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Fourier transform microwave spectroscopy of halogenated triatomic molecules Gatehouse, Bethany 1997

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FOURIER TRANSFORM MICROWAVE SPECTROSCOPY OF HALOGENATED TRIATOMIC MOLECULES By Bethany Gatehouse B. Sc. (Chemistry) University of British Columbia A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  IN THE FACULTY OF GRADUATE STUDIES CHEMISTRY  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA  May 1997 © Bethany Gatehouse, 1997  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.  Chemistry The University of British Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1Z1  Date:  Abstract  Pure rotational microwave spectra of the following molecules have been obtained using a pulsed jet cavity Fourier Transform microwave ( F T M W ) spectrometer.  Nitrosyl Chloride:  C 1 N O Rotational transitions of five isotopic species of nitro-  syl chloride were measured in the 4-26 GHz frequency range. From these transitions, rotational and quartic centrifugal distortion constants were obtained.  The rotational  constants were used in various structure determinations, and the centrifugal distortion constants were used to refine an already known harmonic general valence force field. Quadrupole and spin-rotation hyperfine structure in the measured transitions was analysed to yield diagonal and off-diagonal quadrupole coupling constants and diagonal spin-rotation coupling constants of both the chlorine and nitrogen nuclei. The principal quadrupole coupling constants were evaluated and used to calculate the approximate ionic character of the N - C l bond. The spin-rotation coupling constants were used to calculate the nuclear shielding of the nitrogen and chlorine nuclei.  Sulphur Difluoride: S F The microwave spectrum of the unstable molecule sulphur 2  difluoride, prepared via a pulsed electric discharge in an S F / O C S mixture, has been mea6  sured.  1 9  F hyperfine structure has been resolved in some of the measured transitions, and  unusually small, negative values have been determined for two of the three spin-rotation coupling constants. These constants have been used to calculate the 11  1 9  F principal inertial  axis nuclear shielding components; the determined paramagnetic shieldings are also unusual and produce a large positive average shielding. The shieldings have been compared with the corresponding constants obtained for  OF2, SiF2,  and  GeF2-  The results for  SF are consistent with values determined from earlier NMR experiments and 2  ab  initio  calculations. The origin of the unusual shieldings is discussed, using a semi-quantitative model, in terms of the geometry and the electronic energy level structure of the molecule.  Halogenated Oxo- and Sulphido-boranes: FBO, C1BO, and FBS The unstable XBE species FBO, C1B0, and FBS have been prepared though the use of an electric discharge and their microwave spectra have been measured using FTMW spectroscopy. Hyperfine structure in the observed transitions has been resolved and analysed in terms of quadrupole, spin-rotation, and spin-spin interactions. The determined quadrupole coupling constants have been used to show that the electronic environment surrounding the boron nucleus of all three species is very similar, and the spin-rotation constants have been used to calculate the average shieldings of the CI, F, and B nuclei of these molecules; this is thefirstexperimental determination of these parameters.  Phosphenous fluoride: OPF Free gas phase OPF has been prepared here for the first time by passing an electric discharge through a mixture of PF3 and O2, and the microwave spectra of two isotopomers have been measured in the 4-26 GHz frequency range. These transitions were analysed in terms of rotational, centrifugal distortion, and spin-rotation coupling constants. The determined rotational constants have been used to calculate ro, r , and approximate r molecular geometries, and the spin-rotation coupling, 2  e  constants have been used to calculate the nuclear shielding parameters of the fluorine and phosphorus nuclei. Because both F and P are spin | nuclei, and because both sets of  111  d e t e r m i n e d s p i n - r o t a t i o n c o u p l i n g c o n s t a n t s h a d v e r y s i m i l a r v a l u e s , a s s i g n m e n t o f these c o n s t a n t s t o a p a r t i c u l a r nucleus was not p o s s i b l e ; t h e n u c l e a r s h i e l d i n g p a r a m e t e r s o f t h i s species h a v e b e e n c a l c u l a t e d u s i n g b o t h p o s s i b l e a s s i g n m e n t s .  iv  Contents  Abstract  ii  List of Tables  viii  List of Figures  xi  Acknowledgement  xii  1 Introduction  1  2 Theory  5  2.1  Rotational Spectroscopy  5  2.1.1  Rigid rotor  6  2.1.2  Centrifugal distortion  8  2.1.3  Nuclear Hyperfine Interactions  10  2.2  Molecular Geometry  19  2.3  Harmonic Force Field  24  2.4  FTMW Spectroscopy  25  2.4.1  Theory  25  2.4.2  Fourier transform  30  3 Instrumentation  32  v  3.1  Microwave cavity  32  3.2  Electronics  33  3.3  Pulse sequence  35  3.4  Gas sample  35  3.5  Discharge System  37  4 Nitrosyl Chloride  40  4.1  Introduction  40  4.2  Experimental Methods  42  4.3  Spectral Analysis  43  4.4  Discussion  •'  48  4.4.1  Molecular geometry  48  4.4.2  Force  4.4.3  Nuclear quadrupole coupling constants  52  4.4.4  Nuclear spin-rotation coupling constants  55  field  5 Sulphur Difluoride  50  67  5.1  Introduction  67  5.2  Experimental Methods  68  5.3  Spectral Analysis  69  5.4  Discussion  71  6 Halogenated Oxo- and Sulphido-Boranes  84  6.1  Introduction  84  6.2  Experimental Methods  85  6.3  Spectral Analysis  85  6.4  Discussion  88  vi  6.4.1  Nuclear quadrupole coupling constants  88  6.4.2  Nuclear spin-spin and spin-rotation coupling constants  92  7 Phosphenous Fluoride  110  7.1  Introduction  ,  7.2  Experimental Methods  Ill  7.3  Spectral Search and Analysis  112  7.4  Discussion  118  7.4.1  Molecular geometry  118  7.4.2  Nuclear spin-rotation coupling constants  120  Appendices  110  133  A Measured transitions of Nitrosyl Chloride  133  B Measured transitions of Sulphur Difluoride  152  Bibliography  155  vii  List of Tables  2.1  Character table for the D point group  8  2.2  Selection rules for rotational transitions  8  4.1  Transitions of C1N0 strongly affected by Xab • • • •  57  4.2  Spectroscopic constants of nitrosyl chloride  58  4.3  Structural parameters of nitrosyl chloride  59  4.4  Quadratic force constants (lOONm ) of the general valence forcefieldof  2  a  -1  nitrosyl chloride  60  4.5  Comparison of measured" and forcefieldcalculated parameters of ClNO  4.6  Force Constants" (100 Nm" ) of XEO Compounds (X=-,F,Cl,Br; E=N,C,0) 62  4.7  Principal chlorine and nitrogen quadrupole coupling constants of nitrosyl  b  1  chloride 4.8  63  Ionic character of the N-X Bond, diamagnetic nitrogen nuclear sheildings, and N=0 bond lengths of several nitrosyl compounds  4.9  61  64  Chlorine spin-rotation constants (kHz) and nuclear shielding parameters (ppm) of C1NO  65  4.10 Nitrogen spin-rotation constants (kHz) and nuclear shielding parameters (ppm) of C1NO 5.1  66  Observed transition frequencies, v, and differences between observed and calculated frequencies", A, of sulphur difluoride viii  78  5.2  Spectroscopic constants of sulphur difluoride '  79  5.3  Comparison of the fluorine spin-rotation coupling constants (kHz) and  a  shielding components (ppm) of sulpur difluoride with those derived from ab initio results  5.4  80  Comparison of thefluorinespin-rotation coupling constants (kHz) and nuclear shielding components (ppm) of sulphur difluoride and other difluorides 81  5.5  Excitations giving non-zero values for paramagnetic shielding components, trj (p), of sulphur difluoride  82  3  5.6  Comparison of experimental and calculated F paramagneticfluorineshield19  ing components of sulpur difluoride and oxygen difluoride 6.1  83  Hyperfine component frequencies, v, and differences between observed and calculated frequencies, A, for the J = 1 — 0 transition of FBO  6.2  Spectroscopic constants and correlation matrix for FBO  6.3  Measured hyperfine component frequencies, v, and differences between observed and calculated frequencies, A, of C1BO  6.4  Spectroscopic constants of C1BO  6.5  Hyperfine component frequencies, v, and differences between observed and  97 98  99 101  calculated frequencies, A, for the J = 1 — 0 transition of FBS 6.6  Spectroscopic constants and correlation matrix for FBS  6.7  Comparison of measured boron and chlorine quadrupole coupling con-  102 103  stants (MHz) of FBO, C1BO, and FBS with related species  104  6.8  Isotopic Ratios of the quadrupole coupling constants of FBO, and C1BO  105  6.9  Reduced spin-spin coupling constants, ffi^£) , g  g  and a comparison of the  measured and calculated spin-spin constants (kHz) of FBS, FBO, and C1BO106 6.10 Reduced spin-rotation constants,  of FBO, C1BO, and FBS  ix  107  6.11 Spin-rotation constants (kHz) and nuclear shielding (ppm) of the F, CI, and B nuclei of FBO, C1B0, and FBS  108  6.12 Calculated paramagnetic shielding proportionalities, a (ppm) x AE(Eh), p  for FBO, C1BO, and FBS 7.1  109  Observed transition frequencies, v, and differences between observed and calculated frequencies, A, of OPF  7.2  Spectroscopic constants of phosphenous  7.3  Cj  tT  124 fluoride  . 125  0  constants determined for the studied rotational energy levels, and  the spin-rotation coupling constant dependence of the observed rotational transitions of OPF  126  7.4  Structural parameters of OPF  127  7.5  Comparison of the structural parameters of OPF with those of related species"  7.6  128  Comparison of the reduced spin-rotation coupling constants, and OPF 18  7.7  , of OPF 16  129  a  Fluorine and phosphorus spin-rotation constants (kHz) and nuclear shielding parameters (ppm) of OPF°  7.8  130  Comparison of thefluorinenuclear shielding parameters (ppm) of 0 P F 16  and ONF 7.9  a  131  Non-zero calculated fluorine paramagnetic shielding proportionalities, cr (ppm) x p  AE(E ), h  for OPF and ONF  132  A. l  Measured transitions of nitrosyl chloride  133  B. l  Transitions of sulphur difluoride  152  List of Figures  3.1  Schematic circuit diagram for the FTMW spectrometer  35  3.2  Pulse sequence for an FTMW experiment  37  3.3  Schematic diagram of the electric discharge apparatus  40  4.1  Example b-type transition of C1N0 that is strongly affected by Xab • • •  4.2  Principal quadrupolar axes of the chlorine and nitrogen nuclei  5.1  The 32,i — 4i,4 transition of SF , showing resolved hyperfine structure . .  5.2  Electronic energy level diagrams for SF and OF  6.1  Composite spectrum of the J — 1 — 0 transition of F B O  6.2  Schematic diagram of the electronic excitations of XBE giving rise to non-  37  2  2  47 54 73 76  2  n  88  zero contributions to the X(=C1/F) and B paramagnetic nuclear shielding terms  97  7.1  The l ,i — 0,o transition of OPF, showing resolved hyperfine structure  7.2  The 3i,2 — 3  16  0  0  1]3  and 4  116  — 4i transitions of OPF, showing an increase in 16  1>3  )4  linewidth with increasing J.  117  xi  Acknowledgement  I would like to acknowledge my supervisor, Mike Gerry, and many co-workers for their support and patience throughout the completion of this thesis work. In particular, Chris Chan has been a great asset in the building of the discharge apparatus, and Holger Muller has been a great help with answering many e-mail queries. I also thank Wolfgang Jager, Nils Heineking, Christian Styger, Yunjie Xu, and Kristine Hensel who were there at the beginning to show me how things worked; I also thank Jurgen Preufier, and, of course, my co-worker and friend Kaley Walker for all of her support through the years. Mark Barnes has also been invaluable in trying to explain electronic spectroscopy lingo to me. I would like to thank him and the rest of the neighbours and neighbours-by-proxy: Allison Barnes, Greg Metha, Dave Gillett, Peggy Athanassenas, Jim Peers, and Chris Kingston. And, lastly, I thank Thomas Brupbacher for everything. And Thomas.. ."elephant juice".  xn  Chapter 1 Introduction  Microwave spectroscopy is, in general, the study of rotational transitions of gaseous molecules with electric dipole moments. Rotational and centrifugal distortion constants that contain information about the structure and potential energy surface of the molecule can be obtained from observed microwave transitions. The microwave spectroscopic technique offers both high resolution and high measurement accuracy. Accordingly, if any atoms with non-zero nuclear spins are contained in the molecule, hyperfine splittings can be resolved in the rotational transitions and used to determine hyperfine coupling constants which, in turn, contain information about the molecular electronic structure. With the advent of the high resolution technique of Fourier transform, microwave (FTMW) spectroscopy, very small spin-rotation and spin-spin hyperfine splittings, previously rarely reported from microwave spectra, have become readily observable. The analysis of the small coupling constants determined for transient species has been a major focus of this thesis work. Over the past 50 years, there has been much interest in the spectra of unstable or reactive molecules such as ions and free radicals. Of particular interest have been molecules which play a role in the chemistry of the upper atmosphere [1,2] and the interstellar medium [3-5]. However, since the lifetimes of these species are very short, they have been difficult to study. One easy preparation technique, which can be used to generate 1  CHAPTER  1.  INTRODUCTION  2  these species in situ, is the use of an electric discharge. While a conventional discharge cell has proved to be efficient at producing these transient species, the rotational temperatures obtained using such devices are often high [6], resulting in very cluttered spectra. A recent solution to this problem was to couple a discharge source with supersonic expansion [7]. In this manner, these transient species could be prepared and immediately stabilised in the jet expansion; the low rotational temperature achieved in the jet acts to suppress any transitions arising from higher energy levels, thus greatly simplifying the spectra. In thefirstwork that reported using this technique [7] a discharge took place behind the pinhole of a "continuous wave" expansion nozzle. The technique soon evolved to being used with a pulsed nozzle, and, in the past several years, much work has been reported that makes use of this- pulsed discharge technique to. prepare a variety of different compounds such as ions [8], free radicals [9-11], metal-containing compounds [12-14], and other transient species [15-17] for spectroscopic study. This thesis presents the results of microwave spectroscopic studies of six triatomic molecules of varying stability. In Chapter 4, a microwave study of nitrosyl chloride is presented. This is a complete, classical microwave study of a stable molecule which was prepared by simply allowing gaseous chlorine and nitric oxide to react in an excess of Ne. The determined rotational constants offiveisotopomers of the molecule have been used to calculate the geometric parameters, and the centrifugal distortion constants have been used to calculate an harmonic force field. The hyperfine parameters have been used to obtain information about the N-Cl bonding, this is of particular interest because of the atmospheric importance of the ozone-depleting reaction involving atomic chlorine which is liberated by the rapid photolysis of the Cl-N bond of C1N0 [18]. Structural and force field parameters were already known for this molecule [19] and this study has added only a small improvement in their determination. However, very little was previously  CHAPTER  1.  INTRODUCTION  3  known about the hyperfine constants, and it is here that this study has made its greatest contribution. Moreover, this study represented, to the author, a very good introduction to all aspects of microwave spectroscopy. In the remaining chapters, microwave spectroscopic studies of unstable molecules prepared through the use of an electric discharge are presented. The electric discharge apparatus that wasfirstused in this laboratory [20] consisted of a point-to-point discharge which took place between two wires introduced into a small mixing chamber in the form of a nozzle cap that was mounted in front of the nozzle used to inject samples into the microwave cavity. This design was seen to be rather inefficient and difficult to use. It was changed in the course of this work to follow the design reported by Schlacta et al. [21], where a discharge took place between concentric disc electrodes placed along the molecular expansion channel; a brief history of the design procedure for the discharge i  apparatus is given in Section 3.5, along with a description of the system that is currently used. Chapter 5 presents a study of the microwave spectrum of the main isotopomer of sulphur difluoride, prepared using the electric discharge apparatus. Because this isotopomer has no quadrupolar nuclei, all observed hyperfine structure was due only to the spin-rotation and spin-spin coupling mechanisms of thefluorinenuclei. The information contained in the determined spin-rotation coupling constants was used to calculate the nuclear shielding parameters of thefluorinenuclei. The results were unusual, but were shown to be consistent with a previous NMR experiment [22] and with an ab initio calculation [23]. They have been rationalised using a simple model developed by Corn well [24]. These equations are discussed in some detail in Section 2.1.3. The microwave study of the unstable XBE species FBO, C1BO, and FBS is presented  CHAPTER  1.  INTRODUCTION  4  in Chapter 6. Although these molecules had each been studied previously in the microwave region [25-27], very little hyperfine structure had been observed. The quadrupole constants determined in this study have shown that the electronic surroundings of the central boron nucleus of all three species are very similar, and the spin-rotation coupling constants have been used to determine the nuclear shielding parameters of the X and B nuclei. Since these species have not been studied before using NMR techniques, this work represents the first experimental determination of the X(=F/C1) and B chemical shifts of the halogenated oxo- and sulphido-boranes. The final Chapter of this thesis presents thefirstmeasurements of rotational transitions of the transient species OPF. This molecule had been the subject of only a single previous study [28] of any kind, where ab initio calculations and an infrared spectrum of the matrix isolated species were reported. The current study is thefirstobservation of a spectrum of the free gas phase species. Here, two isotopomers have been investigated and the determined rotational constants have been used to calculate a molecular geometry. Spin-rotation hyperfine structure due to the interaction of the nuclear spins of the phosphorus andfluorineatoms with the magneticfieldgenerated by the rotation of the molecule has also been observed in the measured transitions. Since both of these nuclei have a spin 7=1/2 and very similar couplings, the determined values could not be assigned to a particular nucleus. Therefore, these constants have been used to calculate the nuclear shielding parameters of the phosphorus and fluorine nuclei using both possible assignments. For reading ease, all data tabulated for the experimental work are displayed at the end of each chapter. Figures, however, appear in the body of the text, close to the places where they have been cited.  Chapter 2 Theory  2.1  Rotational Spectroscopy  Each of the molecules studied in this work is a linear or asymmetric prolate top which exhibits rotational transitions that have been split by hyperfine structure. The Hamiltonian used is given by H  where H , rot  ^distortionj  Hi ro  and / / y p e r 6 n e  -)- /^distortion "f" ^hyper-fine  a r e  n  (^-l)  the rotational, centrifugal distortion, and hyper-  fine Hamiltonians, respectively. This Hamiltonian is parameterised in terms of various spectroscopic constants which are determined by performing a least squares fit to the frequencies of the measured rotational transitions. In the work described in this thesis, all the molecules studied contain two nuclei with non-zero spin. The theory that is presented here immediately pertains to the asymmetric molecule of this type; simplifications will occur for linear molecules and for molecules where not both of the coupling nuclei have a quadrupole moment. For a full treatise on the subject of microwave spectroscopy, see, for example, Ref. 29 or 30; further details on nuclear hyperfine couplings can be found in Refs. 31-36 and references therein.  5  CHAPTER 2. THEORY 2.1.1  6  R i g i d rotor  The general form of the rigid rotor Hamiltonian is given by #rot =  BaJa + B J + B J 2  2  b  (2.2)  c  where J are the rotational angular momentum operators, and the rotational constants g  are given by B — h /2I 2  g  g  where the 7 's are the moments of inertia about the principal 5  inertial g = a,b,c axes. In general nomenclature, B , a  B are replaced by the symbols c  A, B, C where, by convention, A > B > C. Molecules are classified according to the relative values of the rotational constants. In a symmetric top, two of them are equal; for a symmetric prolate molecule A > B = C, and for a symmetric oblate molecule A = B > C. In both cases, the rotational Hamiltonian can be solved exactly, and the resulting wavefunctions can be used as a basis set for the treatment of other molecules; in this thesis, the prolate basis set will be used. The basis functions are designated | JK) where J and K are the quantum numbers associated with the total angular momentum and its component along the principal inertial a-axis, respectively. They take the values 7 = 0,1,2,... and K = 0, ± 1 , ± 2 , . . . , ± J. In general, non-zero elements of the Hamiltonian matrix in this basis are given by  (JK \H \ JK) = AK + 2  TOt  (JK±2\H \JK) rot  =  [J(J + 1) - K }  *Ll£[j'j i)-K(K±l)]' +  2  (2.3) (2.4)  x[J{J+l)-(K±l)(K±2)]>  where A, B, C are the rotational constants of the molecule. For a linear molecule, there is no rotational angular momentum about the a-axis and, therefore, A^=0; also, since B = C, the off-diagonal elements of the Hamiltonian matrix disappear, and the energies of the rotational levels are given by:  E = BJ(J+l)  (2.5)  CHAPTER  2.  THEORY  7  For a prolate symmetric top, where K is no longer restricted to having a value of zero, but where B and C are still equal, the rotational energy levels are given by: (2.6)  E = BJ(J + 1) + {A- B)K  2  For an asymmetric top, where B ^ C, the Hamiltonian matrix describing the rotating molecule is not diagonal in K; it must be diagonalised to yield the energies of the rotational energy levels. In this case, K is no longer a "good" quantum number and the energy levels for an asymmetric top molecule are labeled by JK K a  c  where K and K are a  c  the prolate and oblate limits for the value of K. Selection rules The rotational selection rules are determined as follows. The probability, p _+ of a m  n  rotational transition occurring between energy levelsraand n is given by Pm-Yn  =  (2-7)  p(v -+n)B -y m  m  n  where p(v -+n) is the density of the radiation at the transition frequency v ^ m  m  n  and # _>„ m  is the Einstein co-efficient ^ »  = ^ £ l ( " M ™ > |  (2.8)  2  Here the pp are the space-fixed F = X,Y, Z projections of the molecular electric dipole moment. Because the molecular dipole isfixedin a molecule-fixed axis frame, a change of co-ordinates is made (n\p \m) F  (2.9)  = ^p (n\$ \m) g  Fg  9  where g — a,fe, c are the principal inertial axes of the molecule and <&F are the direction 9  cosines between the space-fixed axes F and the molecule-fixed axes g.  CHAPTER  2.  