO CM UO UO UO T P 0 0 T P T P T P oo oo oo oo oo oo co T P oo oo T P CC T P T P CC oo T P CC oo T P Ol T P T P CC T P T P Ol oo T P CC oo T P CH T P T P T P T P cc a T P T P oo oo 0 0 rH 0 0 oo oo o o r- oo oo CM CM 0 0 T P T P oo oo oo rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH 0 0 0 0 0 0 0 0 0 0 0 0 0 0 rH rH rH rH rH rH rH [— 0 0 r- O T P 0 0 oo CM T P ON CD 0 0 ON rH OO CD CM 0 0 H rH O O ON o ON ON ON 0 0 CD 0 0 CM oo T P T P T P 0 0 T P 0 0 T P T P 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 rH rH rH rH rH i—1 rH rH 0 0 0 0 OO 0 0 0 0 0 0 0 0 0 0 r H r H C M C M C M C M OO 0 0 0 0 0 0 T P T P oo oo T P T P CC CH 262 -o o O CN CN O N + H-1 fe CN F--+ fe CN + fe CN m + fe CN + H i II fe CN i H i II • fe CN c - o H i II fe CN H i II fe CN F^  H , II fe CN O N H I II fe ON VD 00 TP VD CO I— TP O LO O LO LO CO I— VD oo O ON 00 TP O CM t o r H O CM [— ON TP r H TP r H r - ON O 00 r H ON 00 VD TP LO ON r H 00 r H oo TP VD 00 TP VD C— CM O CM o VD r H O VD VD VD O r H r H oo r H r H r - VD TP L O 00 O O ON ON CO LO <N 00 oo 00 "-J1 TP ON 00 ON ON 00 ON CO ON CO O CO ON CM O CM O CM 00 00 CO 00 CO 00 00 00 CO CO CO CO 00 TP CO CO CO TP 00 TP CO r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H OO r H r H LO 00 o ON O TP ON 00 VD TP ON CM CO ON VD TP O CM CM r H r H CO ON o 00 CM O CM oo r H 00 LO 00 r H o O r H LO CM VD O CO CM [— ON oo LO r H TP VD r - ON LO VD 00 oo ON TP CM 00 r H r - r H t— VD VD r H r H CM 00 r H r H r - VD TP LO oo 00 O O ON ON oo CM 00 00 OO TP TP ON co ON ON oo ON 00 ON oo 00 O 00 ON CM o O CM CO oo 00 00 CO CO 00 00 00 00 00 00 00 00 TP 00 00 00 TP TP 00 r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H CO O ON ON- r H VD CM o o [— r H CM o 00 00 LO O 00 r H TP 00 LO LO t~- C- LO r H ON VD Tp 00 TP 00 o ON TP r H CM VD ON 00 [— r H CM [—• ON CO [— OO ON CM C— 00 ON o O LO TP TP CM [ — r H t— r - r- r H r H CM 00 r H r H 00 VD TP LO TP TP O O ON ON CO CM 00 00 00 TP TP ON 00 ON ON CO ON CO ON CO CO O CO ON CM o O CM oo co oo 00 00 00 00 CO CO CO 00 CO CO CO TP CO CO 00 TP TP 00 r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H OO 00 00 00 r H r H r H r H TP VD 00 00 [— O CM 00 ON O CM o 00 CM TP CO VD CM CO O VD o r H 00 CM r - LO 00 TP r H ON CM TP r H CM VD ON r H ON o r H r H CM VD LO LO OO CM f - CM CM CM 00 0\J VD LO VD TP TP o o ON 00 CM 00 TP TP ON CO ON ON 00 ON 00 00 O 00 ON O O 00 00 00 CO 00 00 00 00 00 00 00 TP 00 00 TP TP r H r H r H r H r H r H r H r H r H r H r H 00 r H r H r H r H r H -si-1 LO VD o I — r H 00 CM TP r H r H TP VD ON 00 LO LO o o r H o r H t— O VD CM o t— 00 00 r -r - •sp L O 00 CM OO O CM CM 00 00 VD LO ON CM [— CM CM CM ON 00 r - lO VD TP o O ON CO CNJ 00 TP TP ON 00 00 ON 00 ON CO o 00 ON O O oo 00 00 00 00 00 oo CO CO oo TP CO CO TP TP r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H OO OO 00 00 00 00 00 00 00 r H r H r H r H r H r H r H r H r H O VD r - o VD 00 VD ON O TP CM O r - VD ON TP TP CM ON VD o CM ON CM I— O ON TP ON 00 ON ON O ON o 00 00 00 CO TP CO TP r H r H r H r H r H r H r H M tr tr a L O rH CO ON oo oo co ON CO O O TP oo ON oo CO [— ON co VD TP TP [— ON 00 CM L O [— ON CO CM O VD [— ON 00 O O O ON O O TP L O VD O TP ON 00 00 ON ON 00 u tr u tr tr M tr H M tr VD VD VD VD CM TP O TP M tr H tr M tr n tr 00 00 00 00 TP TP TP TP 00 00 TP TP TP TP TP TP PC a tt cu O O O O T P T P C O O O T P T P O O C O T P T P "^J* "^ f* ^ J - 1 "^ "l ""^ p "^ T* ^•J* ^Tj* "^P cc cn cc o> cc cn cc cu cc cy cc o> Appendix 3 263 Hyperfine and Rotational Line Frequencies for the Bands of NbCH The lines are sorted into tables by band, branch, J" and, for the high resolution data, F". The labels r, q and p are used to indicate the value of AF. The