8  THEORY  In microwave experiments, plane polarised radiation is used, and, therefore, the molecular dipole will interact with only one space fixed axis (defined as the Z-axis). The direction cosines give the selection rule A J = 0,±1; selection rules for K and K can be a  c  reasoned using group theoretical arguments. The asymmetric rotor wavefunctions can be classified according to the irreducible representation D , the character table for which is given in Table 2.1. The allowed 2  Table 2.1: Character table for the D point group 2  E A B B B  a  b  c  1 1 1 1  c% C\ 1 1 1 -1 -1 1 -1 -1  Ka  K  e e o o  e o o e  1 -1 -1 1  $  c  Fg  $Za $Zc  transitions are those for which (n \nz\ rn) ^ 0 and which are symmetric with respect to all operations of D . Since (n \pz\ ) — Pa(n \$Za\ rn) + fJ-b{n \$zb \ rn) + p (n \§zc\ rn), m  2  c  Hg must be non-zero and (n \$zg\ ) must be totally symmetric in order for a transition m  to occur. The allowed transitions are thus those that are shown in Table 2.2. Table 2.2: Selection rules for rotational transitions AK  AK  even odd odd  odd odd even  a  a-type fi ^ 0 6-type n ± 0 c-type (i ^ 0 a  b  c  2.1.2  C  Centrifugal distortion  A molecule which is rotating will not retain its shape, but, rather, will be distorted by bond stretching or angle bending. These distortions will increase in importance with  CHAPTER 2. THEORY  9  increasing J and are accounted for by including higher order J-terms in the Hamiltonian. The Hamiltonian of a semi-rigid molecule is given by Hsem'i—rigid  —  H i  =  B Jl-  (2.10)  -(- ^distortion  TO  « h . . . . + Byjy + B J + — ^2 Ta^sJaJfiJ-yJs 4  2  x  2  2  2  Z  (2-H)  where the sum a,(3,j,8 is over the x,y,z molecule-fixed axes. There are, in principle, 81 different rs; however, symmetry considerations reduce these to 9, and, furthermore, commutation relations for angular momenta allow the elimination of terms of the form apap by folding their effects into other co-efficients [29]. The Hamiltonian operator for  T  the semi-rigid molecule can consequently be written as Bsemi—rigid —  B'Jl  +  B' Jl  +  y  B' Jl + £ T JlJ  2  aP  z  (2.12)  where K  B  By  By ~\~ ~^(3T  B'  B  X  x  T  - aa  X  ~\- ~^(3Ty y  Z  2,T y y  XZXZ  2T y y  Z  X  X  ~\~ ~^(^T y y X  XZXZ  )  XZXZ  (2.13) (2.14)  X  2,T  X  2T  X  —  2,Ty ) ZyZ  h  (2.15) (2.16)  ~^~aotaa  1  Tp a  h<  .  •  a^(3  (2.17)  Here B' , B' , and B' are the effective rotational constants. x  y  z  It has been shown that not all of the co-efficients in this Hamiltonian expression can be determined from the rotational energy levels [37-39]. To find which linear combinations of co-efficients are determinable, a unitary transformation is applied, the choice of which depends upon the molecule being studied. Most commonly, Watson's A-reduction [37] is  CHAPTER  2.  THEORY  10  used: 4ot distortion  =  BfU  + B'Wj  =  -A J -A J J -A J -28jj (j -j )  2  + B'} U  2  4  2  J  2  i  JK  K  2  2  2  (2.18)  2  (2.19)  z  - 8 [J (J 2  A  - J ) + (J -  2  2  K  2  X  J )J } 2  2  However, as the molecule becomes near-symmetric, and B — B approaches zero, the x  y  A-reduction breaks down. In these cases, Watson's S-reduction [40] is more appropriate: ^rot ^distortion  =  Bf  U  =  -D J ~Dj J J -D Jt  2  + flf> J  2  X  A  2  J  K  + Bf>  2  z  K  J  (2.20)  2  + d J (J 2  1  2  + J _) 2  +  (2.21)  -d {J*+Jl) 2  where J+ = J — ij and J_ = J + ij . x  y  x  y  It should be noted that effective rotational constants, B' , B', and B' , are determined x  z  from microwave spectra; this will result in the introduction of a very small error into the geometric parameters determined from these constants [29]. 2.1.3  Nuclear Hyperfine Interactions  The hyperfine interaction Hamiltonian is given by ^hyperfine — ^quadrupole ~T" ^spin—rotation "I" ^spin—spin  (2.22)  where the quadrupolar Hamiltonian represents the interaction of a nuclear quadrupole moment with the electric field gradient at the nucleus, the spin-rotation Hamiltonian describes the interaction of a nuclear magnetic moment with the magneticfieldproduced by the rotating nuclei and electrons of the molecule, and the spin-spin Hamiltonian accounts for the interaction between two nuclear magnetic dipoles.  CHAPTER  2.  11  THEORY  In each of the molecules studied in this thesis, there are two nuclei with non-zero nuclear spins which can couple with the rotational angular momenta via the aforementioned hyperfine interactions. In the case of a molecule which has equivalent coupling nuclei, the "parallel" coupling scheme Ij + I = I; I + J = F is most convenient; 2  for molecules with two non-equivalent coupling nuclei, the "series" coupling scheme Ii + J = Fi; Fi + I2 = F is usually more appropriate. All spectroscopic fits presented in this thesis were carried out using the exactfittingprogram SPFIT [41]. Since this program utilises a complete diagonalisation procedure, identicalfitsare obtained regardless of the coupling scheme used; however, in the case of a Civ molecule with identical nuclei, use of the parallel coupling scheme allows a consideration of the symmetry of the nuclear spin wavefunctions. This will be seen to be important in Section 5.3, where the nuclear spin-statistics of the SF molecule are discussed with respect to the rotational transitions 2  that can be split by the spin-rotation hyperfine interaction. Nuclear Quadrupole interaction Nuclear quadrupole hyperfine structure arises because of an interaction between the electric quadrupole moment of a nucleus and the electricfieldgradient at that nucleus. The Hamiltonian for this interaction can be written as the scalar product of two second rank tensors: the electric nuclear quadrupole moment, Q, and the electricfieldgradient at the site of that nucleus, VE. ^quadrupole =  where  — —V  :  =-  ]T}  QijVij i,j=x,y,z  (2.23)  The non-vanishing matrix elements for an asymmetric molecule  containing two quadrupolar nuclei with nuclear spins l\ and I , are given in the parallel 2  coupling scheme by [36]  CHAPTER  2.  (hhl'J'r'F  \H  12  THEORY  qi  + H \ hhUrF)  (-1) r'+j-F  =  Q2  (2.24)  x[(2/' + l)(2J'+l)(2/+l)] xWil'IJ'J,  2F)[C(J2J',  1  1  x{e Qi(qj'M-lf  1  1/2  1  / i ( 2 / i - 1)  +e Q {qj.,j) {-l)  1  2  JOJ)]-  (2/ + l)(/ + l)(2/ +3)  2  2  1/2  2  (2I + l)(/ + l)(2/ + 3) 7 (2/ - 1) 2  2  2  1/2  2  2  xw(i i ri,2i )} 2 2  2  where the Ws are Racah co-efficients; closed formulae for their evaluation are given in Ref. 42. The values for the vector coupling co-efficients C(J2J', JOJ) are given by J(2J+ 1) "I 1/2 C= (J + l)(2J + 3)  J' = J,  (2.25)  1/2  3J  J' = J+1,  C=  J' = J + 2,  6 C= (2J + 3)(J-l-2)  (J + l)(J-r2)  (2.26) 1/2  (2.27)  and the quadrupole coupling constants, e Q(qj>,j), in the space-fixed axis system can be 2  expressed in terms of the elements in the principal inertial axis system as e Q(qj.,j) = e Q ( ^ >  = <*| >Xa. + ( $ |  2  2  8  6  )X66  e  + 2 ( $ $ ) X a b + 2{$ $Zc)Xac Z a  where Xgg'  =  ($z $Zg') g  Q~ig~ip  e2  Z 6  (2.28)  + (*| >Xc Za  +  2($Zb$Zc)Xbc  are the expectation values of the multiplied direction cosines and the a r e  ^  e  <l drupole coupling constants in the principal inertial axis ua  system. Symmetry arguments can be used to determine which of these matrix elements are non-zero. The non-vanishing matrix elements are those for which the direct product of the symmetries of | JK K ), a  c  \ J'K' K' ), a  c  $z , and <&z ' are symmetric with respect to g  g  CHAPTER  2.  THEORY  13  all operations of D , the character table for which is given in Table 2.1. Thus, if the 2  two states are of the same symmetry, only the totally symmetric products of direction cosines give non-vanishing elements; if the two states are of different symmetries, one of the off-diagonal combinations $zg®z '',g g  7^ g' will give non-zero matrix elements: K' K' -KJ< a  c  c  Xaai Xbbi Xcc  ee-ee; oo-oo; eo-oe; oe-oo  Xab  ee-oe; eo-oo  Xac  ee-oo; eo-oe  Xbc  ee-eo; oe-oo  Normally, effects from the off-diagonal quadrupole coupling interactions are negligible. They only become significant when there are near-degeneracies between rotational energy levels of the correct symmetry [43]; the selection rules are A J = 0 , ± 1 , ± 2 and AF = 0 with AK AK a  c  as given above.  In cases where the complete quadrupole coupling tensor is known, the diagonal quadrupole coupling constants, Xx, Xyi  a n  d Xz>  c  a  n  be determined. These constants  represent the coupling along the principal axes of the electricfieldgradient. Since this gradient is due chiefly to the molecular electronic structure near the nucleus, the principal values can be used to infer information about the electronic structure (ie. the bonding) at the coupling nucleus. The electricfieldgradient around the nucleus of a main group element is primarily due to an unequalfillingof its valence shell p-orbitals. The principal quadrupole coupling constants can be written approximately as [29] eQq  =-  - n ) eQq  nl0  = -(U ) eQq  nl0  (2.29)  eQq  y  =~  ~ n ) eQq  nl0  = -(U ) eQq  nW  (2.30)  eQq  z  = - (^s?* - n,) eCfouo =-(U ) eQq  x  x  y  p  p  p z  x  y  nW  (2.31)  CHAPTER  where eQq  2.  nl0  THEORY  14  is the coupling due to an electron in an atomic np-orbital, n is the number g  of electrons in the jo -orbital, and the term in brackets, (U ) , represents the unbalanced 5  p g  p-electronic charge of the n shell of the coupling nucleus relative to the g-quadrupolar axis. When the orbitals are completely filled, the field gradients are zero with respect to all axes; thus, only the valence shell contributions need be considered. The degree to which the valence shell orbitals are filled depends upon the way the electrons are shared between the coupling nucleus and its bonding partners. Thus, the determined nuclear quadrupole coupling constants can be used to gain insight into the electronic structure of the molecule. This type of analysis of the quadrupole coupling constants has been used to interpret the measured quadrupole coupling constants of C 1 N 0 and XBE. Details of each of these analyses can be found in Sections 4.4.3 and 6.4.1, respectively. Nuclear spin-rotation interaction Nuclear spin-rotation hyperfine structure arises because of an interaction between the magnetic moment of a nucleus and the magnetic field generated by the rotation of the molecule. The Hamiltonian for this interaction is given by ^spin-rotation  where Cj  iT  =  Cj l • J  (2.32)  iT  are the rotational state dependent spin-rotation coupling constants. Cj,r  =  jfj EC„(J,T l  +1)  \J \ 2  J,T>  g  (2.33)  here g sums over the a, 6, c principal inertial axis, r = K — K , and C , the principal a  c  gg  inertial g-axis component of the spin-rotation coupling constant, is given by C99 = -gi^Nhgg  (2.34)  CHAPTER  2.  THEORY  15  where gj is the nuclear ^-factor of the nucleus with spin / and h is the principal inertial gg  gg-component of the effective magnetic field. In this work, the signs of these constants follow the usual spectroscopic convention that the value is negative for H2; thus, they are positive for most nuclei in most compounds. For two nuclei which can show spin-rotation coupling, the matrix elements diagonal in the rotational state are given by: (hhl'JrF  \C$h • J + Cfth • A hhUrF)  =  + 1)(2/' + 1)J(J + 1)(2J + 1)]*  (_ )/i+/ +/+./+F+i 1  a  xW(II'JJ-IF)  (2.35)  x {ci;)(-l)  2/l+  ^ ( W / ' ; l / ) [1,(1, + 1)(2/ + 1)]^ 2  +c^(-\f w(i i ir-\h)  [i (i + i)(2/  h+v  2 2  2  2  1  +1)]*}  a  The spin-rotation constants of nucleus A can be written as the sum of two terms [31, 33,34,44,45]: Ct  = C > u c ) + C*(el)  (2.36)  C7A(nuc) = - ^ f ^ E % " " 2  A  R  _ 2ep g B ~ hern A  A  »™  N  C  gg  N  R  "  A  )  "  (2-37)  k)(k [ L /rf \ E^Eo  y(0\TU Y  W ^ A I k)(k | £« E- E  giA  2e x g B hem l  ( 3  ^ (0 [E,- L \ \ A  |  A  gg  giA  k  0)  A  ( e ) ( 2  -  3 8 )  L \0) giA  0  Here, ^AT is the nuclear magneton, g is the (/-factor of nucleus A, B is the rotational A  gg  constant along the inertial <7-axis, e and m are the proton charge and electron mass, c is the speed of light, r  nA  is the distance between nucleus n and nucleus A, L i  g A  is the g-th  component of the orbital angular momentum of electron i about nucleus A, T\A is the distance between electron i and nucleus A, and | 0) and | k) are the ground- and excitedstate electronic wavefunctions at energies E and Ek (here it should be noted that if 0  I 0) is a singlet state, then | k) must also be a singlet state). Whereas the nuclear term,  CHAPTER  2.  THEORY  16  C (nuc), depends only on the geometry of the molecule, the electronic term, Cj^el) A  7  requires knowledge of the ground- and excited-state electronic wave functions and their energies. The spin-rotation coupling constants of a nucleus are related to its nuclear shielding parameters, a . gg  Thus, the determined spin-rotation coupling constants can be used  to determine NMR parameters for molecules which are too unstable to be studied by conventional NMR techniques. The elements of the shielding tensor of nucleus A can, in similarity to the spinrotation coupling constants, be separated into two terms: a diamagnetic term, a (d), K  g g  and a paramagnetic term, cr^(p) [31,33,34,44,45]: <  *<p>  =  +  (2-39)  2  -  ( 2  -  4 i )  Thus, <7^(p) and Cg(el) have the same dependence on the molecular geometry and electronic states; one is easily calculated from the other. Furthermore, the diamagnetic term can be approximated by [31]: <(d)  *  ^ ^ )  +^ Y,'zf z  e  2  +  Here cr£  ee a t o m  n  k  2  v  m  2mc* ^  r  n  c  ,3(r  ~^  n  A  )3 - 3 g  rl  r  A  A  )  (2.42)  l  nA  2  p  3  { A  n  ) n  (d) is the free-atom diamagnetic susceptibility, and {p /3) 2  n  is the average  squared electronic distance from nucleus n; these constants are obtained from tabulated  CHAPTER  2.  17  THEORY  values in Refs. 46 and 32, respectively. In Eq. 2.42, only three terms of a Taylor expansion have been retained. A "dipole" term, which arises if the point charges are not centred on the nuclei, has been neglected because, it is, in general, quite small (on the order of a few ppm) relative to the first two terms [31]. The third term of Eq. 2.42, the "quadrupole" term, which arises because the electronic charge distribution on the nth nucleus is not a point charge but is spatially extended, has been retained because ignoring this term may result in significant errors in the calculation of the individual diamagnetic chemical shielding components [31]. The paramagnetic nuclear shielding terms can also be calculated approximately using a semi-quantitative approach first introduced by Corn well [24]. The paramagnetic components of the shielding can be re-written as follows: A / \  — 4/? ^ 2  ^  (j | IZi Lgio\ k)(k | J2i Lgixlr? \ j) A  j=lfc=JV+l  h  g ^  ^ °  0 |E,-.W^Alfc>(fc|-S<^io|j) ,  j=i k=N+i  2  (0 AA\  i>= ~  E  E  °  Here 3 is the Bohr magneton; L ; A and r,A denote the angular momentum and position S  of the electron relative to an origin at the position of nucleus A, while L i  g 0  denotes the  angular momentum of the electron relative to any common origin. The indices j and k refer to the occupied and unoccupied molecular orbitals, respectively; in the ground electronic state,  orbitals are occupied. The denominator, Ejk — E is the energy 0  change from the ground state to the singlet excited state corresponding to the oneelectron excitation | j) -> | k). The approximations are made that (1) LCAO expansions are substituted for | j) and | k); (2) overlap effects between different atoms are neglected; (3) contributions from only the valence shell p orbitals are included; (4) all terms for atomic orbitals not on atom A for the operator L/r are dropped. This allows Eq. 2.44 3  CHAPTER  2.  18  THEORY  to be re-written as follows: [bfct  • E x (tf eg  - cfbt)  (2.45)  AEj^  k  with expressions for the other components obtained by cyclically permuting the a,fe,c labels. In Eq. 2.45,  (r~ ) & 3  p  is the mean value of  for the ith valence shell  of atom A, tabulated values for which can be obtained from Ref. 47;  bj,cj  p  orbital  and bk,Ck  are the LCAO coefficients of the valence shell pi, and p orbitals on a given atom for the c  molecular orbitals | j) and | k), respectively; X sums over all atoms in the molecule. Thus, if the atomic orbital contributions to the molecular orbitals and the energy differences between these molecular orbitals can be determined, one can estimate the paramagnetic contributions to the nuclear shielding. Nuclear spin-spin interaction The nuclear spin-spin interaction is an interaction between the magnetic dipoles of two nuclei with non-zero nuclear spin. This interaction has both a scalar and a tensor component; however, because the scalar term is usually small, especially for light atoms, and because no effects due to the scalar term have been seen in the spectra analysed in this work, it has been neglected. The tensor portion has both a direct and an indirect contribution and the Hamiltonian for the spin-spin interaction can therfore be written as spin—spin  where  //direct  (2.46)  describes the direct magnetic interaction between two dipoles k and / sep-  arated by a distance ru and //indirect describes the indirect, electron coupled interaction. The indirect term arises through the mechanism of each nucleus interacting with its own electron spin and the electron spins of the two nuclei interacting with each other [48]. The magnetic interaction of one nucleus with the electron of its atom will tend to align  CHAPTER  2.  THEORY  19  that electron antiparallel to the nuclear spin. And, since two electron spins in a singlet state must be antiparallel to one another, the electron of the other atom will align itself parallel to the nuclear spin of the first nucleus. However, this second electron also interacts magnetically with its own nuclear spin. This combination of interactions thus gives rise an interaction between the magnetic dipoles of the two nuclei. In the case of light atoms, especially those not directly bonded, this interaction is negligible [45,48,49]. Consequently, the indirect spin-spin constant has been neglected for all molecules studied in this thesis. The Hamiltonian used in this work is that of the direct spin-spin coupling [48], given by 4pin-spin =  (2J  J^  where k and / are the interacting nuclei, of nucleus k, and  J + [3(/ • J){h • J) ~ (h • h)J ] 2  3)  fc  (2.47)  and If. are the nuclear ^-factor and nuclear spin  is the internuclear separation between the interacting nuclei. The  determinable fitting parameters arising from this Hamiltonian are the principal inertial axis components of the direct spin-spin constants, a ; these depend only upon the gg  molecular geometry and can be calculated using the equation [50] ^ where  = ^#^[3cos ^-l]  (2.48)  2  is the nuclear magneton, and 9 ki is the angle between the kl radius and the g>  principal inertial #-axis of the molecule. Thus, if the molecular geometry is known, the spin-spin coupling constants can be calculated, and vice versa. 2.2  Molecular Geometry  Precise rotational constants can be obtained from microwave spectra, and, since these constants are related to the principal moments of inertia, I , and the principal planar gg  CHAPTER  2.  20  THEORY  moments of inertia, P , of the molecule, they can be used to determine molecular gegg  ometries. The principal moments are obtained by diagonalising the inertia and planar moment tensors, elements of which are given, respectively, by Ixx =  Y^m^yJ  + zf)  i  lyy = J2 i( l + A) m  hz =  i  x  i( l + Vi)  m  i  X  i Ixz  — Izx —  ^ ] fXl{X{Zi i  lyz  Iy  ^ ] rn^y\Z{  Z  and Pxx  ^ 1 1TT,{X^ i  Pyy '= Pzz  =  i m  i  i i Z  ^ ] rnjXjyi i  Pxy  Pyx  Pxz  Pyx — ^ ] rn^X{Z{ i  Pyz  Pyx — ^ y ^1%]}%^%  where ra - is the mass of the i-th atom and i sums over all atoms of the molecule. t  Thus, provided that enough rotational constants are available, the Cartesian co-ordinates (x, y, z) of all atoms in the molecule can be determined.  CHAPTER  2.  21  THEORY  At the vibrational potential minimum, the molecule would be in a so-called equilibrium, or r , structure. However, rotational constants are measured for a particular e  rotational state and the structure obtained from these constants, therefore, represents only the "effective" geometry of that state. Even the ground vibrational state has some "zero-point" vibrational effects which result in its structure being different from the r  e  structure. The rotational constants of a given vibrational state v can be expressed as a power series in (v + 1/2) as = A -Y <{v  A  e  v  /  s  + d /2) + ...  (2.63)  + d /2) + ...  (2.64)  + d /2) + ...  (2.65)  s  s  = B -Y,* (v  B  b  e  v  C  s  s  = C -J2<* s(v  s  C  v  e  s  s  s  where the summation is over all vibrational modes s of degeneracy d . Thus, if rotational s  constants are measured for molecules in excited states of every vibrational mode, the a's can all be determined, and equilibrium rotational constants can be obtained. However, for a general polyatomic molecule, it is difficult to obtain all necessary information, and vibrational effects must be accounted for in another way. Rudolph has developed the programs RU238J and RU111J to calculate r\,-type [51] and r -type [51,52] structures, respectively. In the determination of these structures, 0  isotopic data is used to determine the absolute (r ) or relative (ro) positions of the s  atoms in the molecule; this is possible by making the assumption that the bond lengths and angles are unchanged upon isotopic substitution and, therefore, that changes in rotational constants are due only to the change in molecular mass. The definitions of these structures and the means by which they attempt to compensate for vibrational effects are discussed below; further details can be obtained from Refs. 51-53. The program RU238J can be used to calculate substitution, or r , -type structures [51]. s  In the calculation of a true restructure, the co-ordinates of a singly substituted atom  CHAPTER  2.  22  THEORY  in a molecule are determined in the principal inertial axis system of the 'parent' (unsubstituted) isotopomer independent from the rest of the molecule [54]. To determine a complete restructure, each atomic position must be substituted at least once. This method was modified by Typke [55], who introduced a method whereby isotopomers with multiple substitutions could also be fitted; here, an r -type structure is determined. s  Vibrational effects are partially accounted for in the r and r -type determinations bes  s  cause it is the isotopic differences between the moments of the parent and the substituted molecule which are, in principle,the most important parameters [52]. Thus, the vibrational effects will partially cancel. Some limitations of the restructure determination method are that the co-ordinates of atoms substituted near a principal inertial axis are difficult to determine because of the very small isotopic differences between the resulting rotational constants, and the positions of atoms which have no other stable isotopes cannot be determined. In an r -type structure determination, these problems can be 5  addressed. Here, non-trivial first and second moment conditions: (2.66) (2.67) can be used to determine the co-ordinates of a single (or at most a few) atom(s) from the r co-ordinates of the other atoms in the molecule [52,54]. s  The program RU111J was developed by Rudolph to calculate ro-type [51,52] structures. In an r -structure determination, the ground vibrational state geometrical param0  eters are fitted to the rotational constants, moments of inertia, planar moments, or the differences between these parameters; the main difference between the ro and r structure s  determination methodologies is the fact that in the r determinations, the positions of 0  all atoms in the molecule are determined simultaneously, whereas, for the restructures, the co-ordinates of each substituted atom are determined individually, and independent  CHAPTER  2.  