following symbols are used in this appendix: * a blended or otherwise poor quality line p a perturbed line (also indicated by multiple measurements for a given J) ON II ^ 1 ? ta $ 1 f i-s II ta <N •"5 C CJ £ s 6D * uo o o © o C O * * * OS c- ro © i-H r-00 CO uo uo oq oq 00 -* C N C N C N o >o uo CO uo o o CO CO r H i-H * * * 00 xo r- rH © r H ro o CO f -C N 00 C N r- UO OS Os CO C N C N © ' © © UO UO uo uo UO O o © CO CO CO I-H r H I-H * * * C N cn Oc CO r H CD r H -Tt- I— © © 00 CO ro r- CO OS uo 00 CD r-o CO ro r- UO CO T f •* I-H OS © <N r H r H OS OS Os CO uo uo ro C N C N C N C N C N C N © © © © 00 uo uo CO uo uo uo UO UO UO UO o O o o © CO CD CO CO CO r H I-H I-H I—1 r H * * * * 00 00 CD C N uo I-H o 00 Tj- C N © 00 C N o 00 00 CO CO ro uo r H CO -* CO r—( CO r H OS •"St o t-» T f ro CO CO co CO C N O © Os CO UO uo ro C N C N C N C N C N co' co' C N © © © © oo' oo' r-' uo no UO uo uo UO uo uo uo uo •* T f Tl" O © o o © © CO CO CO CO CO CO r H I-H r H I-H I-H r-H * * * 00 00 O ll", r-~ 00 OS 00 i-H IT- © OS i - H in C N r H o 00 OS r- -* OS C N SO OS CD T r 00 ro ro Os CO UO Os C N CO © uo uo T T i—i p O 00 o r- CO CO CO CO C N C N C N CO CO co' o o co © ' © 00 r-' uo uo uo uo no uo uo uo uo uo uo T t -* o o o © © © © CO CO CO CD CO CO CO r H r H r H r H l H l H cr O. l H cr CH OH H . cr Pi a pi a OH DH r H C N CO -* II •—> II >—> II 1—1 II •—> 265 W u .a o IS c eS .£ / ~ s cT <X I CU .o cu <u e a J3 •O cu C .SP Crf) cs o <u CS H r s cu 15 SB H JS JS •_>l + 1-5 I CS t-+ c s S * 00 s O •<-)• cs a s s o a s a s o o s o s o * * s O o CO s O 00 a s r o a s 00 •* 00 •/-> T—H CS a s <r, v-i 00 p a s C S cs ,—i © s O s O s O s O s O T—i s O s O r—< T-H * * * n o a s T—» 00 r o 00 r o •"St s O r o r o o s O i n a s XO s O T-H r- 00 r- s q s q 00 T-H p p o s ' r s C S •ef T-H* i — ' a s ' s O s O s O s O s O s O WO T-H T-H s O S O t -H T-H * * * * * * r o o O n o a s • * r o o r-T-H a s r - C S r - oo 00 r H r - oo n o o cs s O f - cs r o T-H O S H 00 oo O s a s T-H r - o o s ' <s --I-' T-H n o r s " r i O s r i 00 s O s O s O S O S O s O v o n o s o n o T-H T-H T-H T-H T - H I—I i — i i — i s O s O s O s o s o s o s o s o s o T-H T-H T-H T-H T-H T-H T-H r H r H "H OH lH OH a PH PH P i a P i PH C P H C S CO •* n o II 1—> A A II i—> II i—> 266 Q U T3 e O I CU <u e <u a >> JS •a <u a .Sf *•» es O 3 es H rn 3 es H j s J S cn $1 j s + *T5 S * rs ro r- no r- rs no © ro' r H O * ro rs O no vq p ro vd i — i © rs <N ro © * VO VO ro © * * * * * 0 0 © VO © © -* CO © 0 0 ro ro 0 0 rs OS 0 0 no OS no CO © no CN oo oo ro r- T-l- •<-)• p 0 0 vq © rs , — i rs rs* CO VD ro VD no' r-H -H r H T -H © t-H © © © r-H r-H r H T-H T-H ^ H t-H t — i VO VD VO r-H r-H T-H * * * Os r-H OS r- © © no r- rs CN r- no CO Os 0 0 Os r-rs 0 0 0 0 no 0 0 © no rs t-H so oq tr- •--)- © OS v q T-H ro r-H T-H rs rs ro' v d ro' v d no r-H T-H -H T-H T-H © t-H © © © r-H r-H T-H T-H t-H t-H t -H r H VO VD VO T-H r-H T-H * * * * * * © 0 0 © r-H VD © •"-I- r - ro © no 0 0 f- no r- 0 0 0 0 © 0 0 ---1- © Os no ro 0 0 r- r- no ---r no rs t- r- I—1 ro © r- 0 0 r- no Os rs T-H OS 0 0 OS no no r- Os vq r H ro r-H* T-H r H rH* OS rs* rs* r-' ro* ro* VD* ro* VD no' i—I r H T—1 T-H © T-H -H © r H T-H © r H © © © i—I T - H r—i r H T-H r H r-H r H r-H r H r-H VD VO VO VO VO VO r—* i—1 T-H r H r-H r H * * * * no 0 0 VO no 0 0 VO CN © 0 0 r - © © Os © no r - OS no no oo no rs i r - © -* no Os no OS no 0 0 VO r- vo r- t - 0 0 es T-H t - 0 0 © r- VO rs ro I -H rs •--r ro rs OS © Os vq no 0 0 rs r H © r- rs no T H i— ' r-H* ,—t r-H* © ' Os' rs* rs* r— ro' ro' r- ro' v d no* T-H r H r-H r-H r-H T-H © T-H r H © T-H T-H © t-H © © © t—H r - H 1—1 r—I T -H T -H T -H r H T-H t-H i-H t—i VO VO SO VO VO VO VO VD VO VD VD 1—1 r-H r—1 T-H T-H T -H T-H r H r H t-H r-H a- n, Pi H • * ^ t ? ft mi a VH a-PH PH SH cr* PH PH •-t PH PH PH PH 267 Table 4 Table of assigned rotational Table 5 Table of assigned rotational lines in the A-X 2° 2 band of NbCH lines in the A-X 3°i band of NbCH J R P J R P 6 14871.949 14862.228 2 15148.071 7 72.236 61.227 3 49.065 15143.492 8 72.492 59.996 4 49.630 42.787 9 58.692 5 50.127 41.558 10 57.335 6 50.559 40.402 12 54.567 7 50.936 39.420 14 51.443 8 51.257 38.168 15 49.830 9 51.595 36.895 16 48.111 10 35.599 11 34.291 12 32.967 13 31.610 14 30.095 Table 6 Table of assigned rotational Table 7 Table of assigned rotational lines in the A-X 2°i band of NbCH lines in the A-X (0,0) band of NbCH J R P J R Q P 3 15448.192* 1 16052.391* 4 48.560* 15443.412* 2 53.001 5 48.822 42.572* 3 53.603 16048.259* 6 49.076 41.662 4 54.190 16050.603* 47.209* 7 49.323 40.731 5 54.651 50.229* 46.189* 8 49.534 39.709 6 55.037 49.664 44.966* 9 38.594 7 55.418 49.284 43.869 10 37.419 8 55.722* 48.779 42.607 11 36.225 9 48.259* 41.310 12 34.974 10 47.797 39.940 13 33.705* 11 47.209* 38.627 14 32.226 12 37.200 15 30.765 14 34.146* 16 29.207 15 32.624* 17 27.623* 16 31.028* 18 25.772* 268 Table 8 Table of assigned rotational lines in the 16163 band of NbCH J R Q P 1 16164.159* 16162.712* 2 64.844 62.583* 16160.955* 3 65.366 62.405* 60.140* 4 65.849 62.031* 59.037 5 66.271 61.693 57.937 6 66.624 61.295 56.776 7 66.911* 55.564 8 54.267 9 52.865 10 51.445 11 49.953 12 48.383 13 46.802 14 45.320 15 43.418 16 41.611 17 39.674 Table 10 Table of assigned rotational lines in the 16243 cm"1 band of NbCH Table 9 Table of assigned rotational lines in the 16202 band of NbCH J R P 1 16203.155 2 203.821 16200.028* 3 204.399 199.037 4 204.875 198.028 5 205.286 196.932 6 205.664* 195.779 7 194.547 8 193.249 191 955 9 191.842 190 561 10 190.379 189 080 11 188.827 187 494 12 185 821 13 184 074 Table 11 Table of assigned rotational lines in the 16323 cm"1 band of NbCH J R Q P J R P 1 16244.000* 2 16325.187 16321.256 2 44.535 16240.838 3 25.538 20.319 3 45.112 16242.076* 39.830 4 25.806 19.315p 4 45.520 41.777 38.740 5 18.104 5 41.358 37.592 6 16.094p 6 40.838* 36.331 7 15.037 7 34.996 8 13.694 8 33.581 9 12.041 9 32.079 10 10.492 10 30.493 11 8.807 11 28.840 12 7.029 12 27.095 13 5.203 13 25.295 14 3.205 14 23.433 15 1.225 15 21.621* 16 19.227* 269 Table 12 Table of assigned rotational lines in the 16437 cm"1 band of NbCH J R Q P 3 16426.490* 4 27.034 16423.242 5 27.511 22.940 16419.053 6 27.938 22.573 17.970 7 28.229 22.147 16.773 8 28.556* 21.656 15.530 9 21.094 14.201 10 20.386 12.779 11 11.265 12 9.551 Table 13 Table of assigned rotational lines in the 16437 cm"1 band of NbCH J R Q P 3 16440.056 16434.542 4 40.594 33.553 5 41.229 32.723 6 41.762 16436.325 31.652 7 42.262 36.019 30.665 8 42.721 35.706 29.587 9 43.140 35.366 10 43.536 34.971 11 43.875 34.542* 12 44.166 34.042 13 44.420 33.553* 14 44.631* 32.967 15 32.339 16 31.652* Table 14 Table of assigned rotational Table 15 Table of assigned rotational lines in the 16543 cm"1 band of NbCH lines in the 16590 cm"1 band of NbCH J R Q P J R Q P 1 16544.723 2 16591.992* 2 45.193 3 92.549* 3 * 4 93.083 16589.228* 4 * 16542.474* 5 93.688 88.947 16584.993* 5 46.808 42.190 38.324* 6 94.196 88.741 84.009* 6 47.183 41.842 37.214 7 94.617 88.341 82.949* 7 41.361 36.030 8 94.954 87.944 81.734 8 40.848 34.750 9 87.475 80.513 9 40.211* 33.396 10 86.907 79.190 10 39.476 31.964 11 86.315 77.815 11 38.710 30.411 12 85.672 76.396 12 37.796 28.780 13 84.993* 74.923 13 36.811 27.045 14 84.009* 73.370 14 35.771 25.264 15 83.102* 71.852 15 34.549* 23.386 16 82.145 69.916 16 21.337 17 81.011 68.113 17 19.301 18 79.689 18 17.174 19 14.938 