THEORY  23  from the other atomic co-ordinates. In the calculation of a true r -structure, vibrational 0  effects are not considered; these effects can be partially accounted for in the r -type de0  terminations using two different fitting methods [52,53]. In the first method, an r/ or i£  rp structure is determined; the difference in nomenclature signifies which type of data i£  has been used in the fit. The vibrational effects are taken into account by describing the ground state moments of inertia by the equation 7 = If + e , where g=a,6,c and g  g  £ are the vibration-rotation interaction parameters which are assumed to be isotopomer g  independent. In the second method, an r / or r A  structure is determined. Here the  AP  vibrational effects are taken into account byfittingto the isotopic differences between the input data; the vibrational effects will cancel to the extent that they are isotopically invariant. Both of thesefittingtechniques determine identical structural parameters if the same input data are used; however, the methodologies are very different. The r/  j£  and rp determinations are especially suitable for predictive purposes; this was used to )£  predict the unknown A rotational constants of four isotopomers of nitrosyl chloride; see Section 4.3 for details. A ground state average, or r , structure can also be calculated. The vibration-rotation z  interaction constants, a, of Eqs. 2.63-2.65 can be divided into harmonic, ah, and anharmonic, a , parts. The rotational constants of the ground vibrational state can therefore a  be written as:  S o ^ e - E ^ - E ^  1  (2-68)  Thus, the ground state average rotational constants, B , can be obtained by subtractz  ing the harmonic contributions to the a's from the measured ground state rotational constants: B =B + Y ^ z  0  = B -Y -^ d  e  ±  (2.69)  CHAPTER  2.  THEORY  24  The harmonic vibration-rotation interaction parameters can be obtained from an harmonic force field. Because the r structure represents the average structure of a particular z  isotopic species (normally the most abundant isotopomer) in its ground vibrational state, fitted data must be corrected for the isotopic variations in the bond lengths. This can be done using the equation [56-58]: 8r = ^a8{u ) - SK  (2.70)  2  z  where (u ) and K are the zero-point mean square amplitude of a given bond and its 2  perpendicular amplitude, and a is the Morse parameter for the bond. Both (u ) and K are 2  obtained from the harmonic force field, and the Morse parameters can be approximated from the corresponding diatomic molecules [59]. Eq. 2.70 is derived from an equation developed by Kuchitsu and co-workers [56,58] where the equilibrium bond lengths are related to the r bond lengths by: z  r =r z  + ^a(u } - K 2  e  (2.71)  Neglecting any change in the angle, the equilibrium geometry can, therefore, be approximated from the r parameters. z  2.3  Harmonic Force Field  If only harmonic forces are assumed, the interatomic molecular potential, V, can be represented by the equation v = l.T,fijRiRi where the  (- ) 2  72  are the force constants, and the R{ are the set of (3/V — 6), or in the case  of. a linear molecule, (3iV — 5), internal displacement co-ordinates of the molecule; for triatomic molecules, the force constants represent a bond-stretch, an angle bend, or an interaction constant depending upon the internal co-ordinates involved.  CHAPTER  2.  THEORY  25  If the molecule is rotating, but not vibrating, the potential will act to resist the deformation caused by the rotation of the molecule. The centrifugal distortion constants are thus related to the harmonic force constants by [60]  where 1^ are the equilibrium moments of inertia about the a-axis, and  are  the elements of the inverse force constant matrix; in practice, equilibrium rotational parameters are difficult to obtain, and r values are normally used. Thus, centrifugal 0  distortion constants can be determined from a knowledge of the harmonic force constants of a molecule. The inertial defect of a molecule, A = I — If, — I , can also be used as additional c  a  information to determine the harmonic force constants. The measured rotational constants are related to the equilibrium constants by Eqs. 2.63, 2.64, and 2.65. For a planar molecule in the equilibrium configuration, the inertial defect will be identically zero; however, the measured effective rotational constants will have vibrational contributions, and the inertial defects will, therfore, be non-zero. Darling and Dennison [61] have shown that the inertial defect is dependent only upon the harmonic force constants because in the sum I — I — If,, the anharmonic terms cancel out. Thus, the inertial defects can be c  a  used to calculate harmonic force field parameters. 2.4 2.4.1  F T M W Spectroscopy Theory  In an FTMW experiment, a gas sample is injected into a microwave cavity and is subjected to a pulse of microwave radiation which interacts with the dipole moments of the sample molecules and creates a macroscopic polarisation. After the microwave pulse is  CHAPTER  2.  26  THEORY  turned off, the molecules emit radiation as they relax back to their equilibrium states. This emitted radiation is collected and subjected to a Fourier transform to yield a frequency spectrum. These experiments can best be described using density matrix formalism [62]. Consider a two state rotational system with eigenfunctions (j), and <p at energies E, 2  and E . The state of an individual molecule is given in this basis by 2  | xp) = c,^ + c <t> 2  (2.74)  2  The Hamiltonian of this system is H  — HQ  #0  =  #rot  ^perturbation  =  —  (2.75)  + ^perturbation  (2.76)  2fJ,S COs(ut + <f>)  (2.77)  where p, is the dipole moment operator, 2e is the amplitude of the applied microwave field, u> is its angular frequency, and (j) is its arbitrary phase. In the <f>\,4>2 basis, the matrix representations of H  ROT  H  ROT  —  and ^perturbation are given by £i  0  0  E  (2.78) 2  0  H,perturbation  —2p\ e cos{ut + 4>) 2  -2p e cos(ut + (f>) 12  where it is assumed that fin and fi  22  (2.79)  0  are equal to zero, an approximation which is valid  for linear and asymmetric top molecules. The density operator p is defined as P= I  I  (2-80)  which, in the two state basis, becomes CjCj  ClCr>  c\c c c* 2  2  2  (2.81)  CHAPTER  2.  THEORY  27  and, for an ensemble containing ./V molecules  iV  k=i  At time t — 0, a pulse of microwave radiation is applied. The time dependence of the system is given by ih^  = [H,p} = ihp.  (2.83)  Thus, the time derivatives of the density matrix are Pn  = i(p2i - pu)xcos(u>t + <f>)  P22  — —i(p2i - pi )x cos((jut + <j>)  Pu  = iuoPu + i{P22 - Pu)x cos(ut + <j>)  (2.86)  p  = -iijO p \  (2.87)  21  where x = 2pi e/h 2  (2.84)  2  Q  + i(p22 - Pu)x cos(ut + 4>)  2  (2.85)  and cu — [E — Ei)/% is the angular velocity of the rotational 0  2  transition. A transformation to an axis system rotating at an angular velocity UJ gives Pu = Pn  (2.88)  P22 = P22 .  (2.89)  P12 = pi e'^+*)  (2.90)  2  P2i  =  ~ 2^~  i{M)  P  (2.91)  IX Pn  = j{p2i-Pn)  (2.92)  —IX P22  =  (2-93)  -J-{P21-P12)  P12 = y (^22 ~ Pu + iAu>p ) 12  P21  =  -Z-(p22 ~ Pn - iAupu)  (2.94) (2.95)  CHAPTER  2.  THEORY  28  where Aa; = Uo — u The quantities s,u,v, and w are defined as s = PU+P22  (2,96)  u = P12 + P21  (2.97)  v  (2.98)  = i{p -p ) 2l  u  w = p -/5 n  2 2  ( 2.99)  Neglecting terms in 2a; (rotating frame approximation [63]) and choosing the phase of the microwave pulse such that <j> = 0 gives s = 0  (2.100)  ii = -vAu  (2.101)  v = uAu-xw  (2.102)  ti = xv  (2.103)  Now, consider the microwave experiment. Before the microwave pulse is applied, the population difference between the levels is given by AN  = N1-N2  (2.104)  =  N(p -p )  (2.105)  =  Nwo  (2.106)  u  22  and, since the density matrix is diagonal before the pulse, u' = 0  (2.107)  v  (2.108)  0  0  = 0  CHAPTER  2.  29  THEORY  At time t = 0, a pulse of microwave radiation is applied that is near-resonant with the transition frequency (ie. Ao; is small) and has an amplitude x such that x= ^  » Aa,  (2.109)  In this case, s = 0  (2.110)  ii = 0  (2.111)  v  = -xw  (2.112)  w  = xv  (2.113)  Since v(0) = 0, these differential equations can be solved to give v(t)  =  -wos'm(xt)  (2.114)  w(t)  —  WQZOS(XI)  (2.115)  Thus, it is seen that during the excitation pulse, v(t) and w(t) oscillate between — w and 0  WQ at an angular frequency x. At time t , s,u,u,and w are given by p  v  p  w  p  =  — w s'm(xtp)  (2.116)  =  Wocos(xtp)  (2.117)  0  So, for any time t = mr/2, n being any given integer, the population between the p  states is equalised. This is called the "7T-half" condition. Assuming the amplitude of the microwave pulse 2s to be constant, the pulse length necessary to produce the 7r-half condition will be greater the lower the molecular dipole moment. When the microwave radiation is turned off at time t , e and x become zero. Neglecting relaxation, Eqs. p  2.101-2.103 become ii = -vAu  (2.118)  CHAPTER  2.  30  THEORY  w  uAu>  (2.119)  0  (2.120)  And, after the pulse u(t)  =  v(t)  —  w(t)  =  v  p  (2.121)  sin( Aut)  (2.122)  VpCOs(Aut)  (2.123)  The macroscopic polarisation of the sample is defined by P(t)  =  N(fc)  (2.124)  NTv(pp)  (2.125)  NTr  .  0  Pl2  A*12  0  Pu  Pl2  (2.126)  P21 P22 _  =  Np {pi2 - P2l)  (2.127)  =  Nwopn s'm(xtp) sin(u;o^)  (2.128)  12  and the macroscopic polarisation will thus oscillate at the frequency of the rotational transition. It is seen from Eq. 2.128 that the macroscopic polarisation depends upon the initial population difference, iVu;o, the transition dipole moment, of the microwave pulse,  fii , 2  and the duration  s'm(xt ). p  This treatment has, so far, not considered relaxation effects. Relaxation is treated phenomenologically by introducing the exponential terms e"'/ and e~'/ . These terms Tl  T2  describe, respectively, the relaxation of the population difference back to the thermal equilibrium value with a characteristic relaxation time T\ and the loss of coherence of the sample with a characteristic relaxation time T . During these processes, radiation 2  is emitted at a frequency (u>o) characteristic of the molecule. This time-domain "decay"  CHAPTER  2.  THEORY  31  signal is what is detected and Fourier transformed in the experiments described in this thesis. 2.4.2  Fourier transform  In MWFT experiments, the time domain signal that is collected by the transient recorder is transformed to frequency space using the discrete Fourier transform N-l  F(u) = J2 f(nAt)e- ™ l2  nAt  (2.129)  n=0  Here f(nAt)  is the molecular signal consisting of n data points collected at a sample  interval of At and F(v) is the corresponding function in the frequency domain. The Fourier transform has both real and imaginary parts; in this work, all spectra are displayed as "power spectra" which are calculated by adding together the squares of the real and imaginary components. Because peak distortions can occur for very close lines in power spectra [64], more accurate line positions are obtained by fitting to the time domain data [65]. Because the signals are sampled over a specified amount of time, T = nAt, the uncertainty principle dictates that the energy, and thus the frequency, of the system must have a small uncertainty. The lines displayed in the frequency spectrum therefore have a linewidth that is dependent upon the data acquisition time. The digital resolution is thus limited by the actual measurement time, but, if the molecular signal has completely decayed before the measurement period has expired, the recording of more data points will provide no further information. The spectral resolution can be artificially enhanced at a cost to the signal to noise ratio using "zero filling" where extra zeros are added to the end of the spectrum, thus artificially increasing the measurement period [66]. In order to accurately reproduce the periodic molecular emission signal, it must be sampled at least twice per period. At the sampling rate of 50 ns that has been used in  CHAPTER  2.  THEORY  32  these experiments, the resulting spectral range is pralO MHz. However, since the data are now represented by only a set of data points, there is no means of distinguishing between signals of frequency x and x + 20 MHz; any higher frequency components that are detected are thus "folded" into the spectrum and are represented at false positions. To avoid this problem, the signal can be put through a bandpass filter prior to being Fourier transformed, thus eliminating all unwanted frequencies.  Chapter 3  Instrumentation  3.1  Microwave cavity  The basic procedure of an FTMW experiment involves injecting a gas phase sample into a microwave cavity and applying a pulse of microwave radiation which will cause the sample molecules to rotate coherently. As the molecules relax back to equilibrium, the emitted radiation is collected in the time domain and Fourier transformed to give the frequency domain spectrum. At the heart of each of the two FTMW spectrometers used for these studies is a Fabry-Perot microwave cavity. This cavity is formed by two spherical aluminium mirrors of diameter 28 cm, radius of curvature 38.4 cm, and separation ~30 cm. The cavity is contained in a vacuum chamber which is pumped by a diffusion pump backed by a mechanical pump. The excitation radiation is coupled into the cavity via an antenna or a waveguide that is situated in the centre of one of the mirrors. In order to bring the cavity into resonance with this excitation frequency, one of the mirrors is moved using a micrometer screw. The operating frequency range of both systems used during this work is between 4 and 26 GHz. Two different spectrometers have been used during this work. Each of these spectrometers is built on the same model, with the main difference between the two being that in  33  CHAPTER  3.  INSTRUMENTATION  34  the first spectrometer the microwave cavity must be brought into resonance manually by moving one of the mirrors using a micrometer screw, whereas in the second spectrometer, this is achieved through the use of a motorised actuator (Oriel Motor Mike); thus, the second spectrometer has an automated scanning capability. 3.2  Electronics  A schematic circuit diagram for the FTMW spectrometers is given in Fig. 3.1. During most of the experiments presented here, the microwave source was referenced to an internal standard with an aging rate of 1 x 10  -9  per day. The reference now used is  a 10 MHz Loran C frequency standard; this has an internal reference which has an aging rate of 5 x 10  -10  per day, and is locked to a broadcast source that is accurate  to 10~ . This setup was used for the experiments performed on OPF. The 10 MHz 12  reference signal is also used for both up- and down-conversions, and for control of the timing of the experiment. Both the experiments and data acquisition are controlled by a personal computer; this communicates with the microwave synthesiser via an IEEE bus, and collects the emitted signals using a transient recorder. To perform an experiment, the synthesiser outputs a frequency of VMW + 20 MHz. This signal is mixed with 20 MHz in a single side-band modulator to produce the excitation frequency I^MW- The microwave pulse is generated through the use of a PIN switch and passed through a circulator into the resonant microwave cavity. Here it interacts with a gas sample, causing a macroscopic polarisation. After the microwave pulse, the gas sample emits radiation at a transition frequency of UQ = I^MW + Av; this radiation is coupled out of the cavity through the circulator. The signal is amplified, down-converted to 20 MHz +Av and again to 5MHz — Av, and,finally,put through a 5MHz bandpass  CHAPTER  3.  INSTRUMENTATION  MWmixer  MW-amplifier  20 M H z - Av  A V M W 20 M H z +  RFamplifier \\  detector  protective MW-switch  RFmixer 25 MHz  circulator  5 MHz bandpass 5 MHz + Av  \  MW-switch  RFamplifier x2.5  VMW-  personal computer  20 M H z  transient recorder 10MHz frequency standard  MWsynthesiser 'MW  power divider  10 MHz x2  20 MHz  single sideband modulator  Figure 3.1: Schematic circuit diagram for the FTMW spectrometer  CHAPTER  3.  INSTRUMENTATION  36  filter before being collected by the transient recorder. Many averaging cycles are accumulated by the computer, and the total signal is Fourier transformed to yield the frequency spectrum. 3.3  Pulse sequence  A schematic diagram of the pulse sequence used in an FTMW experiment is shown in Fig. 3.2. All trigger signals are provided by a home built pulse generator. A single experiment is performed in two parts. First, a microwave pulse is created by opening and closing the MW-switch and, after a small delay, the transient recorder is triggered to initialise data acquisition. Next, a gas pulse is injected into the cavity, the electric discharge (if used) is fired, a microwave pulse is applied, and the signal is subsequently collected by the transient recorder. The first collected signal is subtracted from the second in order to cancel out any 'cavity ring' effects; thus, a signal which is due only to the molecular response is left. While the microwave pulses are applied, the protective MW-switch is kept closed in order to protect the detection circuitry from exposure to the full microwave power. 3.4  Gas sample  The gas samples used in this work consist of a small percentage of the sample molecule, or its precursor, in an inert backing gas (usually Ne or Ar) at pressures of up to roughly 6 bar. Samples are injected into the microwave cavity through a General Valve Series 9 nozzle of orifice 0.8 mm. Since there are very few sample molecules present, collisions just in front of the nozzle are mostly with rare gas atoms and, therefore, most of the rotational energy of the sample is converted to a translation along the axis of expansion; thus, a very low rotational temperature is achieved in the jet. Rotational energy is lost  CHAPTER  3.  INSTRUMENTATION  open closed  -\\-  open  -\\-  closed  open  M W pulse  protective switch  -AV-  nozzle  closed  -\v-  discharge trigger  -\V-  transient recorder trigger  Figure 3.2: Pulse sequence for an FTMW experiment  CHAPTER  3.  INSTRUMENTATION  more quickly than vibrational energy is; T  38  rot  is estimated to be around 1 K, whereas T jb v  is much higher. The temperature of the jet is influenced by the composition of the gas sample; using a larger percentage of sample molecules in the gas mixture will result in a higher temperature being achieved in the jet. There are advantages, in microwave spectroscopy, to using a jet cooled sample instead of a static gas. Because of the low temperature of the jet, only the lowest rotational energy levels of the molecule are populated. Problems with sensitivity are thus overcome because transitions arising from these low energy levels will have a greater intensity than they do using a room temperature sample; the spectra will also be simplified because of a lack of transitions arising from higher energy levels. Also, the virtually collision free environment of the jet acts to stabilise reactive species. Line widths of around 7 kHz FWHM can be obtained; there is very little Doppler or collision line broadening. In this instrument, the gas sample is introduced into the cavity through a nozzle positioned near the centre of one of the cavity mirrors. The jet therefore travels parallel to the direction of microwave propagation, and all observed lines are split into two Doppler components. The transition frequency is obtained by taking the average of these two components. 3.5  Discharge S y s t e m  The electric discharge apparatus used in these experiments is shown in Fig. 3.3. The discharge takes place between two electrodes placed one above the other along the molecular expansion channel, following a design first reported by Schlachta et al. [21]. This design was seen to have several advantages over the electric discharge apparatus first used in this laboratory [20] where a point-to-point discharge took place between two wires placed into a small mixing chamber in a nozzle cap attached to the front of the nozzle. Besides the  CHAPTER  3.  INSTRUMENTATION  39  fact that these wires were fragile and quickly eroded during the experiments and had to be replaced often, the old setup also had the disadvantage that the spark-gap could not be maintained at a uniform distance when the electrodes were changed. In addition, the point-to-point discharge had a much smaller cross sectional area than does the discharge that takes place along the axis of expansion. As a result, the new discharge apparatus is easier to use, and more reliable than that of the old setup. The discharge apparatus itself is contained in a nozzle cap that is mounted at the front of the General Valve nozzle. The nozzle cap is made from Vespel, a non-conducting, chemically inert material (SP polyimide or KS aramid resins), and consists of three parts: an endplate, a spacer, and an extension piece. The 2-10 kV discharge takes place between two brass electrodes that are separated by a spacer of variable thickness; for the experiments presented in this thesis, a spark-gap of 1 or 2 mm was found to work best. The electrodes were originally made to be concentric brass discs; however, in order to avoid creating a capacitance between the electrodes, they were first made smaller, and, ultimately, were changed to small brass rectangles which overlap only in the immediate area of the discharge. Gradual eroding of the electrodes did not seem to be a problem. The Vespel endplate protects the valve from stray discharges, and the extension piece provides both electrical isolation for the grounded aluminium mirror and a small extension of the expansion channel where the discharge products can react to form the molecule of interest. The size and shape of this chamber have been found to have an influence on the type of molecules which are observed in the jet [67,68]; for the studies presented in this thesis, a straight channel of 5 mm length and 1 or 2 mm diameter has been used. The timing of the pulsed discharge is manually adjusted relative to the molecular pulse to provide the greatest possible signal intensity.  CHAPTER  3.  INSTRUMENTATION  Figure 3.3: Schematic diagram of the electric discharge apparatus  40  Chapter 4  The Microwave Spectrum of Nitrosyl Chloride, C1NO  4.1  Introduction  The N-Cl bond of nitrosyl chloride is very long and weak, and rapidly undergoes photolysis [18] to yield the products CI and NO. Although nitrosyl chloride is only a minor component in the atmosphere, it is of interest to environmental chemists because atomic chlorine catalyses the conversion of O 3 into 0 . Atomic chlorine is an important contrib2  utor to the depletion of the ozone layer [18]. It is therefore of interest to study nitrosyl chloride in order to elucidate information about the nitrogen-chlorine bond. Although much work has been done on the microwave spectrum of nitrosyl chloride in the past [19,69-71], the analysis is by no means complete. This near-symmetric prolate molecule has a large dipole component along the a-axis and a small dipole component along the 6-axis. Thus, its rotational spectrum will exhibit strong a-type and weak btype transitions. Previous microwave studies, with the exception of one investigation [70] of C1 N 0 (hereafter referred to as C1NO; isotopic substitutions will be indicated 35  14  16  by using superscripts), have reported only a-type transitions, and have thus been able to determine only two of the three rotational constants. Quartic centrifugal distortion constants have been determined [19], at least in part, for only two isotopomers: C1N0 and 37  C1N0. Some hyperfine structure due to a quadrupole interaction has been resolved and  41  CHAPTER  4. NITROSYL  CHLORIDE  42  quadrupole coupling constants of the / C l and N nuclei [69,71] have been evaluated. 