20 12.622 21 10.235 Table 16 Table of assigned rotational lines in the 16909 cm"1 band of NbCH Table 17 Table of assigned rotational lines in the 16929 cm"1 band of NbCH J R P 2 16907.761* 3 16912.141 906.797* 4 12.636 905.843* 5 13.182 904.709 6 13.530* 903.557 7 902.491 8 901.212 9 899.884 10 898.506 11 897.069 12 895.501 Table 18 Table of assigned rotational lines in the 16941 band of NbCH J R P 2 16930.850 16928.806 3 31.438 27.250 4 31.941 25.575 5 32.394 23.977 6 32.752 22.826* 7 33.015* 21.618 8 20.301 9 18.926 10 17.490 11 15.946 Table 19 Table of assigned rotational lines in the 16967 band of NbCH 4 5 6 R 16943.794 44.083 16935.997 34.653 Table 20 Table of assigned rotational lines in the 17033 cm"1 band of NbCH R 1 2 3 4 5 6 7 8 9 16967.908* 68.482 68.957 16963.768 62.690 61.507 60.157* 58.802 57.362 55.695 Table 21 Table of assigned rotational lines in the 17080 cm"1 band of NbCH J R P J P 2 17031.098* 7 17072.297 3 17035.729 30.204 8 70.955 4 36.364 29.278 9 69.428 5 36.896 28.266 10 67.978 6 37.469 27.249 7 37.882 26.146 8 38.166 24.995 9 38.452 23.844 10 22.428 11 21.038 12 19.730 13 18.311 14 16.855 15 15.354 271 Table 22 Table of assigned rotational lines in the 17332 cm"1 band of NbCH J R Q P 1 17333.424* 2 33.975* 17331.812* 3 34.568 4 35.115 31.311* 16328.372 5 35.529 30.966 27.109 6 35.914 30.592 25.991 7 36.161 30.115 24.803 8 36.496* 29.536 23.506 9 29.031* 22.093 10 28.372* 20.777 Table 24 Table of assigned rotational lines in the 15177 cm"1 band of NbCD J R Q P 3 15175.057* 4 15180.493* 74.313* 5 81.013* 73.416 6 81.548 * 7 82.080 * 8 52.583 70.987 9 83.020 70.088 10 83.463 69.130 11 83.862 15175.654 68.196 12 84.247 75.349 67.178 13 84.611 75.057* 66.209 14 84.897 74.700 65.159 15 85.205 74.313* 64.078 16 73.897 62.974 17 61.835 18 60.641 Table 23 Table of assigned rotational lines in the 18258 cm"1 band of NbCH J R P 2 18260.474 18256.668 3 61.022 55.669* 4 61.541 54.666 5 61.957 53.578 6 62.551 52.421 7 62.798 51.173 8 63.082* 50.082 9 63.243* 48.712 10 47.337 11 45.869 12 44.387 13 42.762 14 41.187 15 39.621 Table 25 Table of assigned rotational lines in the 15252 cm"1 band of NbCD J R Q P 3 15250.029* 4 15255.619 49.654* 5 56.372 48.749* 6 56.874 48.049 7 57.480 47.180 8 57.989 46.361 9 58.447 45.471 10 58.937 15251.387 44.575 11 59.388 43.684 12 59.846 50.925 42.750 13 60.244 50.653 41.779 14 60.597 50.354 40.829 15 60.939 50.029* 39.819 16 61.241* 49.654* 38.567 17 61.458* 49.250 37.720 18 48.749* 36.567 19 35.380 20 33.716 21 32.347 272 Table 26 Table of assigned rotational lines in the 15644 cm"1 band of NbCD J R P 5 15647.574 15640.084 6 48.131 39.257 7 48.654 38.377 8 49.133 37.507 9 49.597 36.611 10 50.035 35.676 11 50.454 34.715 12 50.855 33.730 13 51.222 32.744 14 51.549 31.704 15 51.835 30.660 16 29.574 17 28.469 18 27.289 19 26.060 20 24.619 25.820 21 24.254 22 22.824 Table 28 Table of assigned rotational lines in the 16235 cm"1 band of NbCD Table 27 Table of assigned rotational lines in the 16110 cm"1 band of NbCD J R P 2 16111.925* 3 12.553 4 13.166 16106.821* 5 13.722 106.310 6 14.262 105.353 7 14.814 104.493 8 15.314 103.629 9 15.797 102.762 10 16.236 101.837 11 16.693 100.891 12 17.087 99.927 13 17.475 98.956 14 17.834 97.935 15 18.153* 96.910 16 18.396* 95.846 17 94.761 18 93.598 19 92.395 20 91.016 92.189 21 90.659 22 89.257 Table 29 Table of assigned rotational lines in the 16197 cm"1 band of NbCD J R P J P 2 16236.477 16233.191 6 16191.903 3 36.923 32.383 7 90.705 4 * 31.521 8 89.451 5 37.686* 30.579 9 88.089* 6 29.657* 10 86.611* 7 28.482 8 27.382 9 26.202 10 24.963 11 23.798 12 22.405* 273 Table 30 Table of assigned rotational lines in the 16268 cm"1 band of NbCD Table 31 Table of assigned rotational lines in the 16197 cm"1 band of NbCD J R P J P 2 16266.225* 8 16319.960 3 16269.830* 65.345 9 18.762* 4 64.402* 10 17.679 5 70.509* 63.419 11 16.662* 6 70.813* 62.468* 12 15.639 7 61.300 13 13.207 8 60.229 9 59.046 10 57.775 11 56.280* 12 54.833* 13 53.370* Table 32 Table of assigned rotational lines in the 16552 cm"1 band of NbCD Table 33 Table of assigned rotational lines in the 16744 cm"1 band of NbCH J R Q P J R P 2 16554.352* 1 16745.234 3 54.868 16550.260* 2 45.845 16742.589* 4 55.416 49.466* 3 46.298 41.710* 5 55.982 48.489 4 46.730 40.876 6 56.491 47.596* 5 47.164 39.925 7 56.908* 46.727 6 47.532* 38.997 8 57.274* 45.834 7 47.899* 37.985 9 57.680* 16550.968* 44.922 8 36.959 10 58.038 50.609* 43.879 9 35.857 11 * 50.260* 42.808 10 34.691 12 58.706* 49.896 41.763 11 33.436 13 49.466 40.722 12 32.221 14 39.582 13 30.838 15 38.376 14 29.535* 16 37.171 15 28.031 17 35.938 16 26.552 18 34.671 17 24.986* 19 33.366 20 32.108 21 30.700* Table 34 Table of assigned rotational lines in the 16770 cm"1 band of NbCD J P 8 9 10 11 12 16763.121* 62.036* 60.916* 59.753* 58.634* 274 Table 35 Table of assigned rotational lines in the 16868 cm"1 band of NbCD J R Q P 4 16870.596 16864.900 5 71.233 64.317* 6 71.843 63.743* 7 72.984 16867.546* 62.671 8 73.426 67.351* 61.845 9 73.842* * 60.956 10 74.052* * 59.993 11 74.294* 66.378 59.005 12 65.747* 57.821 13 65.369 56.638 14 55.470 15 54.282 16 53.041 17 51.699 18 50.342 19 48.975 20 47.508 21 45.982 22 44.447* Table 36 Table of assigned rotational lines in the 16965 cm"1 band of NbCD J R Q P 2 16965.319* 3 64.940* 4 64.606* 16962.174* 5 64.096 61.067 6 63.571 59.832 7 62.949 58.563 8 62.174* 57.246* 9 61.458 55.863* 10 60.409 * 11 16966.930 59.438 52.615 12 66.478 58.396 50.940 13 65.948 57.246* 49.151 14 65.319* 56.012* 47.286 15 64.606* 54.661 45.359* 16 53.263 43.318* 17 51.794 41.214* 18 50.234 19 48.622 20 46.914 21 * 22 43.318* Appendix 4 275 Hyperfine Line Frequencies for the Bands of TaCH The lines are sorted into tables by band, branch, J" and F". The labels r, q and p are used to indicate the value of AF. The following symbols are used in this appendix: * a blended or otherwise poor quality line p a perturbed line (also indicated by multiple measurements for a given J) 276 r-II fe rN 4 I m I 1-9 JS T-H I II fe JS + II fe JS JS js ll fe e <u S e W) * 0 0 SO CN VO T l T t 0 0 0 0 T i T ) IT- C -cn vo T l f-cn cn T t f -cn vo T f VO r - o OS CN T l c n c n c n c n o 0 0 c n T f T t T f c n O Os » ' t- r-' v d T i r - f - r - r -c n c n vo VO r—t f—H 0 0 CN Os OS t -r -c n SO * rH CN O OS c n r H o o oo' oo' r - r -c n vo * OS CN CN IT- o Os Os 0 0 O 0 0 0 0 0 0 T l ' T l T l r- r- r-c n VO xo r -vo c n T f c-c n VO * * * co h cl "t T f CN OS OS T i CN O OS Os Os Os T l T l ' T l ' T l ' T t r - r - r - r -c n c n VO VO CN c n os c n Tt' r-* * * * * Os VO T l 0 0 o o f - H f~ c n f - H o cn Os CN T l vo T t T l Os SO CN o 0 0 T t CN 0 0 T f OS OS o SO CN CN SO CN o T l T f T t l-H O o o O O OS OS SO » ' » ' » ' VO SO SO 0 0 0 0 SO v i V l ' T t » t - » t - r - r - f- tr- t - t - t - r -c n cn cn cn c n vo SO s o SO so r—1 i — i I-H f - H f - H * * * OS f - H c n SO 0 0 0 0 f - H T l f - H r - 0 0 SO SO 0 0 ,—1 T l SO cn c n O 0 0 OS s o CN f - H » c n T l c n cn OS OS T l T t SO CN OS 0 0 f-H Os 0 0 V I T t T t r H o o o Os Os Os s o SO SO r-' t-' l> VO SO 0 0 0 0 »' T l ' T l ' t - I T - r - r - r - r - r - r - r - r - r - r - I— c n m c n c n s o s o s o SO '—' r H f - H H DH H cr P . * H CJ 1 P H u cr (X •H cr P -c n T ) 0 0 r — c n so OS r -VO o T l cn SO 0 0 T l ' 0 0 t - r -c n cn s o vo t -* * c n c n c n OS OS r -r - r - T t s q s q 0 0 T l ' T ) ' 0 0 r - C - r -c n cn SO s o '—' * * * * * 0 0 o T l T l SO 0 0 o o t - 0 0 0 0 T l T l cn vo o OS OS IT— c n so T t r - SO SO T l T l oq 0 0 T l T l T l c n c n 0 0 r— r - r - r - t— t— r -cn c n c n c n SO s o s o s o 1—1 1—I * * * * * 0 0 i - H r - 0 0 CN T l OS 0 0 f - H c n r- 0 0 c n CN c- Os Os T t o c n 0 0 T t oo T t r - t - r - s q T l T l 0 0 0 0 T l ' T l ' T l ' c n c n c n oo' r - ir- r - t - r - r - r -c n on c n c n s o SO s o SO r H f - H f - H * * * SO r H CN 0 0 CN VO T l SO 0 0 r - 0 0 cn T l l - H o 0 0 c n o c n t - O T i r - r — r - so T l OS 0 0 T l ' T l ' T l ' c n c n 0 0 » t - t - r - r - t> c n c n c n cn s o SO SO SO f—i f - H f - H l - H * c n 0 0 T t O T i T t , — 1 o SO o o 0 0 CN c n SO CN T l OS OS • i—i T i T l T t r - s q T l Os T t 0 0 oo' T l ' T l ' cn 0 0 ir- ir- IT— r - C - r - I— on on c n m c n SO s o s o s o SO i—i I—1 f - H r H f - H a 277 J S I fN fe fN fe f N T-H I II fe fN T-H fN f N J N r-* l II fe e s e Of) c/i CM r- CN Os CO c s no CN - - H os' © ' r- r» CO CO SO VO co no T t Os T t vo f N r-H c s © r- r— CO CO s o VO vo no r -co no r -CO SD * Cs no C -T t oi T t < N 00 Os' C -CO SD * * * T t C s vo Os r - H r -00 •* Os no OS VO 00 o 00 c - Os VO CO no T t T t r - H CO no f N f N <N Os r-H* r - t - IT- r - f - r -r o CO CO CO vo VO sO SO C N VO 00 O c-o C N o * r -* * Cs Os O O CN CN T t T t no' no* t - C -co SO * * r - H C S OS C N O O no co C N *** . no no' no r - r - i— CO VO t -CO vo * * Os r - H r-T t o SO o CN 00 no (N CO CN OS* ,—' r - C - tr-CO CO CO vo SD vo r - H i—I r - H 00 Cs no 00 CN O no •* CN* r H r- C -CO VO o r -CO vo CO T-H O CN CN CO CO CN Cs* © ' r- r-CO SO * SO t -no Os 00 sO VO T t r -Cs oo' SO CO SO f -<N Os Os 00 SD CO VO Os Os co no 00 o •"fr o Os Os r- s o co sO no VO T t T t r-' vo C N T t VO T t C -VO vo T t 00 T t r -so CO vo no C N o no tr-SD CO vo VO 00 00 00 •"-fr r H no no OS r -C - vo CO SD 00 CO no T t CS t-c-T t OS C -co SO r -Cs T t Cs' r-CO vO T t VO O no r o O no r H Os' v d r- vo CO SD * * * * * * OS CN Os OS f N \ — i T t Cs r H o CS sO SO r -SD CN © Cs no VO TTj- no r - Os CN o 00 00 00 T t CN 00 T-r CN co T t Cs r H VO CO T t r H T j " T t T t no no T t CO CN TfJ- o no no no r H no no' no' CN CN ,—i Cs © Cs Cs Cs r - os' SO t - r— r - r— tr- C - IT- r - IT- VO r - SD r - SO CO co co CO CO CO CO SO vo vo VO VO SD vo r - H T - H T - H T - H T - H T - H T - H OS T t T t vo CN r - H Cs CN r H T t r H O T - H O T t T t SO CN CO o VO CO CO no OS o rN no Os' T t CN Os T - H Os' C - VO sO r - VO no CO CO CO co SO VO SO SO l — ' ' 1 T - H r H o r - rN T t O T - H CN CN CO CN Os VO no 00 T t no CN 00 r H no CO no Cs O r s r - no Os T t " CN Os ,—< 00* Os' t VO SO r - vo IT- no CO CO r o CO SO SO SO VO ' 1 '~ H ' 1 CN T t r o f - T t O r o "> no r H r- SO o no tr- T t o CO T t no Os o r o r -Cs' T t <N Os' r H * od C - VO VD f - VO r -r o r o CO CO VO vo SO VO * 00 T t Cs O CN r H VO r o CN T t O O no T t CN 00 Cs SO CO no Os T t no Os o r o C - no Os' T t CN Os T - H 00 Cs* C - VO VO o VO IT- no CO CO r o CO vo SD vo VO r — ' ' " " H T—1 r H OS no T t r- no C - CO r H r - Os Cs CN T t 00 o - t Os C - o r- T t SO T - H T t no CN O o r o r - VO Cs T t Cs CO Os H 00 Os r - VO r - so C - VO C - no co r o r o r o vo VO vo vo ' — ' •—' * * * * * vo o T t SO VO vo co r o Os CN CN O Cs' r o r- vo r o VO O 00 Tt t-oo no O CO OS r H * t— s o co VO ( H C7 1 P H I H C T 1 C H PH O SD O O C N 00 C N r - vo 00* OS* r - no co VO * * * * 1—1 00 00 no no T t e s o VO r o no C - no Os r - r o © o r o 00 tr- vo <N T t r - H 00 fN fN VO r- O r - H 00 no 00 T t r - H CN r o r - H VO o T - H no o no SO 00 T t T t no o CO r - r o no CN SO CN o r o OS VO Os r o T t T t no <N o T t CO CN no O no no no ' — i T t VO