35  37  14  However, these constants have not been determined with much precision, and there has been no resolution of further hyperfine splittings nor any recognition of deviations in the hyperfine structure due to the magnetic interaction between the spins of the CI and N nuclei and the'overall rotation of the molecule. Infra-red data have been combined with microwave data in order to determine an equilibrium structure and force field for the molecule [19]. However, with the harmonic wavenumbers known to only a moderate degree of precision and with very few centrifugal distortion constants known, only five of the six quadratic force constants could be determined; the sixth constant had to be held fixed to a value determined by an SCF ab initio study. This investigation followed a study of the hyperfine coupling constants of nitrosyl fluoride [17]; the initial goal was to investigate the hyperfine structure of some a-type transitions of nitrosyl chloride in order to determine the spin-rotation coupling constants of the chlorine and nitrogen nuclei, and to determine more precisely the known quadrupole coupling constants. These coupling constants can be used to obtain information about the bonding in the molecule. During the course of this work, it was found that there were perturbations in the hyperfine structures of some of the transitions because of near degeneracies between some of the rotational energy levels. Consequently, the scope of the study was extended to search for weak 6-type transitions so that both the off-diagonal quadrupole coupling constants and the A rotational constants could be unambiguously determined. This study was also seen as an opportunity to test the r , r -based, and r structure 0  0  3  determination methods proposed or improved by Rudolph [51-53,72], and to compare the results with those of previous structure analyses [19]. A ground state average, r , strucz  ture was also evaluated. For this, a new harmonic force field was calculated; this was done  CHAPTER  4. NITROSYL  43  CHLORIDE  by refining a previously determined force field through the inclusion of the ground state inertial defects of four of the isotopomers studied here, the inertial defects of the (1,0,0), (0,1,0), and (0,0,1) excited vibrational states of the most abundant isotopomer [73], and the centrifugal distortion constants determined in this study. 4.2  Experimental Methods  The nitrosyl chloride samples were prepared by mixing gaseous nitric oxide and chlorine in a glass sample reservoir and allowing them to react according to Clj + 2NO v=^ 2C1NO. At room temperature, the equilibrium for this reaction lies far to the right (K=2.6xl0  7  at 20°C). To measure weaker transitions of the Cl NO isotopomers, isotopically enriched 15  nitric oxide was used. This was prepared by reacting a 99% N sodium nitrite sample 15  with sulphuric acid in order to liberate N 2 0 3 . Subsequent decomposition of the product 15  yielded NO and NC>2; these were separated by fractional condensation. 15  15  Samples consisting of roughly 1%C1 and 2%NO in 2 bar of Ne were used to measure 2  low J transitions. For higher J transitions, a more concentrated mixture containing about 10%Cl2 and 20%NO in 2 bar Ar was used; the sample contents were adjusted in this manner in order to increase the rotational temperature of the jet so that the higher energy transitions would have a greater intensity. Rotational transitions of nitrosyl chloride were measured in the 4-26 GHz frequency range. Fully resolved lines have estimated uncertainties of ±1 kHz. In the case of unresolvable lines, only those components with a theoretical intensity greater than 25% of the strongest component were included in the fits; those with a theoretical splitting of less than 1 kHz have an estimated uncertainty of ±1 kHz while those with a larger theoretical splitting, and thus an increased linewidth, have an estimated uncertainty of ±2 kHz. In order to avoid distortions due to overlap effects in power spectra, frequencies  CHAPTER  4. NITROSYL  44  CHLORIDE  of closely spaced lines were determined byfittingto the time domain signals [65]. 4.3  Spectral Analysis  Because nitrosyl chloride had been studied previously in the microwave region, a-type rotational transitions having J<2 of C1N0, C1N0, C1 N0, and C1N 0 were,easily 37  15  18  found in natural abundance; later, transitions of C1 N0 were found using the N la37  15  15  belled sample. The data for the first four isotopomers were fit to the rotational constants, the quartic centrifugal distortion constants, the quadrupole coupling constants of chlorine and nitrogen where appropriate, and the spin-rotation coupling constants of both chlorine and nitrogen, using Pickett's exact least squaresfittingprogram SPFIT [41]. Because the splittings due to the chlorine nucleus were much larger than those due to the nitrogen nucleus, the serial coupling scheme, J-f-Ici—Fcf, FCI+IN—F, was used; although Watson's S-reduction is generally more suitable forfittingdata of a near-symmetric top such as C1N0 (K = —0.991), the fits were done using the A-reduction because it had been used in previous studies, and because there was no advantage to using the S-reduction since only a-type and 6-type transitions having K < 1 were measured. a  While the preliminary data fit fairly well for most isotopomers, with standard deviations around 1 kHz, there were several hyperfine components of the 2  1)2  — li,i transition  of the Cl NO isotopomer that were shifted from their calculated positions by as much as 15  94 kHz. These deviations were attributed to the fact that the only non-zero off-diagonal quadrupole coupling constant, \ab, of the quadrupolar chlorine nucleus had not been accounted for. In the case of an interaction between energy levels of the correct symmetry (AF = 0, AJ = 0,±1,±2; K K =ee«-»oe or eo«4oo for C1NO), the off-diagonal a  c  quadrupole coupling constants can have an effect on the hyperfine structures of transitions involving any of the interacting levels; see Section 2.1.3. These effects are usually  CHAPTER  4. NITROSYL  CHLORIDE  45  only noticeable when the levels are separated by a small energy difference. This is the case for C l N O ; the 2 1 5  1)2  and 4 ,4 rotational energy levels are separated by 254.2 MHz. 0  Since off-diagonal quadrupole coupling effects had been seen in transitions involving interacting energy levels of the C 1 N 0 isotopomer, it was of interest to look for similar 15  effects in the spectra of other isotopomers.  Near degeneracies of less than 2.5 GHz  were found between the 4 , and 2 , levels of C 1 N 0 (2158.4 MHz), the 7 3 7  0  4  1 5  X 2  lfi  levels of C1N0 (1807.7 MHz), and the 7  and 8 , 0  8  and 8 , levels of C 1 N 0 (25.6 MHz), The 37  h6  0  8  energy level separations that are quoted here are those which were ultimately found; for the preliminary analysis, it was necessary to use assumed values for the A rotational constants to calculate the relative positions of the rotational energy levels. Some a-type transitions involving these near-degenerate energy levels were measured and were seen to show a significant dependence on Xab'i interestingly, transitions involving energy levels of the correct symmetry separated by as much as about 6500 MHz also were seen to exhibit observable (~3kHz) off-diagonal effects. With these new transitions included in the fits, Xab °f ^ C1 and 35  37  1 4  N were fit as free parameters. However, the A  rotational constant was highly correlated with Xab when only a-type lines were included. Thus, in order to determine uniquely both A and Xab, some b-type transitions had to be measured. Since the A constant of C1NO had been previously determined [70], new 6-type transitions for this isotopomer were easily found. For the other isotopomers, however, finding 6-type transitions could have been difficult because, not only are these transitions much weaker than the a-type transitions because of a much smaller dipole component along the f>axis, but also because these transitions depend upon the A rotational constant, which could not be obtained directly from the measured a-type transitions. As a means  CHAPTER  4. NITROSYL  CHLORIDE  46  of predicting these unknown constants and, thus, limiting the search range, an rj  >e  ge-  ometry was determined. This type of structure determination, described in Section 2.2, allows a partial cancellation of vibrational effects, and is particularly well suited to the prediction of unknown rotational constants [52,53]. Using the r/ geometry, estimates for the unknown A rotational constants were ob)£  tained. Subsequently, 6-type transitions of C1N0 were predicted; these transitions were 37  found within 3 MHz of their predicted positions. These new line positions were then included in a spectral fit, and the resulting rotational constants were used in a new r/  >e  structure determination; the inclusion of the additional A rotational constant resulted in a better prediction of the remaining unknown rotational constants, and this in turn led to a better prediction for the 6-type transitions of these isotopomers. Using this iterative procedure, 6-type transitions were ultimately found for four isotopomers: C1N0, 37  C1N0, C1 N0 and C1 N0. Those of C1N0 and C1N0 were measured in natural 15  37  15  35  37  abundance, and those of C1 N0 and C1 N0 were measured using the N labelled 15  37  15  15  sample. An example 6-type transition of C1N0 which shows a significant dependence 37  on the off-diagonal quadrupole coupling constants of C1 and N is shown in Fig. 4.1. 37  14  The largest shifts in the hyperfine structure, caused by the interaction between the 71,6 and 8 ,8 energy levels, are on the order of 1600 kHz. 0  Because of its low natural abundance, the 0 isotopomer exhibited very weak a-type 18  lines, and none of the even weaker 6-type transitions were looked for. The value for the A rotational constant of C1N 0 used in the spectral fits was the one determined from 18  the final r/ structure fit, where the experimentally determined rotational constants )£  of all five isotopomers studied were included as input data. From a consideration of the differences between the observed and calculated rotational constants of the other isotopomers, the uncertainty (ltr) in the value of A for C1N 0 was estimated to be 0.5 18  CHAPTER  4.  NITROSYL  47  CHLORIDE  9641.4 MHz  9637.8 MHz  Figure 4.1: Example 6-type transition of C 1 N 0 that is strongly affected by Xab- Upper trace: Composite drawing of the measured 8 ,8 — 7 transition. The hyperfine structure is due to quadrupole and spin-rotation interactions. Each component was obtained using 600 averaging cycles and 4K data points. Note that each line is split into two Doppler components. Centre trace: A stick diagram of the Doppler averaged measured positions of the hyperfine components. Lower trace: A stick diagram of the Doppler averaged line positions that are calculated when the off-diagonal quadrupole coupling constants of both the chlorine and nitrogen nuclei are not included. 37  0  1|7  CHAPTER  4. NITROSYL  CHLORIDE  48  MHz; this uncertainty was propagated through the spectral fits. In total, 488 lines of five isotopomers of nitrosyl chloride were measured. All observed hyperfine components of transitions involving any of the closely interacting energy levels are listed in Table 4.1. A complete listing of all assigned line frequencies has been included in Appendix A. In the fits, the centrifugal distortion constants AK, SK and, in the case of C1 N0 and C1N 0, Sj were kept fixed. Those of C1N0 were obtained 37  15  18  from Ref. 19, while those of the other isotopomers were calculated using the ratio of the parameters predicted by the force field to the constants determined for C1N0 in Ref. 19. The uncertainties in these values were taken as given in Ref. 19 for C1N0, and were assumed to be four times those of the corresponding quantities of C1N0 for all other isotopomers; these uncertainties were propagated through the fits. The spin-rotation coupling constants C (N) of C1 N0, and C (N) and C (N) of C1 N0 and C1N 0 15  CC  37  66  15  18  CC  were also kept asfixedparameters; no uncertainties in the spin-rotation constants were propagated through the fits because the uncertainties in these quantities did not affect any of the other determinations. The A rotational constant of C1N 0 was treated 18  as a constrained parameter for which the value and uncertainty were determined from the final r/ structure fit as was discussed above. Because the uncertainty of A was ]£  small,, it had negligible effects on the uncertainties of the other constants. Also, for C1N 0, the 2 18  1;2  and 4 , 4 levels are moderately close ( ~ 4 8 7 4 MHz). However, inclusion 0  °f Xa6(Cl)=±29.9 MHz and ^ (N)==pl.8 MHz asfixedvalues did not improve the quality a6  of the fit. Because neither A nor Xab could be determined precisely for this isotopomer, and because all other constants were affected only within their uncertainties, the offdiagonal quadrupole coupling constants were omitted from the final fit of the C1N 0 18  data. The results of thefinalfitsare presented in Table 4.2.  CHAPTER  4.4  4. NITROSYL  CHLORIDE  49  Discussion  4.4.1  Molecular geometry  In this study, precise rotational constants of five isotopomers of C1NO were determined. This information was used to test the structure models proposed by Rudolph, and to calculate a ground state average structure for the molecule. The programs RU111J and RU238J were used to calculate r -type [51,52] and re0  type [51] structures, respectively; these structure determination methods are discussed in some detail in Section 2.2. Following the recommendation of Rudolph, the ro, r , and s  r p structures, but not the r/ . and r structures, of nitrosyl chloride were calculated A  ]£  z  by fitting to the principal planar moments with P omitted because of the planarity of c  the molecule [72]. In the determination of the r structure, the first and second moment s  conditions in the af>plane were used to help determine the position of the oxygen atom; this atom had only a single isotopic substitution for which the A rotational constant had not been experimentally determined. For both the ro-type and the r -type structure s  determinations, the data were weighted according to the inverse squares of their uncertainties. At first, the uncertainties were input as those given in Table 4.2. However, these experimental uncertainties place too much weight on the data for the main C1N0 isotopomer, and do not reflect the quality of the data; in order to give more appropriate weightings, the uncertainties of C1N0 were increased by a factor of three, and those of C1 N0 were decreased by a factor of two over those given in Table 4.2; all other 37  15  uncertainties were retained as those given in Table 4.2. To evaluate the ground state average, r , structure, an harmonic force field was calz  culated; this is described in the next section. The ground state average rotational constants were obtained by subtracting the harmonic contributions to the a-constants from the measured rotational constants. These data were weighted as for the r -type and 0  CHAPTER  4.  NITROSYL  50  CHLORIDE  r\,-type structure determinations. Isotopic variations in the bond lengths were accounted for using Eq. 2.70, reprinted here for simplicity: Sv = -aS(u ) 2  z  -  SK  The zero-point mean square amplitudes of the bonds, (w ), and their perpendicular am2  plitudes, K, were obtained from the force field and the Morse parameters, a, were approximated from the corresponding diatomics [59]; a for the N=0 bond, 2.549A , was -1  obtained from the tabulated values in Ref. 59, and that for the N-Cl bond, 1.952A , -1  was calculated using the data for the NCI radical obtained from Ref. 74. The r structure z  was evaluated using the program MWSTR to fit to the calculated ground state average rotational constants. All structures determined in this study are presented in Table 4.3. The structural parameters agree with one another within their stated uncertainties. Moreover, those of the r^p and r structures are almost identical; it is shown in Section 2.2 that this should s  be the case. Table 4.3 also gives a comparison of the determined structures with two equilibrium structures calculated in a previous study [19]. These two equilibrium structures were obtained using different methods and are therefore subject to error in different manners. In the first method, the structural parameters were fit to B and C of C1NO and Cl NO; 15  e  e  the accuracy of this structure is therefore limited by the small data set. In this reference, the uncertainties in these structural parameters were estimated in two different ways; those quoted for this structure in Table 4.3 were based on the experimental errors in the equilibrium rotational constants; see Ref. 19 for details. In the second method, equilibrium rotational constants of a large set of isotopomers were derived from the ground state values using a cubic force field; the reliability of this method is difficult to assess because the results are dependent upon the accuracy of the force constants,  CHAPTER  4.  NITROSYL  51  CHLORIDE  some of which had to be held fixed to the SCF  ab initio  values [19,75]. The N-Cl bond  length and the C1N0 angle of the r , r&p, and r structures agree within the stated 0  s  uncertainties with these equilibrium structures. The ro-derived and r -type structure s  determination methods proposed by Rudolph are seen to give a good estimate of the equilibrium geometry of the molecule. 4.4.2  Force field  In order to determine a ground state average structure for C1NO, and to derive values for the undeterminable centrifugal distortion constants, an harmonic force field was calculated. This was done by using the program NCA [76] to refine a previously determined forcefield[19] where the interaction constant  /NO,CINO  had been barely determined, and,  thus, was kept fixed to the value determined from an SCF  ab initio  study. With sev-  eral new centrifugal distortion constants and inertial defects included in the fit, all six quadratic force constants could be determined. The input data were weighted according to the inverse squares of their uncertainties. The harmonic wavenumbers [77] of eight isotopomers of C1N0 were included in the fit. With the exception of wi of C1N 0, which was omitted because of a large Fermi inter18  action between v\ and 3^2, the harmonic wavenumbers were given initial uncertainties of 1 cm" . The ground state inertial defects of C1N0, C1N0, C1 N0, and C1 N0, 1  37  15  37  15  and the inertial defects of the excited (100), (010), and (001) vibrational states [73] of C1NO were also used as input data. The uncertainties of the inertial defects were obtained by propagating the errors from the rotational constants and the conversion factor BI = 505379.07(43) MHzamuA [78]. 2  The refinement of the forcefieldwas done byfirstreproducing the earlier work, and then using an iterative procedure whereby the force constants were adjusted slightly and  CHAPTER  4. NITROSYL  CHLORIDE  52  fit again in order to reproduce the experimental data better. Preliminary fits showed that the harmonic wavenumbers [77] were poorly reproduced. Therefore, their weights were increased by a factor of 1000, and those of the centrifugal distortion constants were lowered by a factor of 4. The final force constants for the vibrational wavenumbers of the main isotopomer are given in Table 4.4; here they are compared with the force constants determined in Ref. 19 and with those calculated in high level ab initio studies [75,79]. As is shown in this table, the determined constants are in good to very good agreement with both the previously determined and ab initio values. The experimental parameters are compared with those calculated from the force field in Table 4.5. Only the ground state inertial defects, A , have been included in this table; those of the excited 0  vibrational states of C1N0 are given in a footnote. Considering the moderate precision of the observed harmonic wavenumbers, the agreement with the calculated values is mostly very good. As far as they have been determined, Aj, AK, SJ, and the ground state inertial defects are reproduced quite well; the agreement is also reasonable for AJK, <$A-, and the excited state inertial defects. Because a large set of input data was used, the present harmonic force field is likely more appropriate than that of Ref. 19. In Table 4.6, the quadratic force constants determined for nitrosyl chloride are compared with those of some related compounds: FNO, BrNO, C1C0, ClOO, NO, CO, and O2. As one would expect, the diagonal force constants decrease from FNO to BrNO, and those of BrNO and C1N0 are very similar; this trend holds to some extent even for the interaction force constants. The XN bonds of the nitrosyl halides are rather long and very weak in comparison with those of NC1 (r=1.7535(20)A, /=2.711) [80,81] and NCI 3  (r=1.6610791(19)A, /=4.039) [74], whereas the NO bond lengths and force constants differ little from those of free NO (r=1.15lA,/=15.955) [82,83]. The bond length of free NO is greater, but, remarkably, the force constant is larger. The bonding situation for  CHAPTER  4. NITROSYL  CHLORIDE  53  the nitrosyl halides is very similar to that of the more weakly bonded C100, and quite similar to that of 0 F, C1C0, and FCO [83]. 2  4.4.3  Nuclear quadrupole coupling constants  Complete quadrupole coupling tensors were determined for the C1, C1, and N nuclei 35  37  14  of the C1N0, C1N0, C1 N0, and C1 N0; this is thefirstsuch determination of the 37  15  37  15  off-diagonal quadrupole coupling constants of nitrosyl chloride, and is one of only a few such determinations for a N nucleus. These tensors were diagonalised to yield values 14  for the principal quadrupole coupling constants, Xggi and the angle between the principal quadrupolar 2-axis and the inertial a-axis, 0 . These results are shown in Table 4.7; as za  can be seen, the principal quadrupole coupling constants of a given nucleus are in agreement within the error limits; moreover, the ratio of the C1 to C1 quadrupole coupling 35  constants  (x  3  5 c  :  X c  7 C  =  1  -  2  6  8  9  4  (  1  3  ) )  a  S  r  e  e  s  w i t h  t h e  37  accepted value of 1.2688773(15) [84].  The quadrupolar 2-axis of the N nucleus approximately bisects the C1N0 angle (i.e. it 14  lies in the expected direction of the non-bonded electron "pair") and that of the chlorine nucleus lies approximately along the Cl-N bond (within ~1°); both findings are in agreement with simple bonding theories. The principal quadrupolar axes of the nitrogen and chlorine nuclei are shown schematically in Fig. 4.2. Because the coupling tensor for the chlorine nucleus aligns itself roughly along the N-Cl bond, the amount of ionic character, i , in the N-Cl bond can be calculated from the c  chlorine quadrupole coupling constants. The total ionic character of the bond, i  c  — i —-n , a  c  depends upon z , the amount of electron density accepted from the nitrogen atom through a  the cr-bond, and 7r , the amount of electron density that is back-donated to the ^-orbitals c  on the nitrogen atom. The amount' of 7r-character in the bond can be calculated from a knowledge of the asymmetry parameter of the quadrupole coupling tensor, rj, and the  CHAPTER  4. NITROSYL  CHLORIDE  Figure 4.2: Principal quadrupolar axes of the chlorine and nitrogen nuclei.  CHAPTER  4. NITROSYL  CHLORIDE  55  ionic character of the cr-bond can be calculated from \z  d Xy  a n  a s  follows.  The asymmetry parameter of the nuclear quadrupole coupling tensor is defined as Xx ~ Xy  =  3(n - n )  =  y  Xz  n +  x  n -2n  x  y  z  where n is the fractional number of electrons in the p-orbital with orientation along the g  quadrupolar g-axis. Since 2(U ) = n + n - 2n = P X  x  y  —  z  (  4  .  2  )  Eq. 4.1 can be re-written as n -n x  y  = -( -£—) \eQq J  r,= -( ~ ) 3 \ eQq Xx  3  nl0  (4.3)  Xy  )  nl0  The chlorine nucleus (valence shell configuration {s p p p\)) of nitrosyl chloride has a 2  2  2  x  p^-orbital, which can participate in 7r-bonding, normal to the molecular plane, and a p^-orbital, which usually has no orbital overlap and therefore cannot participate in irbonding [29], in the molecular plane. The p orbital thus shares its electron density y  and has a reduced n value over that of the unbonded atom. This reduction in electron y  density is equal to the amount of 7r-character in the bond; n = 2 — 7r . Thus, Eq. 4.3 y  c  becomes *c  \  =  3  (4-4)  V Qqmo J e  and the measured chlorine asymmetry parameter can be used to determine the amount of 7r-character in the N-Cl bond. The 2-component of the quadrupole coupling constant is given approximately by f n -\- n Xz = - ( x  v  \ n j eQq z  nl0  (4.5)  where the occupation of the p and p^-orbitals remains as determined above, and that of x  the /vorbital is increased over its free halogen value by the amount of electron density  CHAPTER  4. NITROSYL  CHLORIDE  56  that is acquired from the N atom upon formation of the cr-bond; n = (1 + i ). Eq. 4.5 z  a  then becomes (4.6) Substituting in the expression determined above for 7r yields c  (4.7) Thus, the ionic character of the <7-bond and the overall ionic character of the N-Cl bond can be determined from the quadrupole coupling constants. A recent study of nitrosyl bromide [85] has shown that the principal quadrupolar z-axis here is also along the nitrogen-halogen bond, and the ionic character of the NBr bond has been calculated for comparison. The results are shown in Table 4.8. It is interesting to note that for both of these compounds there seems to be a significant amount (~12%) of 7r-character in the nitrogen-halogen bond. 4.4.4  Nuclear spin-rotation coupling constants  The spin-rotation coupling constants, C , of both chlorine and nitrogen have been detergg  mined. The nuclear contributions were calculated using Eq. 2.37 and subtracted from the experimental values to give values for the electronic contributions. These have been used to calculate the paramagnetic and diamagnetic nuclear shielding terms using Eqs. 2.41, and 2.43. The results are given in Tables 4.9 and 4.10. As is seen there, the agreement between the shielding parameters determined for different isotopomers is quite good for both the chlorine and nitrogen nuclei; because the uncertainties determined for the spinrotation coupling constants of the last three isotopomers listed here were much larger than for the first two isotopomers, and because in the case of the nitrogen nucleus, some spin-rotation coupling constants of the last three isotopomers listed were held fixed in the fits and were assigned arbitrary uncertainties, the calculated nuclear shielding terms  CHAPTER  4.  NITROSYL  CHLORIDE  57  of the first two isotopomers must be considered as being closest to the true values. The chemical shift of the chlorine nucleus of this molecule has not been measured previously; however, that of the nitrogen nucleus has. The absolute value of the nitrogen nuclear shielding [86], obtained from NMR experiments, has been compared with the average shielding calculated from the spin-rotation constants in Table 4.10. The agreement is quite good. Since the diamagnetic shielding contributions depend only on the molecular geometry, they are an indication of the amount of electron density on the atom in question. The diamagnetic nuclear shielding terms for the nitrogen nuclei of different nitrosyl halides and of nitric oxide itself, calculated using Eq. 2.42, are presented in Table 4.8. These calculations show that the amount of electron density on the nitrogen atom increases from the fluoride to the bromide: <r£(FN0)< <7£(C1N0)< cr^(BrNO), a trend which is reflected by the calculated ionic character of the N-X bond. These data would both suggest that the chlorine atom is a better electron density acceptor than is bromine, as would be expected from a consideration of the differing electronegativities of the two halogens. The trend in the ionicity of the N-X bond of the nitrosyl halides is also backed up by a consideration of the N=0 bond lengths. For all nitrosyl halides, this bond is considerably shorter than that of NO itself because of the halogens' acceptance of some of the electron density from the highest occupied anti-bonding molecular orbital of the N=0 group. Moreover, the bond length decreases from bromine to chlorine tofluorine,corresponding to an increase in the ionic character of the N-X bond. The N=0 bond lengths of several nitrosyl halides and of nitric oxide itself are presented in Table 4.8.  CHAPTER  4. NITROSYL  CHLORIDE  58  Table 4.1: Transitions of C 1 N 0 strongly affected by Xab j"  ,J'  K h'c k ' . ' i . F £ , F" F £ ,  A /kHz with without X a b  a  F'  v /MHz  X o 6  35 ,14 16 C  7l,6 -" 7i,7 7.5 6.5 7.5 7.5 8.5 7.5 6.5 5.5 6.5 6.5 7.5 6.5 8.5 7.5 8.5 8.5 9.5 8.5 7.5 7.5 7.5 5.5 6.5 5.5 6.5 6.5 6.5 8.5 8.5 8.5 5.5 5.5 5.5 7.5 6.5 6.5 5.5 4.5 5.5 6.5 6.5 7.5  6.5 8.5 5.5 7.5 6.5 9.5 7.5 6.5 6.5 8.5 5.5 6.5 4.5 6.5  8o,8 - ?1,7 8.5 7.5 6.5 6.5 7.5 6.5 6.5 5.5 8.5 7.5 7.5 6.5 8.5 9.5 7.5 8.5 7.5 8.5 6.5 7.5 8.5 8.5 7.5 7.5 7.5 7.5 6.5 6.5 9.5 8.5 8.5 7.5 6.5 5.5 5.5 4.5 9.510.5 8.5 9.5 6.5 7.5 5.5 6.5 7.5 7.5 7.5 6.5 9.5 9.5 8.5 8.5 6.5 6.5 5.5 5.5  N  -1.1 -0.8 -24.0 -22.0 -17.9 -17.6 • -2.2 0.0 -23.1 -19.4 -0.6  11920.5579(10) 11921.5054(10) 11921.5440(10) 11921.6456(10) 11921.6738(10) 11922.9828(10) 11922.9152(10) 11923.1935(10) 11923.2164(10) 11923.3544(10) 11923.4485(10) 11923.9019(10) 11924.7590(10) 11924.7914(10)  -0.3 0.4 -0.9 0.8 -1.1 -0.6 -0.1 0.3 0.0 0.7 0.5 -0.2 0.5 -0.1  17.7 1.8 17.5 19.3 0.2 19.3 1.0 0.7 24.6 0.8 24.8 1.3 0.7 22.8  2.5 2.5 1.5 1.5 2.5 2.5 3.5 3.5 1.5 1.5 1.5 0.5 0.5 0.5  3 2 2 1 2 3 3 4 2 1 1 1 0 1  1.5 1.5 1.5 1.5 2.5 2.5 2.5 2.5 0.5 0.5 0.5 0.5 0.5 0.5  2 1 2 1 2 3 2 3 1 1 0 1 1 0  21651.6264(20) 21655.0902(20)  N  X  C  -0.2 0.0 0.3 0.3 -0.3 0.3 0.3 0.2 -0.6 -0.1 -0.4  C  u /MHz  A /kHz without  b  N  X  a  b  0  9662.9722(10) 9663.2581(10) 9664.7540(10) 9665.1968(10)  -2.3 -2.3 -0.3 -0.1  65.1 61.4 1580.7 1435.5  9665.9739(10) 9665.4651(10) 9667.5495(10)  -1.3 -0.7 -0.3  173.0 13.9 1330.9  9668.2886(10) 9662.3188(10) 9664.9198(10) 9668.2026(10)  0.0 -2.4 -0.2 -0.4  16.5 64.8 -0.2 1330.9  9638.2287(10)  1.5  -62.8  9 638.4054(10)  1.7  -52.5  9639.6164(20)  0.0  -20.3  9638.0202(10) 9639.7862(10) 9638.2941(10)  -1.6 -0.7 -0.1  -1598.9 -0.6 -1556.6  9641.1895(10) 9639.8515(10)  -0.8 0.2  -6.4 -1348.2  3 C1 N 0 7  0  0.9  a  37 ,14 16  0  10112.6547(10) 10112.9924(10) 10113.0413(10) 10113.5540(10) 10114.9213(10) 10115.2692(10) 10115.6730(10) 10115.8195(10) 10116.1351(10) 10118.2236(10) 10118.6396(10)  35 |15 16  with  52.5  21153.1646(20)  15  16  0.3  4.8  0.9  0.8  21155.9308(20)  0.9  0.8  21658.9427(10) 2 1 658.9575(10) 21 663.9774(20) 21663.9921(20) 21668.3999(10)  0.1 0.1 -2.6 1.8 -0.1  51.6 51.5 88.9 93.3 0.0  21668.4371(10)  -0.7  -0.7  21158.9428(10) 21158.9613(10) 21 162.8866(10) 21162.9013(10) 21166.4506(10) 21 166.4677(10) 21166.4876(10) 21170.3468(10)  -1.3 1.1 -1.6 1.8 1.2 -0.5 -1.8 1.2  3.0 5.4 7.0 0.3 1.2 -0.4 -1.8 0.8  21170.3673(20)  -0.8  -1.2  CHAPTER  4. NITROSYL  CHLORIDE  59  Table 4.2: Spectroscopic constants of nitrosyl chloride"  35  AJA-  A 6J  .  0  3 7  C  1  i 4  N  i 6  35  0  C 1  15 16 N  3 7  0  C  1  i s  N  i 6  35  0  C 1  14 18Q N  Xaa(C\)  x-(ci) Xaft(Cl) Xaa(N)  X-(N) Xa6(N)  (Cl)  C&&(C1) C (C1) CC  o  a  (N)  Cw(N) C C  d  d  rf  d  d  rf  d  c  SK  a a  6.3444(21) 6.0709(21) 6.253(10) 5.96(10) 5.641(33) -61.019(76) -60.144(78) -54.25(19) -53.45(20) -60.62(13) 4394.3(27) 4373.8(100) 3975.7(100) 3956.4(100) 4178.8(100)^ 0.501940(57) 0.469805(57) 0.51038(99) 0.4766(20) 0.4444(20) 40.300(59) 38.65(20) 39.61(20) 37.98(20) 35.85(20) c  A  C  N  6  Aj  C  14 16  87374.4480(31) 87269.458(10) 83459.619(12) 83356.002(45) 84433.00(50) 5737.78058(15) 5601.33053(41) 5693.93966(47) 5556.24830(90) 5439.56510(50) 5376.23181(15) 5255.87213(41) 5322.28942(48) 5201.38800(92) 5102.99503(50)  A B C  C  C 1  (N)  -49.05967(78) 9.38484(90) ±29.00(23) 0.98115(111) -8.56752(78) ^1.85(65) 42.82(33) 8.367(69) 5.308(73) 42.61(55) 1.598(80) 1.119(84)  -38.73042(104) -49.3627(23) 7.46419(94) 9.6947(28) ±22.6341(36) ±28.51(19) 0.98629(91) -8.57268(85) Tl.710(12) 35.17(37) 6.741(68) 4.263(72) 42.63(66) 1.501(82) 1.072(85)  40.19(54) 8.38(17) 5.28(20) -58.4(13) -2.65(42) -1.55 6  -38.9718(20) 7.7105(29) ±24.0(22) -  d  d  -48.3588(15) 8.6909(38) -  0.9399(17) -8.5232(50) -  33.52(62) 6.69(31) 3.85(54) -62.3(16) -2.17 -1.52 6 e  42.23(66) 7.71(49) 5.08(58) 40.3(15) 1.52 1.06 e  e  Units of MHz for the rotational and quadrupole constants, kHz for the centrifugal distortion and spin-rotation constants; uncertainties ( l a ) are given in parentheses. Determined from a fit to the rotational constants of all other isotopomers; see text for details. Constrained to values obtained from Ref. 19. From an harmonic force field calculation; see text for details. Fixed at values calculated by scaling those of C 1 N 0 ; see text for details. a  b  c  d  e  3 5  1 4  1 6  CHAPTER  4. NITROSYL  CHLORIDE  60  Table 4.3: Structural parameters of nitrosyl chloride  r(N=0) / A This work:  r  0  ri,e  r  s  r  z  Previous work:  r  a e  r(N-Cl) / A  Z(CINO) /deg  1.14029(57) 1.13644(23) 1.13858(40) 1.13859(77) 1.1471(80)  1.97510(58) 1.97214(41) 1.97286(19) 1.97286(38) 1.9690(79)  113.291(30) 113.564(15) 113.413(27) 113.413(52) 113.72(36)  1.1336(17) 1.135710(68)  1.9745(17) 1.972626(67)  113.320(87) 113.4053(34)  Ref. 19; fit to B and C of C1 N 0 and C1 N 0. See the reference for an explanation of the uncertanties. Ref. 19; fit to cubic force constants. a  35  e  b  e  14  16  35  15  16  CHAPTER  4. NITROSYL  61  CHLORIDE  Table 4.4: Quadratic force constants (lOONm ) of the general valence forcefieldof nitrosyl chloride l  INO  this work 15.282 Ref. [19] 15.424 ab initio 14.758 ab initio 15.248 b  0  a 6 c  fciN  1.257 1.254 1.269 1.311  fciNO  1.248 1.299 1.282 1.316  fNOfilN  1.249 1.44 1.238 1.328  INO,CINO  fciN,ClNO  0.260 0.417 0.249 0.271  Fixed at a value obtained from an SCF ab initio calculation. CCSD(T)/TZ2P; Ref. 75. CCSD(T)/cc-pVTZ; Ref. 79.  a  0.109 0.1505 0.128 0.135  CHAPTER  4.  NITROSYL  CHLORIDE  62  Table 4.5: Comparison of measured and force field calculated parameters of C I N O 0  35  C1 1 4  N  16  obs.  U>2 Aj A SJ SK A K  0  calc.  1835.6 603.2 336.4 6.3444 -61.019 4394.3 0.501940 40.300 0.13922  37  1835.7 603.2 334.9 6.3093 -69.316 4314.0 0.502029 35.994 0.13931  C1 1 4  N  16  U>2 U Aj  3  AJAA " SJ SK A A  0  d  d  35 , 1 5 C  obs.  wi U/2 Ul  1753.3 579.8 323.2  3  Aj A/c *j *jf A 0  N  18  c  CI N 1 5  l e  d  d  d  CI  1 5  N  l s  1 8  0 calc.  1786.1 595.5 329.3 5.641 -60.62 4178.8 0.4444 35.85 0.14222  1786.3 596.3 327.3 5.628 -68.28 4102.0 0.4440 32.03 0.14168  c  d  d  d  d  C  1803.5 587.4 328.8 5.94 -61.04 3884.3 0.4765 33.92 0.14266  N  obs.  37 ,14  calc.  1803.4 587.8 330.3 5.96 -53.45 3956.4 0.4766 37.98 0.14256  calc.  C  O  obs.  37  1753.2 580.1 321.4 5.32 -60.32 3683.6 0.4227 30.18 0.14522  l s  1803.5 588.4 332.8 6.210 -62.05 3903.3 0.50981 35.38 0.14259  C  0  35 ,14  N O calc.  37  1835.6 602.1 330.8 6.0373 -68.161 4293.9 0.469708 34.52 0.13937  1 5  1803.6 588.8 334.3 6.253 -54.25 3975.8 0.51038 39.62 0.14247  calc.  1835.6 602.2 332.3 6.0708 -60.144 4373.8 0.469804 38.65 0.13929  CI  obs.  0  obs.  wi  35  0  6  N  l s  O calc.  obs.  1753.4 580.7 327.3  1753.2 581.2 325.6 5.55 -61.41 3702.3 0.4532 31.53 0.14515  O  obs.  calc.  1786.3 595.2 323.2 5.38 -67.05 4082.2 0.4145 30.67 0.14173  1786.3 594.5 325.2  Vibrational wavenumbers from Ref. 77, centrifugal distortion constants from this study or Ref. 19, and Ao (amu A ) from this study; exp(calc) A „ of C 1 N 0 : A( o)=0.13469(0.13178), A ( , i ) =0-34547(0.33632), A( ,o,i) =0.22916(0.22846). a  2  3 5  1 4  1 6  10>  0  0  b  c  d  Units of c m ' f o r the vibrational wavenumbers and kHz for the centrifugal distortion constants. Omitted from the fit because of a large Fermi interaction between v\ and 3f2. Derived values; not used in the fit. -  0  CHAPTER  4. NITROSYL  CHLORIDE  63  Table 4.6: Force Constants" (100 Nm" ) of XEO Compounds (X=-,F,Cl,Br; E=N,C,0) 1  FNO  IEO  fxE fxEO JEO,XE /EO,XEO fx E,XEO  a 6 c d e  C1N0  C  15.912 15.282 2.133 1.257 1.8414 1.248 1.902 . 1.249 0.323 0.260 0.2358 0.109  N0  IEO  6  e  15.955  C0  e  19.019  BrNO  ClC0  e  C100  15.254 14.964 1.1011 1.173 1.0859 0.944 1.413 1.15 0.294 0.026 0.1031 0.122  10.599 0.509 0.810 0.604 0.294 0.032  rf  0^  11.766  Deformation constants normalized to 100 pm bond length Ref. 87 This work Ref. 88 Ref. 83  e  CHAPTER  4. NITROSYL  CHLORIDE  64  Table 4 . 7 : Principal chlorine and nitrogen quadrupole coupling constants of nitrosyl chloride  35  C  1  14  N  16  0  3 7  C  1  i 4  N  i 6  0  3 5  C  1  i 5  N  i 6  0  37  C 1  15 16Q N  X„(C1)  /MHz  -58.63(14)  -46.1306(31)  -58.59(11)  -47.1(14)  X^(C1)  /MHz  38.79(14)  30.4975(31)  38.75(11)  31.5(14)  (Cl)  Xyy  /MHz  19.83742(84)  15.63311(99)  -18.26(38)°  -18.1051(74)°  19.8340(26) -17.93(31)°  15.6307(25) -18.7(43)°  X,,(N)  /MHz  -5.32(39)  -5.2485(71)  —  —  ( N )  /MHz  1.52(39)  1.4553(71)  —  —  (N)  /MHz  3.79319(95)  3.79321(88)  —  —  X  M  X  V  Y  106.4(65)°  105.34(12)°  CHAPTER  4. NITROSYL  65  CHLORIDE  Table 4.8: Ionic character of the N-X Bond, diamagnetic nitrogen nuclear sheildings, and N=0 bond lengths of several nitrosyl compounds  ic FNO CINO BrNO NO  Ref. 87 Ref. 19 This work Ref. 88 Ref. 89 ^ Ref. 82 a  b c  d  e  d  448 29% 41% 12% 473 24% 36% 12% 545 391  ppm ppm ppm ppm  r (N=0)  r (N=0)  1.13155(23)° 1.1336(17) 1.133(20)  1.136(3) 1.13858(40) 1.146(l)  e  6  d  1.151'  s  a  c  e  CHAPTER  4. NITROSYL  66  CHLORIDE  Table 4.9: Chlorine spin-rotation constants (kHz) and nuclear shielding parameters (ppm) of CINO  3 5  C (Cl)  42.82(33)  a a  3 7  C1N0  35.17(37)  3 5  C1  1 5  N0  3 7  C1  1 5  N0  C1N  1 8  0  40.19(54)  33.52(62)  42.23(66)  C (C1)  8.367(69)  6.741(68)  8.38(17)  6.69(31)  7.71(49)  C (C1)  5.308(73)  4.263(72)  5.28(20)  3.85(54)  5.08(58)  66  CC  ci^(ci)  dc  n )  (ci)  d a'(ci) e  -0.27  -0.23  -0.26  -0.22  -0.26  -0.299  -0.243  -0.30  -0.24  -0.28  -0.297  -0.242  -0.29  -0.24  -0.28  43.09(33)  35.40(37)  40.45(54)  33.74(62)  42.49(66)  cl (ci)  8.666(69)  6.984(68)  8.68(17)  6.93(31)  7.99(49)  dc (ci)  5.605(73)  4.505(72)  5.57(20)  4.09(54)  5.36(58)  ^ ( C l )  -827(6)  -816(9)  -812(11)  -815(15)  -843(13)  *L (C1)  -2531(20)  -2510(24)  -2553(50)  -2511(112)  -2462(151)  ^ (C1)  -1747(23)  -1725(28)  -1755(63)  -1583(209)  -1761(190)  aiv'(Cl)  -1702(16)  -1684(20)  -1707(41)  -1636(112)  -1689(118)  1148(5)  1148(5)  1148(5)  1148(5)  1148(5)  1230(5)  1230(5)  1230(5)  1230(5)  1230(5)  1235(5)  1235(5)  1235(5)  1235(5)  1235(5)  1204(5)  1204(5)  1204(5)  1204(5)  1204(5)  e )  e )  p)  }  ^(ci)  a  ^(Cl)"  331(10)  336(12)  ffw(Cl)  -1301(21)  -1280(25)  -1323(51)  -1281(113)  ^(Cl)  -512(24)  -490(29)  -520(64)  -347(210)  -525(191)  ^av(Cl)  -497(17)  -480(21)  -502(42)  -432(113)  -484(119)  ffaa(Cl)  a  C1N0  321(8)  Uncertainties are estimated.  333(16)  305(14) -1232(152)  CHAPTER  4.  NITROSYL  67  CHLORIDE  Table 4.10: Nitrogen spin-rotation constants (kHz) and nuclear shielding parameters (ppm) of C1NO  3 5  C (N) C (N)  42.61(55)  a a  1.598(80) 1.119(84)  f c 6  C (N) C C  42.63(66) 1.501(82) 1.072(85)  3 5  C1  1 5  N0  3 7  1 5  a  C1N  N0  -62.3(16) -2.17(42)  -58.4(13) -2.65(42) -1.55(42)  C1  -1.52(42)  a  a  3.5  -2.5  C  (N)  -0.387  -0.377  0.54  0.53  -0.37  dc (N)  -0.522  -0.510  0.73  0.71  -0.50  d ^ N )  45.20(55)  45.22(66)  t  0  1.06(42)  3.5  6  1 8  40.3(15) 1.52(42)°  -2.59  n )  -61.88(13)  -65.77(16)  42.81(15)  C 6 (N)  1.985(80)  1.878(82)  -3.19(42)  -2.70(42)  1.89(42)  dc (N)  1.641(84)  1.582(85)  -2.28(42)  -2.23(42)  1.56(42)  -1202(25)  -1279(31)  -1153(40)  (  e)  e )  a  ^ ( N )  -1178(14)  -1178(17)  ^ ( N )  -786(32)  -763(33)  -908(120)  -786(123)  -789(176)  ^ ( N )  -694(36)  -685(37)  -693(128)  -694(131)  -693(187)  ^ ( N )  -886(27)  -875(29)  -934(91)  -920(95)  -878(134)  393(5)  393(5)  393(5)  393(5)  393(5)  479(5)  479(5)  479(5)  479(5)  479(5)  <Taa(N)  546(5)  546(5)  546(5)  546(5)  546(5)  473(5)  473(5)  473(5)  473(5)  473(5)  -785(15)  -785(18)  -809(26)  -886(31)  -760(41)  -308(33)  -284(34)  -429(121)  -308(124)  -310(177)  ^cc(N)  -148(36)  -138(38)  -147(129)  -148(132)  -147(188)  cT (N)  -413(27)  -402(30)  -461(92)  -447(96)  -406(135)  av  cr (N) a v  c  C1N0  -2.59  (  fe  b  3 7  C^(N)  n )  a  C1N0  c  -357  Values were fixed i n the fits; uncertainties were arbitrarily set equal to t h a t of C t t ( C l N O ) . U n c e r t a i n t i e s are estimated. Ref. 86. 1 5  Chapter 5  Hyperfine Interactions in Sulphur Difluoride, S F  5.1  2  Introduction  The  1 9  F average nuclear shieldings of the second row, p-blockfluorides,CF , NF , 0F , 4  3  2  and F , decrease across the row. This behaviour is expected if one considers only simple 2  shielding ideas [24,90-92] which argue that the electron density, and thus the shielding, of the fluorine atom should decrease as the electronegativity difference betweenfluorineand its bonding partner decreases. Using this argument, the analogous third row fluorides would be expected to show the same trend. It is seen, however, that while this trend does hold for the first twofluoridesof this series, SiF and PF , the F average nuclear 1 9  4  3  shieldings in both SF and C1F deviate significantly from this trend [22,24]. For these 2  compounds, the shieldings are unexpectedly large. Because of the direct relation between the nuclear spin-rotation coupling constants and the shielding of a given nucleus (see Section 2.1.3), both C1F and SF should also have 2  unusualfluorinespin-rotation coupling constants. In the case of C1F, this phenomenon has been found [24,93,94]: the F spin-rotation coupling constant was determined to 1 9  be negative. In the case of SF , no F hyperfine structure had been previously observed 1 9  2  and, therefore, nofluorinespin-rotation coupling constants had been determined. This chapter describes a study in which sulphur difluoride was prepared in an electric 68  CHAPTER  5. SULPHUR  69  DIFLUORIDE  discharge, and its rotational spectrum observed by FTMW spectroscopy. Because there were very few transitions available within the operating range of the spectrometer, the measured line positions were used in a combined fit with those of a previous microwave study [95] in order to determine precise values for the rotational and centrifugal distortion constants. Hyperfine splittings resolved in some of the rotational transitions measured in this work have been analysed to yield unusualfluorinespin-rotation coupling constants, and correspondingly unusual shielding terms. Thesefindingsare shown to be in agreement with the experimentally observed average chemical shift [22], and with diagonal components of the F shielding tensor calculated using ab initio techniques [23]. The 1 9  origin of the unusual shielding has been determined using the semi-quantitative model originally presented by Cornwell in his attempt to rationalise the unusual F shielding 1 9  of C1F [24]; details of this model can be found in Section 2.1.3. 5.2  Experimental Methods  Sulphur difluoride was prepared by passing an electric discharge through a sample containing 0.5% SF and 0.5% OCS in roughly 6 bar Ne. Transitions in the 4-26 GHz 6  frequency range were measured. Frequencies of all lines were determined byfittingto the time domain signals [65]. Line positions of strong, well resolved lines determined in this manner are estimated to be accurate to better than ±lkHz; for very weak transitions, such as the 6i,6 — 52,3 transition which had only a moderate signal to noise ratio after 10 000 signal averaging cycles, the determined line positions are less accurate. Measured frequencies of the 6i,6 — 52,3 transition, for example, are estimated to be certain to about ±5kHz.  CHAPTER  5.3  5. SULPHUR  70  DIFLUORIDE  Spectral Analysis  Sulphur difluoride is an unstable molecule which disproportionates into SSF2 and SF4 [22, 96]. Incorporation of an electric discharge apparatus into the sample inlet system of the FTMW spectrometer provided both an easy preparation technique and a means of stabilising the reactive species in the subsequent supersonic expansion. The rotational temperature achieved in the jet is estimated to be roughly IK, and, therefore, only the lowest rotational energy levels of the molecule are populated. In the case of SF , where 2  the rotational constants are fairly large and the energy levels are widely split, this means that only a few transitions within the operating frequency range of the spectrometer are strong enough to be observed. Also, with the additional consideration of spin statistics, the number of observable transitions that can be used to determine the hyperfine coupling constants is further diminished because only transitions between levels of the appropriate symmetry can have hyperfine structure. Sulphur difluoride has C „ symmetry and equivalent fluorine nuclei (/ = 1/2); the 2  6-axis is the symmetry axis.  The most appropriate coupling scheme is I + I2 = I; x  I + J = F. Here Ii and I2 are the nuclear spin angular momentum vectors of the two fluorine nuclei. Because of spin statistics, the quantum number / is restricted to values of 0 or 1 for rotational levels with (K + K ) — even or odd, respectively. For / = 0, no a  c  hyperfine splittings occur, whereas for / = 1 there is a splitting of each rotational level into three hyperfine levels. Rotational transitions lying in the 4-26 GHz frequency range were predicted using the ground state rotational and centrifugal distortion constants given in Ref. 97; these constants had been determined by reanalysing the data of Ref. 95 using Watson's A-reduction Hamiltonian [37]. Using these predictions, the frequencies of several transitions without hyperfine structure were measured and added to the earlier data set. The combined data  5. SULPHUR  CHAPTER  71  DIFLUORIDE  were then fit to rotational and centrifugal distortion constants using Pickett's exact fitting program S P F I T [41]. In order to achieve a reasonable standard deviation in the fit, it was necessary to include some sextic centrifugal distortion constants. Although their determined orders of magnitude are reasonable, the sextic constants should be considered merely as fitting parameters. The resulting rotational and quartic centrifugal distortion constants obtained in this "preliminary" fit are in good agreement with the previous results and this work represents only a small improvement in their precision. The main goal of this investigation, however, was to determine the F spin-rotation 1 9  coupling constants. Thus, it was necessary to measure and assign transitions showing hyperfine structure. In order to predict the patterns of the hyperfine components within the K K a  = eo f-> oe transitions, starting values for both the F spin-spin and spin1 9  c  rotation constants were needed. The dominant, direct portion of the tensor spin-spin coupling constant was calculated using Eq. 2.48 and the geometry of Ref. 98, and, for the reasons pointed out in Section 2.1.3, all other spin-spin contributions were neglected. The spin-spin constant was held fixed at this calculated value in all fits. And, because, as was also discussed in Section 2.1.3, the spin-rotation coupling constants are proportional to the rotational constants, starting values were obtained by scaling the known spin-rotation constants of 0 F [99], the second row analogue of SF , by the ratios of the respective 2  2  rotational constants. Only three transitions showing hyperfine structure were observed in the operating frequency range of the spectrometer at the low rotational temperature of the jet. The strongest, l  l j 0  — lo,i, was predicted to consist of six well resolved hyperfine components;  however, only two components were resolved. It was clear that basing the prediction of the spin-rotation constants on those of 0F was incorrect, and that, moreover, assignment 2  of this transition would be difficult without a better prediction of the hyperfine structure.  CHAPTER  5.  SULPHUR  72  DIFLUORIDE  Fortunately, two weaker transitions, 32,1 — 4  1)4  and 61,6 — 52,3, were each split into three  components which were easily assigned on the basis of their relative intensities. The 32,i  —  4i, transition is shown in Fig. 5.1. 4  Fitting of the hyperfine data was done in two stages. First, the frequencies of the hyperfine components of the 32,i —4 and 6i, — 5 ,3 transitions were added to the data set 1>4  2  6  used in the "preliminary" fit and a newfitwas carried out with the linear combinations of the spin-rotation coupling constants C — | (Cbb + C ), \ (Cbb + C ), and | (Cbb — C ) aa  cc  cc  cc  now included in the set offittingparameters. The spin-spin coupling constant, c*(F-F), was retained as afixedparameter, as described above. Although the F spin-rotation 1 9  constants resulting from this new fit were poorly determined, they were significantly different from the assumed starting values and gave a good enough prediction of the li,o  —  lo,i transition that it could be assigned and a final fit performed. For this fit,  the spin-rotation constants C , Cbb-, and C were used. The line positions measured aa  cc  in this work are presented in Table 5.1; a complete listing of all frequencies used in the fit is given in Appendix B. The spectroscopic constants resulting from the final fit are presented in Table 5.2. 