r o O o CO r - vo no no' CN* Os' no' r-H* Cs d Cs Cs Cs t - Cs vd Os' T t Os' ro' Cs r - H 00 Os r - IT- IT- c - r - ir- r - r - r - so c - vo r - vo 1— VO r - VO c VO r - no co r o co co r o co r o r o r o CO CO SO VO VO VO VO VO vo vo VO •vo vo p d O P n P H P H P H P H PH PH PH PH PH PH PH PH PH PH PH PH r o .11 278 * 00 r-CN CN © Os co * OS r-o CN SO Os CO SO * Os o CN SO OS o so SO SO OS cn SO * o r-r-o r-OS cn so o r-' OS * * * * * cn r - SO xn T t r-H r H T t cn r - xn T t » r H CN o f-H xn r -r H CN xn 00 SO CN CN f-H » xn so T t o d d xn xn so sb xn r-' OS OS OS Os 00 Os 00 Os cn cn cn m m cn cn cn so SO so so so so so SO • — l '—' i-H * * * * * * * * * * * * * O xn xn cn CN cn O SO CN r H xn xn SO so OS o O •-fr T t CN r- r- cn CN r- xo O 00 so CN T t T t OS T t xn r- T-H T t r- XI T t 00 OS r - r- r- o i-H OS cn r- cn CN cn © Os CN CN CN xn T f T t r- xn r H xn so T t O cn cn i-H cn d d d T t xn 00 00 xn C-' SO so SO x-i OS OS OS OS Os OS OS OS OS 00 00 OS 00 OS 00 OS 00 OS cn cn cn cn m cn cn cn cn cn cn cn • cn cn cn cn cn so so so so SO so so so SO so so so so so SO SO so rt rt • — ' ,—1 * * * * * * * * CN SO 00 t-H cn cn CN r—H T t T t CN o © T t Os o r H o T f CN CN cn i> 00 cn o cn T-H O 00 CN r H 00 l-H cn 00 CN cn xn O r - so T t OS r - SO r - xn Os o r - © CN xn cn cn cn ' — J OS CN CN xn cn I—t T t T f so xn l-H xn SO T t cn cn cn ,— ' cn d d T t OS xn 00 00 xn C-" SO s d sb xn OS Os Os OS OS OS OS OS 00 OS 00 00 OS 00 Os 00 OS 00 cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn so so so so so so so so so SO so so SO SO so so ~ 1 ' T-H r H r H ' 1 ' 1 r H • - f r CN cn SO * o so T t » 00 xn cn 00 Os cn o SO o T t CN C- OS UO T t so o xn o T t cn SD » SO o CN 00 SO T t o 00 xn OS Os r - tn xn cn CN SO xn cn cn SO 00 xn f - OS cn m UO. Tl CN CN © OS OS CN xn cn r H T t s q T t i—i T t xn T t o CN CN CN cn cn r H cn cn d T t OS xn oo' xn r-' SO SO sb xn r-' OS OS OS OS OS OS OS OS OS OS 00 OS 00 Os 00 OS 00 OS 00 OS cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn cn SO so SO so so so so so so vo so SO SO so so so '—' • _ l • _ l ' — 1 T-H i—i r H r H u cr OH tH cr o . tH cr OH tH cr u cr OH cr OH Pi Pi CM Pi PH OH OH Oi OH Pi OH Pi OH Pi OH Pi 279 fN t r -I fN V) I t - B II fe fN CO K4| 4l JN T—I II fe fN fO + , II fe fN + fN t— + •"-9 B cu s a .SP m ro as tr-' Os ro sO CN sO OS r -CO SO * * * * Os o o U0 uo o CO OO T-H CO •"-I-CN c - T-H OS CO r- CN tr-' 00 Os 00 Os CO CO CO CO sO sO sO sO * * * * * 00 •-t sO Os CN 00 sO CO -* o o o uo sO •* C - » - H Os CN r-H t - CN r-' 00* 00 Os 00 Os IT-CO CO CO CO CO sO sO sO sO sO r-' '—' r-' H *—' * * * * * 00 Os c- uo T-H ro I— CO 00 fN •-t sO T - H Os OS 00 o •* I— Os T-H I—1 I—I "-* CO fN sO T - H Os 00 CN T-H r-' CO t— CN* I— © ' 00* 00 Os 00 Os 00 Os 00 r-CO CO CO CO CO ro ro co sO VO sO sO sO sO sO sO * — ' * * * * * * Os fN Os sO o\ sO r - 00 ro uo o CN T-H T-H CO ro tr- © CO CO Os sO sO 00 00 o ro ro 00 CO CO CO fN sO p Os 00 i—i uo CN r-' CO r-' CN r-' © ' 00* Os* 00* 00 Os 00 OS 00 Os 00 OS r - IT-CO CO CO CO CO ro ro ro co ro sO sO SO sO sO sO sO sO sO sO '—•' '—1 * * * * * IO Os sO © ro sO © ro © i—i CN uo fN T-H ro © Os CN i—( sO r - tr- sO Os UO © sO rN sO CO co CN sO 00 00 uo CN 00 r-' co' tr-' C - © 00* OS 00* sO* 00 OS 00 Os Os 00 Os r - tr- c -CO CO CO CO ro ro ro CO ro ro sO sO sO sO sO sO sO sO sO sO T-H T-H T-H T-H ' ' T 1 fN CO --J- r - sO Os ro r - rN 00 IT- sO IT- r H Os T-H © ro ro sO T-H T-H CO uo sO OS 00 ro OS ro CO CO CN sO o 00 tr- © uo '—i 00 r - CO r - fN* tr-' © ' 00* Os 00 s d 00 Os 00 Os 00 Os 00 Os [- r - r -CO CO CO CO CO CO ro ro ro ro ro sO sO sO sO sO sO sO sO sO sO sO T-H Pi OH Pi PH Pi PH Pi PH Q u « H C+-o •o B es £> + O IX I + o m cu JS a CU e 13 cu B .SP *8B o CU 3 es H rn cu 3 es H fi cu a a, •SP' tn v> < * Os T 1 © © Os ro © Tt-Os © © T H © © Os Os CO sO Os 00 © 00* 00 ro sO CN OS • * 00 00 ro sO * * r - 00 r - 00 T-H Os •<* \—i C - •* UO CO 00 sO uo © -* © © ' — ' Os' Os Os' © © ' 00 00 00 00 OS Os 00 ro CO ro sO sO sO T-H I—I T-H IH ZT OH Pi )H U PH IH CT ft Pi PH 280 A I J S | m i l l I JS J i II fe «s II fe JS JS A, js in + js r-A| II fe a Ml •-fr oo CN Os CO SO * -* SO CN OS CO SO * CN SO r-r-co' Os co SO * t -wo wo o CO OS CO SO •-fr OS CN Os SO 00 OS 00 CO SO •se- * * * * * * o s -fr 00 SO Os o Os r - . r-H l-H CO 00 SD XO Os r—1 i-H -fr CO i-H SO SO CO -fr 00 CO 00 CO 1> 1 —1 OS t--' I—' CN CN CO CO -fr •-fr 00 Os Os OS OS Os Os Os CO CO CO CO CO CO CO CO SO SO SD SO SO SO SO SO ' — 1 7—1 •""' r-H * * * * * * * * * * * * * * * r - r - SO r - xo r-H CO SO i-H i-H r - Os CN 00 SO o o -fr so CN •-fr i-H 00 SO i-H SO o CN CN O CN l-H r -<T- xo r-H OS co CO o r-H -fr r - 00 l-H O CN o 00 X 0 •"fr -fr CN 00 OS_ co_ -fr CO s q c- r - r-H Os O Os --H CN r-H r - t-' r-H r-H xo' CN •-fr CO CO co CN •-fr' 1—I r-H -fr d XO Os' 00 00 OS OS 00 OS 00 OS 00 OS 00 Os 00 00 Os 00 Os t -CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO SO SO SO SO SO SO SO SO SO SO so SO so SD SD so s o r-H r" ' 1 —1 1 —1 I—I 1—I 1—1 I—I r~l r-H l-H 1—I r-H •— 1 r-H 7-1 •i(- * * * * * * c SO 00 XO » I—1 -fr OS r-H r - CN 00 xo X 0 r - l-H CO SO xo OS CN CO CO OS OS CN CO o r-H -fr CO CN 00 xo CN Os 00 CN l-H l-H l-H OS o SO OS Os so --fr SO CN » l> Os CO CN 00 •-fr CN s q » r-H oq CN r-H © r-H SO 1—I xo CN xo CN -fr CO CO CN -fr ,—< xo Os' OS OS 00 Os 00 OS 00 Os 00 OS 00 00 OS 00 Os f-CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO SO SO so so SO SO SO SO SO SO SO SO so SO SO SO 7—1 * * © CO OS r-H CO CO xo o r- CN xo CO 00 CO o o OS CO -fr OS xo SO os CO r-H 00 r - OS -fr i-H CN 00 o I—I l-H 00 o i-H CN SD CN 00 o uo •-fr CO CN o r - SO o Os OS o r - 00 r-H -fr • - f r r - o Os SD CO CN SO SO •-fr CN r - r - Os CO r-H r - •-fr CN xo r - o oq OS 00 O CN I—1 d d r - ,—I s b r H xo CN xo' CN -fr CO co' co' CN "-fr r-H d •"fr d xo OS OS OS 00 OS 00 OS 00 OS 00 Os 00 Os 00 OS 00 Os 00 00 OS 00 Os » CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO so SD SO SO SD SD so so so SO SD so so so SO SD so SD so SD s o 1 —1 r-H H o 1 n Oi P H P H P , P H P, PH Pi PH Pi PH Pi PH PH PH PH PH Pi PH PH PH 281 cu S G e o U CU 3 es H JN IT-•ii rN in I II fe m A, J N II fe JN r H Al JN r n + 1-5 II fe JN un Al JN Al e CU S s •Sf *•» < * VI CN rs oo r-m vo * ON O 00 T-H 00 r-m VO O 00 cn oo' r-m V O r-m vo CN v> V D r-' r-m vo r-o ir> r-m vo C M •*| IT Q U es H «<-• o •a e es + o <X i i—I CU a • a CU s • es «*-O CU 3 es H -rf 3 es H JN r-I >-5 uo A >i fe fN m I II fe fN *»\ II fe A, fN m Ai fN + ! JN Ai c cu C M l * m m •--l-r-vd vo m vo * * O V m T-H o V O m ON t-H cn -<-"• ON c-~ 00 r- r- r-vd vd vd vd vo vo vo vo m m cn cn vo vo vo vo T H r H T-H T-H * * VD cn ON cn C\ i -H I -H t-H VD r H I O r-H ON 00 00 00 vd V D V D V D VD V D V D V D cn m cn cn vo vo vo vo 1—H T-H t-H r-H o o •* r - xo m r- T-H vo m m cn r-' r-' r-' V D VO VO m vo u D 1 ft 0? * V I ON rs t—i rs "/"> ON 00 VD VD VD VD m m V O vo H C ft * * * m O T j -H H rs H h • * oq r- v> vo vo vi VD V D V O m m m V O V D V D t y ft xo 00 00 V ) V I • 5 t T-l- •"-J-vd vd V D vo m m vo vo •—' r H * * * t-H CN CN 00 vo V0 ON r- r----)• vd vd vd V O vo V O m m cn V O vo V D t-H t-H '—• * V D ON O V ) vd V D cn vo r H * * * 00 r H r H r-H o 00 XO rs OS V I V I vd vd vd V O V O vo m m cn vo V D vo t—i r H * V O ON O V I vd V O cn vo t y ft 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0061350/manifest

Comment

Related Items