5.4  Discussion  The determined F spin-rotation constants are very striking. Although the uncertainties 1 9  are relatively large, C  aa  and Cbb are evidently negative, whereas C  cc  has a "normal"  positive value. Negative F constants are very unusual, with the only previously reported 1 9  values being those of C1F [24,93,94], IF [100], and BrF [100]. These results can, however, be accounted for in terms of the geometry and electronic structure of SF . 2  The nuclear spin-rotation contributions for SF were calculated using Eq. 2.37, and 2  subtracted from the experimental values to yield the electronic portions, C (el); these F  CHAPTER  5. SULPHUR  73  DIFLUORIDE  F = 4-5 F-3-4 F = 2-3  Figure 5.1: The 3 ,i — 4 transition of SF , showing resolved hyperfine structure. This spectrum was obtained using 5000 signal averaging cycles and 4K data points. 2  lj4  2  CHAPTER  5. SULPHUR  74  DIFLUORIDE  results are shown in Table 5.3. The nuclear contributions are straightforward, and are similar to those of molecules of similar geometry, such as SiF2 [101] and GeF2 [101]. Thus, it is in the electronic contributions that the origin of the unusual spin-rotation constants must be found. In order to discuss these unusual spin-rotation constants, it is perhaps easiest first to convert them to the F nuclear shieldings, a, using Eqs. 2.39, 2.41, and 2.43. The 1 9  calculated nuclear shieldings are presented in Table 5.3 along with the calculated and experimentally determined [22] average shielding,  <7  av  =  1/3 zZ  g  °~gg-  The latter values  are in agreement within one standard deviation uncertainty. In this table, the ab initio determined shielding components [23] determined by Schindler are also presented. These values were calculated by first converting his principal shielding components to the inertial axis system using the equilibrium geometry of Ref. 98 and assuming the SF bond to be a principal axis of the shielding tensor. The diamagnetic terms, calculated from the geometry using Eq. 2.42, were then subtracted off to yield the paramagnetic terms, the electronic portions of the spin-rotation constants were obtained from the derived paramagnetic shieldings, and these were added to the nuclear contributions obtained from the geometry to give the overall spin-rotation constants. The ab initio results are seen to be in good agreement with the experimental values. It is instructive to compare the findings for SF with its analogue OF and also with 2  2  the geometrically similar molecules SiF and GeF . Values of C (nuc), C (el), c (p), 2  2  35  gg  fl5  and o- (d) were calculated for OF using the spin-rotation coupling constants of Ref. 99, gg  2  the rotational constants of Ref. 102, and the geometry of Ref. 103. For SiF and GeF , the 2  2  data in Ref. 101 were used. As can be seen from Table 5.4, the nuclear contributions to the spin-rotation constants, and the diamagnetic shielding terms, both of which depend only on ground state parameters, are comparable for all four molecules. However, the  CHAPTER  5. SULPHUR  75  DIFLUORIDE  paramagnetic shielding terms of SF are substantially different from those of the other 2  three molecules: though the c-components are similar, those along the a- and 6-axes of SF are unusually small, and the components of the overall shieldings along these axes 2  are therefore dominated by the diamagnetic terms. In order to rationalise the anomalous values of cr (p) and <T (p) for SF and to explain aa  6(>  2  the qualitative difference between it and it's analogue, 0F , the paramagnetic shielding 2  terms have been calculated approximately using Equation 2.45. Group theory can be used in order to determine which excitations | j) —> | k) will contribute to <^(p)- The symmetry species of the product of the two involved molecular orbitals must transform as L i (ie. as a rotation about the (/-axis). From the Civ character table, it can be seen g  that the electronic excitations giving non-zero values for the <^(p) are those given in Table 5.5; these excitations are also indicated in the electronic energy level diagram given in Fig. 5.2. The magnitudes of the principal inertial axis contributions were estimated using the atomic orbital contributions to the molecular orbitals determined in a SIAN  GAUS-  94 [104] (MP2/STO-3G) calculation. For SF , the energies of the filled molecular 2  orbitals were determined from photoelectron spectroscopy [105], and the energies of the empty orbitals were obtained from electronic spectra [106-109] and from ab initio results in the literature [110]. For OF , results from photoelectron spectroscopy were used to 2  determine the energies of the filled orbitals [111], and, since no experimentally determined electronic spectra have been reported, ab initio results from the literature [112] were used for the energies of the empty orbitals. The (r~ ) constants were obtained from 3  Ref. 47. The individual contributions from each electronic excitation and the overall paramagnetic shielding terms for both SF and OF are compared with the experimental 2  2  values in Table 5.6. As can be seen from Table 5.6, the results for OF are very good. The calculated 2  CHAPTER  5. SULPHUR  — 10  9a, 6b  W  OF,  M  7a, 5b, A  -LUMO  2  .HOMO,  3b,  I  76  SF,  r—14 12  DIFLUORIDE  — 8  2b,  I—  6  — 4  6a, 4b,  8a,  5b la,  2  la, 3b 5a, lb,  2b, 4b 7a,  2  2  o„  a,bb  Figure 5.2: Electronic energy level diagrams for SF and OF . The excitations contributing to the paramagnetic parts of the F shieldings are indicated. 2  1 9  2  CHAPTER  5.  SULPHUR  77  DIFLUORIDE  paramagnetic shielding values of all components are quite close to the experimentally determined values. For SF2, the agreement is not as good; this might be expected considering that parameters for molecules containing third row elements are usually more difficult to calculate by ab initio methods and that the approximations implicit in Eq. 2.45 are likely not as severe for the second row elements as for those in the third row. Nevertheless, the results are quite encouraging. For SF2, there are two excitations, both from the 36i orbital (the HOMO), which largely cancel out all other contributions to ^aalp)  a n  d crbb(p). The corresponding excitations exist also for OF2, but their contribu-  tions to <r (p) and crjf,(p) are much smaller because of a much larger energy difference aa  between the involved electronic energy levels; thus, full cancellation of the other contributions does not occur. The origin of the anomalous F shielding and spin-rotation 1 9  values of SF and the reason for the great difference in values between the closely related 2  molecules SF and 0 F is thus rationalised. 2  2  The mechanism leading to the anomalous SF shieldings can be compared to the one 2  leading to the unusual F shielding of CIF. For C1F, the excitation causing the anomaly is 1 9  a TT* —>• a* excitation between two antibonding orbitals which are largely localised on the CI atom [24]. The situation for SF is analogous: the ab initio calculation shows that the 2  36i orbital is an out-of-plane n* orbital located largely on the S atom and the 66 and 9ai 2  orbitals are in-plane er* orbitals, both also located largely on S. The excitations causing the anomalous <7 (p) and o&&(p) values are 3&i -> 9a and 36i -> 66 , respectively; both aa  x  2  are thus rr* —> a* excitations between molecular orbitals largely localised on the S atom. The origin of the anomalous shielding is essentially the same as for CIF. A final contrast is found between SF and the geometrically similar molecules SiF2 2  and GeF . For the latter two molecules, the F shieldings are remarkably "regular". 1 9  2  The paramagnetic contributions have large negative values, and all three components  CHAPTER  5. SULPHUR  78  DIFLUORIDE  are of a similar magnitude. An ab initio calculation for SiF shows the wave functions of 2  the molecular orbitals to be similar to those of SF . However, since SiF has two fewer 2  2  electrons than SF , the 3b, orbital is unoccupied in the ground electronic state. The 2  excitations giving rise to the anomalous paramagnetic shieldings in SF are therefore not 2  possible for SiF . Indeed, for ground state SiF , the 3b, molecular orbital is the LUMO 2  2  rather than the HOMO and the lowest energy excitations contributing to its shielding are to the 3&i level rather than from it. No significant positive contributions to the paramagnetic shielding were found for SiF . It is thus reasonable that no anomalies are 2  found for it or for its fourth row analogue GeF . 2  CHAPTER  5. SULPHUR  79  DIFLUORIDE  Table 5.1: Observed transition frequencies, v, and differences between observed and calculated frequencies", A, of sulphur difluoride  I'  F'  I"  F"  v/MUz  A/kHz  -li.i 2,0 - 3 3, 1,3 1,0 - l o . i  1 1 1 1 1 1 0 0 0 1  5 6 7 4 3 2 2 2 4 2  1 1 1 1 1 1 0 0 0 1  4 5 6 5 4 3 1 3 3 2  5 500.1578(50) 5 500.2176(50) 5 500.2917(50) 5 934.7779(10) 5 934.8352(10) 5 934.8706(10) 14175.9558(10) 15 979.0300(20) 18 727.7059(10) 20 084.3027(10)  -5.9 -6.6 -6.9 -0.7 -0.2 -0.6 0.0 0.1 -0.9 -1.0  0 1 2  1 1 0  ;  20 084.3376(10)  1.3  2Q,2  1 1 0  22 672.1355(10)  0.2  Jk ,K -J'L,K a  c  c  1,6  2,1  —  52,3  - 4  M  0,2  L I 3  —  1,1  a  —  2  2  2  j  These differences are from the overall fit to the constants in Table 5.2.  CHAPTER  5. SULPHUR  80  DIFLUORIDE  Table 5.2: Spectroscopic constants of sulphur difluoride' '  1 1  /MHz /MHz /MHz  26930.46302(104) 9212.13272(37) 6845.86488(27)  Aj /kHz A /kHz A - /kHz /kHz 5A /kHz  12.1228(69) -68.948(63) 361.936(41) 4.1955(21) 19.944(83)  /Hz ®JK /Hz $ - /Hz /Hz &r / H Z  -0.0635(95) -3.59(21) 12.60(19) -0.0287(34) -14.64(75)  C (F) /kHz C (F) /kHz C (F) /kHz  -11.66(270) -5.88(296) 13.49(150)  A B C  JK  A  A  00  66  CC  a(F-F) /kHz  c  -7.73  ° Determined from a combined fit of the data of Table 5.1 and that of Ref. 95. Uncertainties are one standard deviation in units of the last significant figures. The spin-spin coupling constant, a(F-F), was calculated using the geometry of Ref. 98.  6 c  CHAPTER  5. SULPHUR  DIFLUORIDE  81  Table 5.3: Comparison of the fluorine spin-rotation coupling constants (kHz) and shielding components (ppm) of sulpur difluoride with those derived from ab initio results  Experiment  Cbb Cc c  ab initio  0.  -11.66(270) -5.88(296) 13.49(150)  C (nuc) C(,(,(nuc) C (nuc)  -9.42 -7.06 -7.64  -9.42 -7.06 -7.64  CUel) C&(el)  -2.24(270) 1.18(296) 21.13(150)  3.56 -0.64 22.69  00  cc  6  Ccc(el)  6  6  6  6  6  6  <7aa(p) Vbb(p) ^cc(p)  15(19) -22(56) -539(38)  <Taa(d) <7&&(d)  541(5) 606(5) 655(5)  541 606 655  556(19) 584(56) 116(38) 419(71)/355.7  518 618 76 404  ^cc(d) Vaa  0~bb 0~cc  -23 12 -578 c  c c  c  c  c  rf  a 6 c d  -5.86 -7.70 15.05  Derived from the ab initio shieldings of Ref. 23; see discussion section for details. Calculated from the molecular geometry using Eq. 2.37. Calculated from the molecular geometry using Eq. 2.42; uncertainties are estimated. NMR average shielding from Ref. 22.  CHAPTER  5. SULPHUR  82  DIFLUORIDE  Table 5.4: Comparison of the fluorine spin-rotation coupling constants (kHz) and nuclear shielding components (ppm) of sulphur difluoride and other difluorides  SF  C Cbb aa  Cc C  C (nuc) aa  C66(nuc) C (nuc) cc  Caa(el) C (el) w  C (e\) cc  OF  2  -11.66(270) -5.88(296) 13.49(150) -9.42 -7.06 -7.64  SiF  2  59.60(7) 25.05(11) 51.39(8) -10.45 -6.66 -7.24  -2.24(270) 1.18(296) 21.13(150)  70.05(7) 31.71(11) 58.63(8)  <7 c(p)  15(19) -22(56) -539(38)  -208.1(2) -508.2(18) -1117.8(15)  cr b(d) 0" (d)  541(5)° 606(5)° 655(5)°  509(5) 577(5)° 602(5)°  cr {p) aa  C  b  cc  o~bb &CC  <7av  6  -8.87 -6.33 -6.88  -9.98 -8.79 -9.17  74.00(36) 18.88(22) 17.00(19)  45.52(20) 20.34(15) 16.32(6) -517(2) -453(3) -550(2)  531(5) 599(5) 635(5)°  593.(5) 669.(5)° 768.(5)°  109(6) 239(6) 200(7) 183(4)  76(6) 216(6) 218(6) 170(4)  a  c  ° Calculated from the molecular geometry; uncertainty is estimated. b  Ref. 22.  c  Ref. 113.  2  35.54(20) 11.55(15) 7.15(6)  a  301(5) 69(6) -516(6) -49(3)/-59.3  GeF  65.13(36) 11.85(22) 10.12(19)  -422(2) -360(4) -435(5)  a  556(20) 584(57) 116(39) 419(24)/355.7  2  a  CHAPTERS.  SULPHUR  DIFLUORIDE  83  -  Table 5.5: Excitations giving non-zero values for paramagnetic shielding components, crj (p), of sulphur difluoride 3  gg  Excitations  aa bb  a, <-> b, a «-> 6 a, f-> a b, 6  cc  a!  2  2  6  2  2  2  a <->• 2  CHAPTER  5. SULPHUR  84  DIFLUORIDE  Table 5.6: Comparison of experimental and calculated F paramagnetic fluorine shielding components of sulphur difluoride and oxygen difluoride 1 9  SF  Eq. 2.45 la 66 36x -> 9ai 26j -> 9a! 0"aa(p) /PPm  -369.9 494.5 -243.0 -118.3  36i -> 66 26j -> 66 la —> 9a! ^fcfc (p) /ppm  584.8 -227.0 -472.0 -114.2  2  2  2  2  2  8aj H> 66 7a! — > 66 56 ->• 9a i 46 -> 9a! 2  2  2  2  °"cc(p) /ppm  OF  2  85.6 -475.2 -174.6 -440.4 -1004.6  Experiment  Eq. 2.45  Experiment  <7aa{?) /ppm  -263.1 140.9 -171.4 -293.6  -208.1(2)  56 16i ->• 56 la —> 7ai cw.(p) /PPm  191.5 -231.2 -422.2 -462.0  -508.2(18)  14.4 -452.3 -369.7 -282.1 -1088.6  -1117.8(15)  la —y 5b -> 7aj I6i -» 7a 2  2  2bi  x  15(19)  2bi  2  2  2  -22(56)  6ai — > • 56 5ai — > 56 46 ->• 7aj 36 — > 7ai 2  2  2 2  -539(38)  2  o"cc(p) /ppm  Chapter 6 Hyperfine Interactions in the Halogenated Oxo- and Sulphido-Boranes: F B O , C1BO, and F B S  6.1  Introduction  The XBE species FBO, C1B0, and FBS are unstable molecules which undergo rapid polymerisation to form cyclic trimers [27,114,115]. They are therefore difficult to study by NMR; however, these unstable species can be formed in situ using an electric discharge and stabilised in the virtually collision free environment of the supersonic jet expansion used for FTMW studies. The inherently high resolution of the FTMW technique can then be used to determine the spin-rotation coupling constants and the nuclear shielding parameters, parameters which are usually obtained from NMR spectra. Each of these species has been studied before by microwave spectroscopy [25-27] and partial or complete r structures have been determined; since fluorine has no naturally s  occurring second isotope, its position was determined in the FBO and FBS molecules usingfirstand second moment conditions, respectively. The previous investigations have been able to determine only the quadrupole coupling constant of the chlorine nucleus of the C1 B 0 isotopomer and the boron nucleus of F BS. No spin-rotation or spin-spin 35  11  16  U  coupling constants were known for any of these species. This chapter describes the observation and measurement of pure rotational transitions  85  CHAPTER  6. HALOGENATED  0X0- AND  SULPHIDO-BORANES  86  of two isotopomers of FBO, four isotopomers of C1B0, and one isotopomer of FBS. Resolved hyperfine structure in these spectra was analysed to yield precise / C l and / 3 5  3 7  n  1 0  B  quadrupole coupling constants, / C l , / B , and F spin-rotation coupling constants, 35  37  U  1 0  1 9  and the X-B spin-spin coupling constants for all three molecules. The spin-rotation constants have been used to calculate the shielding parameters of the CI, F, and B nuclei; these results have been rationalised in terms of CornwelPs spin-rotation theory outlined in Section 2.1.3. 6.2  Experimental Methods  The XBE molecules FBO, C1B0, and FBS were prepared by passing an electric discharge through samples containing a mixture of (0.5%BF and 0.5%O) or (0.25%BC1 and 3  2  3  0.25%O) or (0.5%BF and 0.5%OCS), respectively, in roughly 6 bar Ne. Frequencies 2  3  of transitions lying in the 4-26 GHz frequency range were measured. All line positions have been determined byfittingto the time domain signals [65]; their uncertainties were estimated from the range of values resulting from several different measurements of each transition. Frequencies of strong lines are deemed to be accurate to better than ±lkHz uncertainty; those of weaker or very closely spaced lines are less precise. 6.3  Spectral Analysis  Pure rotational spectra were measured for F B O , F BO, C1 B0, C l B O , C1 BO, u  37  10  35  U  37  n  35  10  C1 BO and F BS. The observed transitions of each species were fit to rotational and 10  U  centrifugal distortion constants, and appropriate quadrupole, spin-rotation, and spin-spin coupling constants using Pickett's exactfittingprogram SPFIT [41]. Details of each of the fits are given below. FBO: For this molecule, only one transition was available in the operating frequency  CHAPTER  6. HALOGENATED  0X0- AND  SULPHIDO-BORANES  87  range of the spectrometer. Fig. 6.1 shows a composite spectrum of this transition for the F B O isotopomer; there are six resolved hyperfine components. For the corresponding u  F BO transition, only five components were resolved. Since these data were to be fit to 10  four hyperfine coupling constants each, an option of SPFIT which allows the simultaneous fitting of different "states" of a molecule was used. Here, each of the two isotopomers was defined as a molecular "state", and the ratio of the direct spin-spin coupling constants of these "states" was held fixed to the ratio of the ^-factors of the boron nuclei. Thus, the set of fitting parameters was reduced by one. The centrifugal distortion constants were heldfixedat the values given in Ref. 25, and all other constants were independently determined. The results are shown in Tables 6.1 and 6.2; there are no correlations greater than 0.35, and all constants are well determined. C1BO: Fitting of the C1BO data was straightforward. For each isotopomer studied, there were sufficient hyperfine components measured to determine all coupling constants completely. The centrifugal distortion parameters of all isotopomers were heldfixedat the values given in Ref. 26. The results are shown in Tables 6.3 and 6.4. FBS: There are two transitions of FBS which lie within the operating frequency range of the spectrometer. However, since the J=l-0 transition of the F B S isotopomer (~80% n  natural abundance) was very weak, neither the J=2-l transition for this isotopomer nor any transitions due to the F BS species were sought. Thus, no combinedfitsof the type 10  done for the FBO data were possible, and it was necessary to fit a total of six transition frequencies to five parameters. Attempts to lower the number of fitting parameters byfixingthe value of the spin-spin constant to that calculated using Eq. 2.48 and the molecular geometry of Ref. 27 did not result in any improvement in the quality of the fit; moreover, the constants resulting from bothfitswere virtually identical, with differences well within the determined uncertainties. In thefinalfit,only the centrifugal distortion  CHAPTER  6. HALOGENATED  0X0- AND  SULPHIDO-BORANES  88  1.5,1 -1.5,1 1.5,2 -1.5,2  0.5,1 -1.5,2  18695.75 M H z  18693.75 M H z  Figure 6.1: Composite spectrum of the J = 1 - 0 transition of F B 0 . These spectra were obtained using 100 averaging cycles and 4K data points. u  CHAPTER  6. HALOGENATED  0X0- AND  89  SULPHIDO-BORANES  constant was heldfixed;its value was obtained from Ref. 27. As in the case of FBO, there are no large correlations and all constants are well determined. The results are shown in Tables 6.5 and 6.6. 6.4  Discussion  Although FBO, C1B0, and FBS had all been previously studied by microwave spectroscopy, very little hyperfine structure had been resolved and imprecise quadrupole coupling constants had been determined only for the CI nucleus of C1 B0 and the 35  U  35  U  B nucleus of FBS. In the present study, all quadrupole, spin-rotation, and spin-spin  coupling constants have been determined. 6.4.1  Nuclear quadrupole coupling constants  All species studied here have isoelectronic valence shell configurations. It was pointed out in Section 2.1.3 that the quadrupole coupling constants of main group elements can be discussed in terms of the valence shell p-electron density. Thus, one would expect the boron atoms to have similar quadrupole coupling constants in all three species. This is what is found. The quadrupole coupling constants determined in this study are compared to previously determined values and to the quadrupole coupling constants of the related molecules HBO, HBS, and CH BS in Table 6.7; those determined for the CI nucleus of 3  3 5  C l B O and the B nucleus of F BS are in fair agreement with the previous findings [26, n  U  27] and the improvement in the precision of these values is easily seen. In Table 6.7, the boron quadrupole coupling constants of the non-halogenated species are shown to be similar to one another and somewhat different from those of XBE. This result can be rationalised in terms of Eq. 2.31 where is is seen that the coupling constant along the quadrupolar z-axis (in the case of a linear molecule, this corresponds to the principal  CHAPTER  6. HALOGENATED  0X0- AND  SULPHIDO-BORANES  90  inertial a-axis) depends upon the occupation of the valence shell p orbitals: n + n.y x  2  )  (6.1)  Eq. 6.1 differs slightly from Eq. 2.31 in that a proportionality rather than an equality is given. This is because for the central boron nucleus, one must consider hybridisation [29] of the 2s and 2p orbitals; since this hybridisation should not change with a change in the X moiety of the XBE molecule, the hybridisation effects have been implicitly included in the proportionality. Since the boron nucleus has one electron in each of the two 2s2phybridised orbitals directed along the molecular axis which are available for <r-bonding to the CI and 0 atoms, and one electron in a 7r-orbital available for 7r-bonding to the O atom, the smaller absolute value of the boron quadrupole coupling constants found for the halogenated species can be easily rationalised as having two possible contributions. First, and more importantly, the more electronegative halogen atom will withdraw electron density from the pj-orbital of the boron atom along the X-B cr-bond more effectively than the H or CH group will, thus decreasing n and lowering | Xz I- Secondly, each 3  z  of the halogens has electrons in the p and p orbitals which are available for possible x  y  back-donation to the boron nucleus, thus increasing the electron density in the 7r-orbitals, and resulting in a lowering of the n and n contributions to Xz'i such an effect is not x  y  possible in the case of the H- or CliVcontaining molecules because these groups have no available zr-electrons to donate, and therefore cannot participate in any Tr-bonding. It is also expected that the value of the quadrupole coupling constant determined for a particular nucleus in any given species should be independent of isotopomer. The quadrupole coupling constants determined for the boron nuclei of C1BO are indeed in very good agreement; there are no differences within the uncertainty limits of these values. On the other hand, the CI coupling constants are determined much more precisely and do show isotopic variations: the differences in their values are an order of magnitude larger  CHAPTER  6. HALOGENATED  0X0-  AND  SULPHIDO-BORANES  91  than the uncertainties arising from the fits. Also, the isotopic quadrupole ratios are expected to be independent of the pair of isotopomers chosen; these ratios are presented in Table 6.8. Once again, it is seen that the boron constants are in agreement, while the chlorine isotopic ratios significantly differ depending upon the pair of isotopomers chosen. The isotopic differences in the chlorine quadrupole coupling constants of C1B0 are likely due to zero-point vibrational effects. It was shown in Section 2.2 that the rotational constants determined from measured transitions are merely effective constants for the vibrational state being studied. Similarly, the effective quadrupole coupling constants will differ slightly depending upon the isotopomer chosen because of differing amounts of vibrational contributions. During this work, none of the excited vibrational states were studied; thus, the equilibrium quadrupole coupling constants cannot be determined, and one can only surmise as to the origin of the relatively large differences in the chlorine quadrupole coupling constants. Ground vibrational state transitions of C1B0 have been measured; therefore, the determined quadrupole coupling constants are the expectation values of Xaa in the ground vibrational state: Xaa = X«<1 - | sin Oza)  (6.2)  2  where 0  za  is the angle between the z-quadrupolar axis and the a-principal inertial axis  and Xzz is the coupling constant along the B-Cl bond. For a linear molecule in the equilibrium configuration, Xaa = Xzz', however, a non-zero 0  za  arises through a bending  vibration. In the limit of a small 6, Eq. 6.2 can be written approximately as: X.. = X « ( l - | ( 0 ) The variation of x  aa  (@za)'i  (6-3)  with isotopomer in the ground vibrational state is thus a measure of  while the average value of this angle, 0 , is zero, the average of the squared angle za  CHAPTER  6. HALOGENATED  0X0- AND  92  SULPHIDO-BORANES  is non-zero. Intuitively, one might expect (9 ) to be slightly larger for a B isotopomer 10  2  za  than for a corresponding B isotopomer because of the smaller mass involved. Therefore, X1  it is expected that \aa should be smaller in those isotopomers containing a B nucleus, 10  as is found. Moreover, it seems likely that (9 ) will not change significantly with a 2  a  change in the chlorine isotopomer; thus, the / C l quadrupole coupling constant ratio 35  37  between isotopomers containing a common boron nucleus are expected to be close to the to the ratio of the equilibrium constants. Table 6.8 shows that this is the case: the ratios of the quadrupole coupling constants determined for isotopomers with a common boron nucleus are in good agreement with one another and with the literature value, while the two ratios between isotopomers containing different boron nuclei are very different from both. The average / C l quadrupole coupling constant ratio is also seen in Table 6.8 to 35  37  be in good agreement with the literature value. The determined chlorine quadrupole coupling constants have also been used to calculate approximately the ionic character of the Cl-B bond of C1BO. Because this is a linear molecule and the quadrupole coupling tensor therefore has no asymmetry, the 7r-character of the Cl-B bond cannot be directly calculated in the way used for the Cl-N bond of C1N0 (see Chapter 4 for details on this calculation). In the present case, an assumption must be made regarding the ionic character of the a-bond, i \ if this is taken to be the absolute a  value of one half the electronegativity difference of the two bonded nuclei [29], 2.0 for boron and 3.0 for chlorine [29], then i becomes 50.0%, and the Tr-character of the bond, a  calculated from Eq. 4.6 (reprinted here for simplicity) Xz = ~ ( l - ic ~ Y)  Q<lnW  e  becomes 11.8%. Thus, the total ionic character of the bond, i = i — TT , is equal to c  a  C  38.2%. This compares favourably with that calculated for C1BS [116]: i = 50.0%; TT = a  22.5%; i = 27.5%. c  C  CHAPTER  6.4.2  6. HALOGENATED  0X0- AND  SULPHIDO-BORANES  93  Nuclear spin-spin and spin-rotation coupling constants  As was shown in Section 2.1.3, the tensor spin-spin coupling constant has a direct, geometry dependent dipole-dipole contribution, and an indirect, electron coupled contribution which, in most cases, need not be considered. Thus, the spin-spin coupling constants can be calculated approximately from a knowledge of the geometry of the molecule. Furthermore, the direct contributions depend on the ^-factors of the two interacting nuclei and the ratios of the spin-spin constants to nuclear ^-factors for different isotopomers of a given molecule should therefore be equal. This relation has been used to reduce the set of fitting parameters in the fit of the FBO data by fixing the ratio between the spin-spin constants of the B and B isotopomers; this was described in Section 6.3. U  10  The spin-spin coupling constants of all XBE isotopomers studied were calculated using the X-B distances given in the literature [25-27]. These are compared with the measured values in Table 6.9; the ratios between the X-B spin-spin constants and the X and B nuclear ^-factors, a(X-B)/g^g^  are also given here. The differences between the  calculated and experimentally determined constants are within one standard deviation experimental uncertainty for C1B0 and FBS, and within two standard deviations uncertainty for FBO. No evidence of an indirect contribution is seen for any of the species studied. In this study, the spin-rotation coupling constants have also been precisely determined for all species studied. These constants were shown in Section 2.1.3 to be proportional to the rotational constants of the molecule, and to the g-factor of the nucleus in question. Thus, the quantity C jg B for the nucleus k should be constant for all isotopomers. k  k  These ratios are presented in Table 6.10; all are in agreement within the stated uncertainties. Moreover, in the case of the boron nucleus, there is agreement from molecule to molecule. This is further evidence suggesting that the electronic surroundings of the  CHAPTER  6. HALOGENATED  0X0- AND  94  SULPHIDO-BORANES  boron nucleus are very similar in each of the three molecules, thus giving rise to similar "reduced" spin-rotation coupling constants, C/gB. As was shown in Section 2.1.3, the spin-rotation constants of a nucleus are also related to the nuclear shielding. Therefore, high resolution Fourier transform microwave spectroscopy can be used to determine the chemical shifts of unstable molecules which are otherwise difficult to study using NMR techniques. The nuclear shieldings of the X(=F/C1) and B nuclei of FBO, C1B0, and FBS have been determined byfirstseparating the spin-rotation coupling constants into their nuclear and electronic components and then using these to obtain the paramagnetic, diamagnetic, and total nuclear shielding parameters. The equations for calculating these parameters are given for a prolate asymmetric top in Section 2.1.3. They are written explicitly for a linear molecule as: C  A  (  N  U  C  )  =  -  W  ^ nC  ^  ^  (  C (el) = C - C ( n u c ) A  A  _  *  -  (d)  °i =  .  4  )  (6.5)  A  <">  • „A/,x  6  nA  r  A  efiC (nuc) A  ^ e e atom " S m C ^ B  * (p) + <Ad) A  ^  (6.8)  The results are presented in Table 6.11. All the paramagnetic and diamagnetic shielding contributions are completely usual; the diamagnetic portions are large and positive, and the paramagnetic portions are large and negative. Since the diamagnetic contribution depends only upon the molecular geometry, it is only from the paramagnetic term that one could expect to find strange behaviour. Eq. 2.45 shows how the paramagnetic contributions can be calculated approximately from a knowledge of the molecular orbital energies and their atomic orbital contributions. Thus, one can look at this mechanism  CHAPTER  6. HALOGENATED  0X0- AND  SULPHIDO-BORANES  95  to see whether the determined constants make sense. The theoretical method for calculating the paramagnetic shielding contributions can be used to show that the only positive contributions to the paramagnetic term of the X or B nucleus come from transitions between an X-B antibonding TT orbital and an X-B antibonding a orbital largely localised on the other (B or X) nucleus and that these contributions will only be significant if the electronic excitation energy is small [24,117]. In the absence of any data regarding the energies of the molecular orbitals, at best only relative magnitudes of the individual contributions can be calculated. The atomic orbital contributions to the molecular orbitals have been calculated for FBO, C1B0, and FBS using the program G A U S S I A N 94 [104](MP2/STO-3G). While this program can determine the relative positions of the molecular orbitals fairly reliably, the determined energies of the unoccupied molecular orbitals are usually incorrect, and were not used in any calculations. Factors proportional to the individual paramagnetic shielding contributions (cr(p) x AE) were calculated for FBO, C1B0, and FBS; these are given as "paramagnetic shielding proportionalities" in Table 6.12. The .electronic excitations which have a non-zero contribution to the paramagnetic shielding of the X(=C1/F) and B nuclei of FBO, C1B0, and FBS are indicated on a schematic diagram of the electron energy level diagrams given in Fig. 6.2. For each of these molecules, it is seen that the only significant positive contribution to the halogen paramagnetic shielding comes from a transition between the (2/3/3)TT and (9/ll/ll)<7 orbitals of (FB0/C1B0/FBS). Since each of these contributions is of the same order of magnitude (FBO) or smaller (C1B0/FBS) than a negative contribution with a smaller transition energy, (2/3/3)7r to (8/10/10)c, the halogen paramagnetic shielding term is expected to be negative. In the case of the boron paramagnetic shieldings, the excitation with the smallest energy difference, (2/3/3)rr to (8/10/10)cr, has a positive contribution; however, the magnitude  CHAPTER  6. HALOGENATED  0X0- AND  SULPHIDO-BORANES  96  of the proportionality factor here is insignificant with respect to many other negative contributions, and the overall sign of the paramagnetic shielding term is expected to be also negative. Thus, the theory is in agreement with the experimental findings.  CHAPTER  6. HALOGENATED  0X0- AND  SULPHIDO-BORANES  C1BO  FBO  97  FBS 11a  11a  10a  10a  4it  4TC  9a  3ic  3K  8a  2ic  9a  3iu  9a  2n  2it  8a  8a  7o  7a  7a  lit  6a  6a  6o  5a  lie  5a  lie  5a  4a  4a  4a  3a  3a  3a  2a  2a  2a  la  la  la  Figure 6.2: Schematic diagram of the electronic excitations of XBE giving rise to non-zero contributions to the X(=C1/F) and B paramagnetic nuclear shielding terms  CHAPTER  6. HALOGENATED  0X0- AND  SULPHIDO-BORANES  98  Table 6.1: Hyperfine component frequencies, w, and differences between observed and calculated frequencies, A, for the J = 1 — 0 transition of FBO  F"  F"  F'  F'  v /MHz  A /kHz  F BO  1.5 1.5 2.5 2.5 0.5 0.5  2 1 2 3 0 1  1.5 1.5 1.5 1.5 1.5 1.5  2 1 1 2 1 2  18694.2151(10) 18 694.2434(10) 18 694.8789(10) 18694.8991(10) 18 695.3967(10) 18 695.4076(10)  1.0 -1.0 -0.3 0.3 -1.2 1.2  F BO  3 3 4 4 2 2  3.5 2.5 3.5 4.5 1.5 2.5  3 3 3 3 3 3  18 697.6973(10) 18 697.7150(10) 18 698.7967(10) 18698.8119(10)  -0.8 0.8 -0.2 0.2  18 699.1821(10)  0.0  u  10  3.5 2.5 2.5 3.5 2.5 \ 3.5 |  CHAPTER  6. HALOGENATED  0X0- AND  99  SULPHIDO-BORANES  Table 6.2: Spectroscopic constants and correlation matrix for FBO  F BO  F  u  B/MHz D /kHz  0  (B) / M H z C {B) / k H z C (F) / k H z Xaa  bb  bb  a(B-F) / k H z  6  9347.38431(22) 3.5273 -2.6288(24) 3.02(27) 5.71(100) -54.82(185)  1 0  BO  9349.27115(23) 3.5335 -5.4811(40) 0.95(17) 5.96(124) -18.36(62)  Correlation M a t r i x :  F BO u  B Xaa(B)  C (B) C (F) bb  bb  1.000 0.068 0.346 0.087  1.000 -0.285 0.118  0.000 0.001  -0.001 -0.003  -0.004  0.009  -0.008  1.000 -0.139  1.000  -0.000 0.001  -0.003 0.016  0.001 -0.005  0.003 -0.014  -0.006 0.085  0.079 0.010  1.000 0.062  0.011  0.190  -0.060  -0.165  0.023  0.048  -0.015  1.000 0.165  1.000  F BO n  B Xaa(B)  C (B) C (F) bb  bb  F  n/io  a(B-F)  a  fc  B  0.004  O  1.000  H e l d fixed at the value given i n Ref. 25. Spin-spin constant ratio was held fixed i n the fit; 5 ( B - F ) / 5 ( n  1 0  B-F) =  g( B)/g( B). n  10  CHAPTER  6. HALOGENATED  0X0- AND  SULPHIDO-BORANES  100  Table 6.3: Measured hyperfine component frequencies, u, and differences between observed and calculated frequencies, A, of C1BO 3 5  F"  1-0  2-1  Cl BO n  3 7  Cl BO n  F"  F'  F'  v /MHz  A /kHz  v /MHz  A /kHz  1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5  1 2 1 0 2 3 2 1 3 2 3 2 1 3 3 2 1 0  10394.5946(10)  -0.1  10175.3368(10)  0.1  10394.9929(10)  0.1  10175.7308(10)  0.3  10395.0004(10)  0.4  10175.7408(10)  0.1  10395.4181(10)  0.1  10176.1583(10)  -0.2  10406.9287(10)  0.3  10185.1112(10)  0.1  10407.1369(10)  0.1  10185.3135(10)  -0.1  10 407.3398(10)  0.4  10185.5196(10)  0.1  10407.5767(10)  0.0  10185.7604(10)  0.2  0.5 0.5 0.5  0 1 1 1 3 3 2 2 2 3 3 2 2 2 4 1 1 1 1 1 1  1.5 1.5 1.5  2 1 0  10416.8895(10)  0.4  10193.0209(10)  0.6  0.5 0.5 0.5  2 2 2  1.5 1.5 1.5  2 1 3  10416.9033(10)  -0.3  10 193.0388(10)  0.0  1.5 1.5 1.5 1.5 1.5 2.5 3.5 3.5 3.5 2.5  2 3 0 1 2  -1.5  20 797.4414(20)  0.6  20810.1158(20)  0.1  1.5 1.5 1.5 1.5 1.5  1 2 3 2 3  1.5 1.5 1.5 1.5 1.5  2 2 1 1 1 2 3 2 4 3 2 2 2 3 3  20 797.4268(20)  3 4 3 5 4  0.5 0.5 0.5 0.5 0.5 1.5 2.5 2.5 2.5 1.5  1.5 1.5 1.5 • 1.5 1.5 1.5 1.5 1.5 1.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5  20810.5160(20)  -0.7  20810.6340(20) 20810.7524(20)  -1.2 0.4  20818.9122(20)  -0.5  20374.2500(20)  -1.4  20819.3323(20)  0.2  20374.6693(20)  -1.2  CHAPTER  6. HALOGENATED  0X0- AND  SULPHIDO-BORANES  101  Table 6.3: Measured hyperfine component frequencies, v, and differences between observed and calculated frequencies, A, of C1BO cont'd 3 5  J"-J' 1-0  2-1  F£,  F"  F'  F'  1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5  1.5 1.5 4.5 4.5 2.5 2.5 3.5 3.5 3.5  1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5  2.5 1.5 3.5 4.5 3.5 1.5 3.5 2.5 4.5  2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 0.5 0.5 0.5  3.5 3.5 3.5 4.5 4.5 2.5 2.5 2.5 5.5 1.5 1.5 0.5 2.5 2.5 2.5  1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5  3.5 2.5 4.5 3.5 4.5 3.5 2.5 1.5 4.5 2.5 1.5 1.5 3.5 2.5 1.5  0.5 0.5 0.5  3.5 3.5 3.5  1.5 1.5 1.5  3.5 2.5 4.5  1.5 1.5 1.5 1.5 1.5  3.5 3.5 2.5 4.5 1.5  0.5 0.5 0.5 0.5 0.5  3.5 2.5 2.5 3.5 2.5  cx  v  C1 BO  37 ,io  1 0  /MHz  C  A /kHz  v  /MHz  B O  A /kHz  10438 9363(10)  -0.2  10 222 2503(10)  0.0  10439 2410(10)  0.1  10 222 5556(10)  0.1  10439 5846(10)  0.4  10 222 8970(10)  0.1  10439 9133(10)  -0.2  10 223 2336(10)  -0.2  10451 2072(10)  0.1  10 231 9565(10)  -0.2  10451 2712(10)  0.1  10 232 0375(10)  0.3  10451 5526(10)  -0.2  10 232 3138(10)  -0.1  10451 8444(10)  0.0  10 232 6040(10)  -0.1  10451 9530(10)  -0.1  10 232 7188(10)  -0.2  10452 2192(10)  0.1  10 232 9788(10)  0.3  10461 2666(10)  -0.3  10 239 9830(10)  0.0  10461 2835(10)  0.3  10 240 0032(10)  0.0  20886.1246(20) 20886.1429(20)  0.3 2.3  20886.1512(20)  -1.5  20886.1815(20)  -1.3  CHAPTER  6. HALOGENATED  0X0- AND  SULPHIDO-BORANES  102  Table 6.4: Spectroscopic constants of C1BO  3 5  B/MHz D /kHz Xaa(Cl) / M H Z Xaa(B) / M H Z a  C {C\) / k H z C (B) / k H z bb  bb  a(B-Cl) / k H z  Cl BO n  3 7  5202.39501(12) 1.2960 -48.3742(19) -2.5994(33) 0.55(20) 1.53(27) -2.58(64)  Cl BO  3 5  n  5091.74175(16) 1.2412 -38.1230(20) -2.5993(36) 0.52(21) 1.42(32) -1.97(68)  C1  C1 B0 U  B Xaa(Cl) Xaa(B)  C (C\) C (B) bb  bb  a(B-Cl)  a  1.000 0.014 -0.080 0.127 0.095 0.091  1.000 -0.126 -0.158 0.081 0.287  1.000 0.078 -0.036 0.297  H e l d fixed at the value given i n Ref. 26.  1.000 0.128 -0.197  BO  5224.57791(14) 1.304 -48.3569(18) -5.4164(49) 0.66(20) 0.52(14) -0.74(35)  Correlation M a t r i x :  3 5  1 0  1.000 -0.147  1.000  3 7  C1  1 0  BO  5115.21418(15) 1.252 -38.1105(19) -5.4173(49) 0.54(20) 0.60(16) -0.52(36)  CHAPTER  6. HALOGENATED  0X0- AND SULPHIDO-BORANES  103  Table 6.5: Hyperfine component frequencies, u, and differences between observed and calculated frequencies, A, for the J = 1 — 0 transition of FBS  F BS n  Fg  F"  F  B  F'  v /MHz  A /kHz  1.5 1.5 2.5 2.5 0.5 0.5  2 1 2 3 0 1  1.5 1.5 1.5 1.5 1.5 1.5  2 1 1 2 1 2  9907.1714(10) 9 907.1990(10) 9 907.8288(10) 9907.8475(10) 9 908.3493(10) 9908.3576(10)  0.2 -0.2 -0.1 0.1 -0.3 0.3  CHAPTER  6. HALOGENATED  0X0- AND  SULPHIDO-BORANES  T a b l e 6.6: S p e c t r o s c o p i c c o n s t a n t s a n d c o r r e l a t i o n m a t r i x for F B S  F BS n  B/MHz D /kHz" aa(B) / M H Z C (B) / k H z C (F) / k H z X  bb  bb  a(B-F) / k H z  4953.85499(22) 0.92 -2.6131(24) 1.73(27) 5.53(100) -50.72(209)  Correlation M a t r i x :  B Xaa(B) C (B) C (F) bb  bb  a(B-F)  a  1.000 0.068 0.346 0.087 0.012  1.000 -0.287 0.108 0.215  H e l d fixed at the value given in Ref. 27.  1.000 0.168 -0.068  1.000 -0.185  CHAPTER  6. HALOGENATED  0X0- AND  105  SULPHIDO-BORANES  Table 6.7: Comparison of measured boron and chlorine quadrupole coupling constants (MHz) of FBO, C1BO, and FBS with related species  Xaa( B)  X.a( B)  -2.6288(24) -2.5994(33) -2.5993(36)  -5.4811(40)  U  10  Xaa( Cl) 35  X a( Cl) 37  a  This work: FBO Cl BO Cl BO  35  n  3 7  n  35  C 1  io  -38.1230(20) -5.4164(49) -5.4173(49)  B O  C1 BO FBS  37  -48.3742(19)  10  -48.3569(18) -38.1105(19)  -2.6131(24)  Previous work: FBS CH BS HBO HBS Cl BO a  6  3  c  d  n  C\ BS n  f  Cl BS 10  a b c d e 5  Ref. 27 Ref. 118 Ref. 119 Ref. 120 Ref. 26 Ref. 116  e  e  -2.54(4) -3.714(20) -3.80(10) -3.71(3)  -7.743(50) -8.20(44) — 7.81(3) -47.7(15) -42.45(1) -42.56(2)  -33.53(1) -33.58(3)  CHAPTER  6. HALOGENATED  0X0- AND  SULPHIDO-BORANES  106  Table 6.8: Isotopic Ratios of the quadrupole coupling constants of FBO, and C1BO  x(£|) 2.0850(27) 2.0850(27) 2.084(2)  F BO:F BO exp. average literature" 10  n  C1 BO: C1 C1 BO: C1 Cl BO: Cl Cl BO: Cl exp. average literature"  BO BO BO BO  35  U  35  10  35  U  37  10  37  n  35  10  37  n  37  10  2.0837(32) 2.0841(32) 2.0838(34) 2.0841(34) 2.0839(33) 2.084(2)  Cl BO: Cl BO C1 BO: C1 BO C1 BO: C1 BO C1 BO: C1 BO exp. average literature" 35  u  37  n  35  U  37  10  35  10  37  U  35  10  37  10  1.268898(83) 1.269314(81) 1.268444(82) 1.268860(79) 1.268879(81) 1.2688773(15)  " Literature values for the ratios of the nuclear quadrupolar moments are from Ref. 84 for the chlorine nuclei and Ref. 29 for the boron nuclei.  CHAPTER  6. HALOGENATED  0X0- AND  SULPHIDO-BORANES  107  Table 6.9: Reduced spin-spin coupling constants, (B)g, d comparison of the measured and calculated spin-spin constants (kHz) of FBS, FBO, and C1BO a n  a(X- B)  a(X- B)  10  u  a(X-B)  35 37  a  meas.  meas.  calc.  FBO  -0.582(20) -54.82(185)  C1B0 C1B0  -0.263(65) -0.241(83)  -2.58(64) -1.97(68)  -2.38 -1.98  FBS  -0.538(22)  -50.72(209)  -51.42  a  a  -51.50  calc.  -0.582(20) -18.36(62)  -17.25  -0.74(35) -0.52(36)  -0.80 -0.66  a  -0.225(106) -0.190(132)  this ratio was fixed in the spectral fit; see text for details.  CHAPTER  6. HALOGENATED  0X0- AND  SULPHIDO-BORANES  Table 6.10: Reduced spin- rotation constants,  cm  cm g^B  F BO F BO  0.116(20) 0.121(25)  0.180(16) 0.169(30)  C1 B0 C1 B0  C1 BO  0.193(70) 0.224(90) 0.231(70) 0.231(86)  0.164(29) 0.156(35) 0.166(45) 0.195(52)  F BS  0.212(38)  0.195(30)  n  10  35 37  U  U  35 37  of FBO, C1BO, and FBS  C 1  io  B O  10  n  108  CHAPTER  6. HALOGENATED  0X0- AND  SULPHIDO-BORANES  109  Table 6.11: Spin-rotation constants (kHz) and nuclear shielding (ppm) of the F, CI, and B nuclei of FBO, C1BO, and FBS  B  X=(C1/F) C(nuc)  C(el)  C  C(nuc)  C(el)  C  F BO F BO  -5.36 -5.36  11.07(100) 11.32(124)  5.71(100) 5.96(124)  -3.51 -1.17  6.53(27) 2.12(17)  3.02(27) 0.95(17)  Cl BO Cl BO  C1 BO  -0.25 -0.20 -0.25 -0.20  0.80(20) 0.72(21) 0.91(20) 0.74(20)  0.55(20) 0.52(21) 0.66(20) 0.54(20)  -2.39 -2.34 -0.80 -0.78  3.92(27) 3.76(32) 1.32(14) 1.38(16)  1.53(27) 1.42(32) 0.52(14) 0.60(16)  F BS  -3.77  9.30(100)  5.53(100)  -2.31  4.04(27)  1.73(27)  n  10  3 5 3 7  n  n  35 37  io  C 1  B O  10  U  B  X=(C1/F) *(P)  cr(av)  538(5) -138(12) 538(5) — 141(15)  400(13) 397(16)  330(5) -238(10) 330(5) -232(19)  92(11) 98(19)  Cl BO Cl BO  C1 BO  525(5) -172(43) 525(5) -191(55) 525(5) -196(43) 525(5) —196(53)  353(43) 334(56) 329(43) 329(53)  359(5) -258(18) 359(5) -252(21) 359(5) -259(27) 359(5) -277(32)  102(18) 107(22) 100(28) 82(32)  F BS  559(5) -219(23)  341(24)  361(5) -279(19)  83(19)  10  3 5 3 7  n  n  35  C 1  io  B O  10  n  a  "(P)  F BO F BO n  37  cr(av)  Estimated uncertainty of 5 ppm.  CHAPTER  6. HALOGENATED  0X0- AND  SULPHIDO-BORANES  110  Table 6.12: Calculated paramagnetic shielding proportionalities, a (ppm) x AE(Eh), for F B O , C1BO, and F B S p  C1BO  FBO  2TT -» 9<r ITT -> 9a 2TT ->• 8<T lrr -» 8a 7a -» 3rr 6<7 —> 3TT 5<T —>• 3TT 4(7 ->• 37T 3(7 —» 3TT 2cr 3TT la -4 3TT  F  B  77 -185 -62 -105 -18 -44 0 -2 0 0 0  -20 -22 2 -1 -9 -4 -1 0 0 0 0  CI 3TT 11(7 78 2TT -> 11(7 -165 ITT -4 11(7 0 3TT -»> 10(7 -183 2TT -> 10(7 -141 lrr 10(7 0 9(7 —• 4TT -39 8(7 - > 47T -3 7a -4 47T -2 6cr ->• 4TT 1 5(7 -4 47T 0 4cT ->• 47r 0 3(7 47T 0 2a -> 4rr 0 la ->• 47T 0  FBS B  -10 -30 0 3 -4 0 -13 0 -1 -1 0 0 0 0 0  F  3TT -4 11(7 77 2TT ->• 11(7 -200 ITT -4 l l o r 0 3TT -4 10(7 -53 2TT -4 10(7 -90 ITT - V 10(7 0 9(7 -4 4TT -17 8(7 -4- 4TT -57 7(7 -4 4TT 2 6(7 4TT -2 5c7 -4 4TT 0 4a "4 4 7 T 0 3a -4 47T 0 2(7 -4 4rr 0 1(7 - > 4 7 T 0  B  -26 -18 0 1 0 0 -10 -5 -2 0 0 0 0 0 0  Chapter 7 The Molecular Geometry and Hyperfine Coupling Constants of Phosphenous Fluoride, O P F  7.1  Introduction  Phosphenous fluoride belongs to the family of transient triatomic molecules of the form ABC where A is a halogen, B is a group 15 element, and C is a group 16 element. Another molecule which belongs to this family is nitrosyl chloride, the analysis of the microwave spectrum of which was the topic of Chapter 4. While the nitrosyl halides have been studied extensively in the past by both microwave and infrared spectroscopic techniques [17,19,69-71,73,77,121-125], studies on the phosphenous halides have been rarely reported. In fact, the entire family of phosphenous halides [28, 126-128] and the analogous arsenic, antimony, and sulphur containing compounds OAsCl [129,130], OSbCl [129,130], and SPX (X=F,Cl,Br) [131-133] have been studied by only one group using cryogenic matrix isolation infrared spectroscopy and ab initio calculations. Characteristically, the nitrosyl halides are seen to have very long X-N bonds which have a significant amount of ionic character; the electronegative halogen atom is seen to withdraw some of the electron density from the highest occupied anti-bonding molecular orbital of the N=0 moiety, thus giving the nitrosyl halides shorter N=0 bonds than that found in free NO. The ab initio structure [28] and harmonic force field calculated  111  CHAPTER  7. PHOSPHENOUS  FLUORIDE  112  for OPF in the previous work [28] indicate that in OPF this is not the case. For OPF, both the P-F and P=0 bonds are similar in length to those of PF and PO. This would 3  indicate that OPF has a less ionic F-E (E=P,N) bond and, therefore, a much different electronic structure than that of the lighter analogue ONF. This difference in electronic structure should manifest itself in rather different nuclear shielding parameters for the two molecules. In this work, pure rotational transitions of two isotopomers of OPF have been measured. This study represents the first observation of spectral transitions of a free gas phase phosphenous halide. The determined rotational constants have been used to calculate ro, v and approximate r geometries; these parameters have been compared with z  e  those obtained using ab initio techniques and with those of related species. The measured spectra have also been observed to exhibit small hyperfine splittings due to the presence of the spin-1/2 phosphorus and fluorine nuclei. Because both these atoms have the same nuclear spin and the determined coupling constants are of a similar magnitude, unique assignment of the determined values to a particular nucleus was not possible. The nuclear shielding parameters of the phosphorus and fluorine nuclei have been calculated using both possible spin-rotation constant assignments. The fluorine shielding parameters are compared with those of the first period analogue ONF. 7.2  Experimental Methods  The unstable molecule OPF was prepared using the pulsed discharge apparatus, in a manner analogous to that used to prepare SF , FBO, C1B0, and C1BS. The discharge 2  was passed through a gas phase sample consisting of 0.5% PF and 0.5% 0 in ~5 bar 3  2  Ne. Rotational transitions were measured in the 4-26 GHz frequency range using the automated spectrometer. To measure transitions of the 0 isotopomer, a 50% 18  18  0  CHAPTER  7. PHOSPHENOUS  113  FLUORIDE  enriched 0 sample, obtained from Cambridge Isotope Laboratories, was used. Line 2  positions have been determined by fitting to the time domain signals [65], and their uncertainties have been estimated from the range of values resulting from each of several different measurements of each transition. Strong, well separated lines are accurate to better than ±lkHz, while weaker or closely spaced lines are less precise. 7.3  Spectral Search and Analysis  The only previous study [28] of phosphenous fluoride was carried out using ab initio techniques and matrix isolation infrared spectroscopy; thus, the rotational constants of this species were not previously known. The ab initio calculated structure of Ref. 28 was used to estimate the principal moments of inertia and the corresponding rotational constants of the molecule in order to predict the positions of rotational transitions lying in the 4-26 GHz frequency range. Phosphenous fluoride is a planar asymmetric molecule with dipole components along both the a- and b principal inertial axes; thus its spectrum will exhibit both a-type and 6-type transitions. However, because of the large rotational constants and the low rotational temperature of the jet, there were few transitions available in the operating frequency range of the spectrometer. Initially, some a-type transitions were sought using the automatic scanning capability of the spectrometer; the scans were done using 256 signal averaging cycles and frequency increments of roughly 0.4 MHz. The regions 16 900-17 300 MHz and 16 800-16 900 MHz were scanned, and a transition was located at roughly 16 871.9 MHz; this transition showed a hyperfine structure which was consistent with that of a molecule containing two spin-1/2 nuclei, and was dependent upon the use of the discharge. It was assigned as the l ,i — 0,o transition of OPF. A 0  o  weaker transition was subsequently found at 5115.4 MHz after scanning the regions 5 2005 400 MHz and 5 100-5 200 MHz; this transition was also seen to be discharge dependent,  CHAPTER  7. PHOSPHENOUS  114  FLUORIDE  and was assigned as being the Q-branch 2^ — 2  lj2  transition. These two transitions  were fit to determine the B and C rotational constants of the molecule, and, from these determinations, a rough value for A was obtained. The A constant wasfirstcalculated from the determined B and C constants assuming that the inertial defect of the molecule was equal to zero, a criterion which is strictly applicable only to a planar molecule in its equilibrium configuration; see Section 2.3. Using this calculated value, 6-type transitions were predicted,and the strongest of these, 3o,3 — 2 , was sought, again using the automated scanning. After a 100 MHz region had 1)2  been searched with no positive results, an attempt to improve the prediction of the A constant was carried out. This was done by using the force constants of Ref. 28 to calculate the expected ground state inertial defect; this and the B and C rotational constants that were determined above were then used to calculate A. Using this new constant, the 3o,3 — 2i transition was predicted to lie roughly 500 MHz below the previously predicted )2  position. A 60 MHz region in this area was searched, and a transition was located. This transition was split into four hyperfine components, as is consistent with an assignment to the 3o,3 — 2i transition of OPF. j2  All three rotational constants of the normal isotopomer could be independently determined from the three observed transitions, and new transitions could then be predicted with a reasonable degree of accuracy. Two more a-type Q-branch rotational transitions of the normal isotopomer were thus easily found. A second 6-type transition, 3 , — 41,3, 2 2  predicted to be at 24504.3 MHz was also located at roughly 24503.98 MHz; however, it was very weak, and had a correspondingly high uncertainty in its measured line position. This transition, therefore, was not included in the spectral fit; however, it did confirm the assignment of thefirst6-type transition. Rotational transitions for OPF were located using a similar procedure. Preliminary 18  CHAPTER  7. PHOSPHENOUS  FLUORIDE  115  rotational constants for this isotopomer were obtained by scaling those calculated from the ab initio geometry by the ratio between the measured and predicted constants of the main isotopomer; assignments of the measured transitions were confirmed by the similarity of the hyperfine structure to the analogous transitions of the 0 isotopomer. 16  Some of the measured transitions were seen to exhibit hyperfine splittings due to nuclear spin-rotation interactions. The lo,i — 0o,o transitions were each split into three distinct hyperfine components, the 30,3 — 2^2 transitions were split into four components, and all measured Q-branch transitions showed no hyperfine splittings, but did show a slight increase in line width with increasing J . The lo,i — 0o,o transition of OPF is 16  shown in Fig. 7.1 and the 3^2 — 3i 3 and 4i,3 — 4i 4 transitions of OPF are compared in 16  (  t  Fig. 7.2 where it can be seen that the linewidth shows a slight increase for the higher J transition. As was shown in Section 2.1.3, the hyperfine splittings of the rotational energy levels are dependent upon the rotational state dependent spin-rotation constant, given by Cj, = J2 Cgg(Jg); here g sums over the a,b,c principal inertial axes, and the C are r  g  gg  the spin-rotation coupling constants along the g-axes. Expressions for the Cj, s for all T  energy levels involved in the transitions measured here have been calculated, and the spin-rotational coupling constant dependence of all observed transitions is presented in Table 7.3. Here it is seen that the hyperfine splittings of the Q-branch transitions depend only upon the quantity C b — C , and that the splittings should increase with increasing b  cc  J, as was observed. Table 7.3 also shows that the l ,i — 0,o transition depends only on 0  Cbb + C ,  a n  cc  d that the 3o,3 — 2  1)2  o  transition depends on all three principal axis values of  the spin-rotation coupling constants. Thus, the combinations of spin-rotation coupling constants that were used asfittingparameters were C — \{Cbb + C ), \(Cbb + C ) , and aa  \{C  bb  — C ). cc  cc  cc  CHAPTER  7. PHOSPHENOUS  116  FLUORIDE  1,2-1,1  16871.650 MHz  16872.150 MHz  Figure 7.1: The l ,i — 0 o transition of OPF, showing resolved hyperfine structure; the components are labelled according to the quantum numbers I, F. This spectrum was obtained using 128 signal averaging cycles and 4K data points. 16  0  0)  CHAPTER  7. PHOSPHENOUS  J =  FLUORIDE  117  3-3  V 10229.25 MHz  10228.45 MHz  J = 4-4  17039.43 MHz  17038.63 MHz  Figure 7.2: The 3 — 3 and 4j — 4 transitions of 0PF, showing an increase in linewidth with increasing J. Top trace: 3i, —3i, transition recorded using 512 averaging cycles and 4K data points. Bottom trace: 4i —4i transition recorded using 1024 signal averaging cycles and 4K data points. 16  1)2  li3  ]3  lj4 2  3  )3  )4  CHAPTER  7. PHOSPHENOUS  118  FLUORIDE  The hyperfine patterns of the l ,i — 0 o and 3,3 — 2 0  O)  0  lj2  transitions were predicted by  using as starting values for the spin-rotation coupling constants those of ONF [17], scaled by the appropriate factors. Both the lo,i — 0o,o and 3o,3 — 2i transitions were predicted )2  to each show one strong hyperfine component plus two, or three, weaker ones, respectively. The strongest component of each rotational transition was easily assigned, and the weaker components were systematically rotated through all possible combinations. The assignment which produced the fit with the lowest rms deviation was taken to be correct; all other rms deviations were at least one order of magnitude larger. The measured transitions were fit to the rotational, centrifugal distortion, and spinrotation coupling constants of the molecule using the exactfittingprogram S P F I T [41]; the coupling scheme I + I = I; I + J = F was used. In the preliminary fits, the centrifugal x  2  distortion constants, with the exception of 5j, were heldfixedto the values obtained from the harmonic forcefieldcalculated using the data of Ref. 28; for the final spectroscopic fit, the centrifugal distortion constants were re-calculated from the forcefieldusing the r  0  geometry determined here. The <5/'s of both OPF and OPF were fit as free parame16  18  ters; their determined values are slightly larger than those calculated from the force field, and their ratio (1.1130(63)) is in agreement with the ratio between the calculated values (1.11317). The hyperfine splittings were fit to the spin-rotation combination constants given above; since the Q-branch transitions showed no significant hyperfine effects, the fitting parameter \(Cbb — C ) of each nucleus was held fixed at a value of zero. The cc  remaining spin-rotationfittingparameters were determined from the measured splittings between the hyperfine components of the l ,i — 0,o and 3o,3 — 2 0  o  1)2  transitions. Nuclear  spin-spin effects were neglected because these constants could not be determined from the limited spectroscopic data, and because inclusion of these parameters asfixedconstants, the values of which were calculated from the molecular geometry using Eq. 2.48, did not  CHAPTER  7. PHOSPHENOUS  119  FLUORIDE  improve the quality of the fit and did not significantly affect any of the other determinations. A complete listing of all observed transitions is given in Table 7.1, along with the differences, A, between the measured values and those calculated from the derived constants. The determined spectroscopic constants of OPF are presented in Table 7.2. The rotational constants are precisely determined for both isotopomers. Similarly, 8j is well determined, and agrees well with the value estimated from the harmonic force field, which is also given in the Table. The spin-rotation coupling constants are also precisely determined, however their accuracy is questionable since thefittedconstants were each determined from a fit of only two or three hyperfine splittings. These constants could not be uniquely assigned to a particular nucleus because both nuclei have the same spin and coupling constants of a similar magnitude. In Table 7.2, the labels (1) and (2) have been used to represent the F/P nuclei. 7.4 7.4.1  Discussion Molecular geometry  In this work, the ground state rotational constants of two isotopomers of OPF have been determined; these have been used to calculate an ro geometry for the molecule using the program RU111J. As is recommended by Rudolph [72], this structure was determined by fitting to the planar moments of inertia, with P omitted because of the planarity c  constraint. The data were weighted according to the inverse squares of their uncertainties. Because the experimentally determined uncertainties in the rotational constants are identical for both isotopomers studied, no adjustments of the weights were necessary [52]; the experimental uncertainties aptly represent the quality of the data. In contrast to the study on CINO, it was not possible here to calculate an r/ or r^p structure because of i£  CHAPTER  7. PHOSPHENOUS  120  FLUORIDE  insufficient information. For OPF, four independent rotational parameters were determined for two isotopomers of this planar molecule. An r/ fit for a non-linear triatomic ]£  molecule requires at least six pieces of data to determine a total of three geometric parameters plus three vibration-rotation interaction parameters; in an r&p fit, it is necessary to have a total of at least three independent rotational constant differences in order to determine the three parameters that describe the geometry of a non-linear triatomic molecule. An r structure has also been calculated. For this purpose, an harmonic force field z  was required. This was taken to be that of Ref. 28 because it reproduced the inertial defects and Sj values well (see Table 7.2), and because the new data obtained in this study were insufficient to make significant improvements. The ground state average rotational constants were obtained by subtracting the harmonic contributions to the a's from the measured rotational constants, and the isotopic variations in the bond lengths were accounted for using Eq. 2.70; the zero-point mean square amplitudes of the bonds and their perpendicular amplitudes were obtained from the force field and the Morse parameters were obtained from tabulated values [59]. The r geometry was evaluated z  using the program MWSTR; the data were weighted according to the inverse squares of their uncertainties. An approximate equilibrium structure was also calculated using Eq. 2.71 and the r structure; here the bond angle was assumed to be the same as for the r z  z  structure. The determined r , r , and r geometries are presented in Table 7.4 where they are 0  z  e  compared with the ab initio geometric parameters obtained using the program GAUSSIAN94  in this study and with the ab initio parameters calculated in Ref. 28. Here it  is seen that the experimental geometries are in agreement, and that OPF has indeed been very well characterised by the theoretical methods. The differences between the  CHAPTER  7. PHOSPHENOUS  FLUORIDE  121  experimental and calculated geometries are very small. A comparison is made between the analogous molecules OPF and ONF in Table 7.5. It is seen for all of the ONX (X=F,Cl,Br) species that the N-X bonds are very long in comparison to those of the NX3 molecules, and that the N=0 bonds are somewhat shorter than that for the free NO species. This trend is not reflected by OPF. It is seen in Table 7.5 that the P=0 and P-F bond lengths determined for OPF are very similar to those of the PF3 and PO species. Both bonds are seen to become marginally longer in OPF. Interestingly, the ONH and ONF species show bond length trends that are similar 3  to those of the OPH and O P F 3 species, indicating that it is ONF and not OPF which is somewhat unusual. The experimentally determined OPF geometric parameters support the conclusion drawn by Ahlrichs et al. that OPF does not share many similarities with the nitrosyl halides, and that its structural parameters are better compared with those of the isoelectronic species NSF, SiF2 and SO2.  A final structural comparison can be made between OPF and the related molecules NSF, SiF and SO2; this is also presented in Table 7.5. The bond angle of OPF is 2  seen to be intermediate between those of SiF and SO2, as might be expected from a 2  consideration of the relative positions of the Si, P, and S nuclei in the periodic table. The NSF species, however, is shown to have a somewhat shorter N=S bond than does free NS, and an S-F bond that is of a similar magnitude to the axial S-F bond of SF . Apparently, 4  NSF has a bonding situation which is intermediate between that of phosphenous fluoride and nitrosyl fluoride. 7.4.2  Nuclear spin-rotation coupling constants  The spin-rotation coupling constants determined for OPF are given in Table 7.2. Since the nuclear spins of the fluorine and phosphorus nuclei are both equal, and the determined  CHAPTER  7. PHOSPHENOUS  FLUORIDE  122  spin-rotation coupling constants have very similar values, it was impossible to assign a particular set of values to a particular nucleus; accordingly, in Table 7.2, the labels (1) and (2) are used to identify the coupling nuclei. As was shown in Section 2.1.3, the reduced spin-rotation coupling constants, C^/g^B,  where (x) is the nucleus in question, should  be independent of isotopomer. These have been calculated for OPF and OPF and 16  18  are compared in Table 7.6. They agree within the error limits. The nuclear and electronic contributions to the spin-rotation coupling constants of OPF were calculated using Eqs. 2.36, 2.37 and 2.38. The nuclear shielding parameters of OPF were then calculated from these and the ro geometric parameters using Eqs. 2.39, 2.41, and 2.42; these have been determined using both possible spin-rotation coupling constant assignments. The results are shown in Table 7.7. Although these resulting values have large error limits, and there is no real means of deciding which assignment is best, they can be commented on in comparison to the isoelectronic molecule ONF, the spin-rotation coupling constants for which have been calculated in Ref. 17. Thefluorinenuclear shielding parameters of ONF have been calculated using the spin-rotation coupling constants of Refs. 17 and the geometry of Ref. 123. These are compared to the fluorine nuclear shieldings of OPF in Table 7.8. Despite the differences in structure, the diamagnetic shielding components are fairly similar for both species; the majority of the differences in the nuclear shielding terms comes from the differences in the paramagnetic shieldings. As was pointed out in Section 5.4, the paramagnetic shielding terms normally have large negative values which counteract the large positive diamagnetic terms, resulting in a moderate overall absolute chemical shift. In the case of OPF, the paramagnetic shielding components along the a- and c- principal inertial axes are of relatively the same order of magnitude for both OPF and ONF; however, the 6-axis component for OPF is about half the magnitude of that of ONF, thus giving rise to a  CHAPTER  7. PHOSPHENOUS  123  FLUORIDE  more positive fluorine chemical shift for OPF. Because the electronic structures of these two species are so different, it is a question of whether this difference in paramagnetic shielding is due to a large difference in the HOMO/LUMO energy gap (as was seen to be a large factor in the comparison of the chemical shifts of SF and its analogue OF ; see 2  2  Section 5.4), or merely to a large difference in the way in which the molecular orbitals are formed from the atomic orbitals. Considering that ONF can be considered more as an NO moiety with an F atom loosely bonded to it, whereas in OPF, the bonds are more similar in strength, it is likely the latter contribution which accounts for the majority of this difference in nuclear shielding terms. The atomic orbital contributions to the molecular orbitals have been calculated for ONF and OPF using the program GAUSSIAN 94 [104](MP2/STO-3G), and factors proportional to the individual paramagnetic shielding contributions (cr(p) x AE) were calculated using Eq. 2.45; these factors are given as "paramagnetic shielding proportionalities" in Table 7.9. As was pointed out in Section 6.4.2, the energies of the unoccupied molecular orbitals calculated using this program are usually incorrect, and should not be used in any calculations; thus, this information cannot be used to calculate the paramagnetic shielding terms directly. It is seen in Table 7.9 that the paramagnetic shielding contributions are quite different between the two molecules, yet, overall, the results are not different enough to provide any real information. This would indicate that the differences in the paramagnetic shielding terms calculated for both molecules are due both to differences in the electronic energy level structures and to differences in the molecular orbital arrangements. In this study, the type of spin-rotation coupling constant analysis used to explain the unusual nuclear shielding results obtained for SF (see Section 5.4) has not proved 2  to be particularly fruitful. In the SF case, the energy levels of both it and its analog, 2  CHAPTER  7. PHOSPHENOUS  FLUORIDE  124  0F , had been previously determined, either by experimental or ab initio techniques. 2  Such information for OPF would be helpful in the analysis of the spin-rotation coupling constants, and could, perhaps, assist in the assignment of the spin-rotation coupling constants to the appropriate nuclei. Useful information could also be obtained from a comparison of these results with those calculated using high level ab initio techniques.  CHAPTER  7. PHOSPHENOUS  125  FLUORIDE  Table 7.1: Observed transition frequencies, u, and differences between observed and calculated frequencies, A, of OPF i 6  K ,K a  r  F'  i"  F"  1 0 1 1  3 2 2 1  1 0 1 1  3 2 2 1  3i 3  1 0 1 1  4 3 3 2  1 0 1 1  4 3 . 3 2  0Q,O  K ,K  J  J c  a  2i,i — 2 i  3l,2  lo,i  4l,3  —  —  - 4i  ]2  )4  3o,3 - 2 ,  1 2  c  0  P  18  F  v /MHz  A /kHz  OPF  v /MHz  A /kHz  5115.3930(20)  -0.3  4 769.4710(20)  -0.2  10 228.8764(20)  0.3  9 537.2852(20)  0.1  1 1 1 1 0 10 0 12 11  16 871.8598(10) 16 871.8816(10) 16 871.9000(10)  0.0 0.0 0.0  16 013.2621(10) 16 013.2829(10) 16 013.3006(10)  0.0 0.0 0.0  1 0 1 1  5 4 4 3  1 0 1 1  5 ) 4 4 3  17039.0464(20)  -0.1  15 587.6318(20)  0.0  1 0 1 1  4 3 3 2  1 0 1 1  3 2 2 1  19 397.2502(10) 19 397.2650(10) 19 397.2751(10) 19 397.2877(10)  -0.6 0.6 0.6 -0.6  17 665.7416(10) 17 665.7520(10) 17 665.7647(10) 17 665.7766(10)  0.4 -0.4 -0.4 0.4  CHAPTER  7. PHOSPHENOUS  126  FLUORIDE  Table 7.2: Spectroscopic constants of phosphenous fluoride" 16  A B C A  18  OPF  41886.65211(219) 9288.59876(44) 7583.31579(44)  ^(000)  0.1666  0.1696°  c  8.52033" -86.7088" 1083.77° 2.4507(93) (2.42054) 23.2609°  AJAA A  SJ  c  SK c (iy  h(Cbb + C )(l) (C -C )(l)  121.0(100) 23.0(12) 0.0  C (2) k(C + C )(2) \{C -C ){2Y  103.1(128) 16.1(18) 0.0'  aa  cc  bb  cc  e  aa  e  bb  bb  cc  cc  40474.01447(219) 8801.63574(44) 7211.67691(44) 0.1726  0.1696  6  OPF  /  7.69522° -83.5791" 1026.03° 2.2021(93) (2.17446) 20.5652° c  121.1(77) 21.9(12) 0.0/ 91.3(104) 15.5(18)) 0.0/  " U n i t s of M H z for the rotational constants, k H z for the centrifugal d i s t o r t i o n and spin-rotation constants; uncertainties ( l c ) are given i n parentheses. A ( ) is the ground state inertial defect. Force field predicted values. B  0 0 0  c  F i x e d at the values obtained from an harmonic force field analysis using the force constants of Ref. 28. d  Because the spin-rotation coupling constants could not be assigned to a p a r t i c u l a r nucleus, the labels (1) and (2) are used. f F i x e d ; see text for details. e  CHAPTER  7. PHOSPHENOUS  127  FLUORIDE  Table 7.3: CJ constants determined for the studied rotational energy levels, and the spin-rotation coupling constant dependence of the observed rotational transitions of OPF IT  0o,o lo,i 2i,i 2l,2  o.oc  a  a  o . o c  a  a  1.0C 1.0C  3o,3  o . o c  a  +  aa  a  1.0C  a  o  o  aa  o.oc  c  c  CC  6  4l,4  i . o c  +  6  66  oo  l.OCaa  a  6  66  3l,2 3l,3 4l,3  i . o c  o.oc  + 1.0C + l.OCcc + 4.0C + 1.0C + 1.0C 6 + 4.0C c + 5.6C + 6.4C + 8.5C + 2.5C + 2.5C + 8.5C + 14.3C 6 + 4.7C + 4.3C 4- 14.7C C  66  CC  66  CC  bb  CC  6  CC  W  CC  measued transition C -dependence 5g  2i,i - 2 3l,2 - 3 i , 4l,3 - 4 lo,i -0 ,o 3o,3 - 2 l l 2  3  M  0  U  3.0C 6.0C66 - 6.0C 10.0C - 10.0C l.OCw-f-LOC^ -1.0C + 4.6C + 2.4C 3.0C66  —  CC  CC  bb  aa  CC  66  CC  CHAPTER  7. PHOSPHENOUS  128  FLUORIDE  Table 7.4: Structural parameters of OPF  r(0=P) / A  r(P-F) / A  Z(OPF) /deg  1.4542(4) 1.4527(64) 1.4497(64)  1.5786(4) 1.5807(62) 1.5762(62)  110.221(6) 110.216(77) 110.216(77)  HF(6-31G*) HF(D95V*) HF(D95V+(3df,2p))  1.4369 1.4479 1.4254  1.5727 1.5953 1.5495  109.301 108.390 109.410  Previous work: SCF CI(SD) CPF  1.426 1.440 1.456  1.549 1.559 1.576  109.9 109.7 110.0  ab initio results:  GAUSSIAN 94:  6  r parameters determined from r structure using Eq. 2.71; uncertainties are assumed to be equal to those determined for the restructure. Ref. 28. a  e  6  z  CHAPTER  7. PHOSPHENOUS  FLUORIDE  129  Table 7.5: Comparison of the structural parameters of OPF with those of related species"  r(P/N=0) / A r(P/N-F/H) / A OPF * OPH * OPF^ PF* PO'  1.4542(4) 1.512 1.436(6)  ONF ONH * ONFg NF NO*  1.13146(44) 1.212(1) 1.158(4)  6  c  1.5786(4) 1.433 1.524(3) 1.563(2) c  L /deg 110.221(6) 104.7  1.431  3  /l  1.51666(46) 109.919(14) 1.063(2) 108.6(2) 1.431(3) 1.3648(20)  3  1.151 r(0/N=S) / A  SiF< SO^ NSF™* SF°  1.43076(13) 1.448(2)  SN  1.4938(2)  p  /deg  r(S/Si-F) / A  L  1.5901(1)  100.77(2) 119.33(1) 116.91(8)  1.643(2) 1.545(3) 1.646(3)  Unles otherwise indicated, r parameters are given. This work. Ref. 134; P-H bond distance fixed to that of PH. Ref. 135. Ref. 136. Ref. 137. Ref. 125. Ref. 138. Ref. 139 Ref. 140. Ref. 82. ' Ref. 141. Ref. 142. Ref. 143. Ref. 144 Ref. 145 * restructure. ^ r structure; from electron diffraction data. * restructure. a  6  e  c  d  e  m  a  1  9  n  h  0  p  i  3  k  CHAPTER  7. PHOSPHENOUS  130  FLUORIDE  Table 7.6: Comparison of the reduced spin-rotation coupling constants, and  1 8  OPF  °f  1 6  0PF  a  16 p 0  Scheme I  a  1 8  F  Sch eme I P  C (F)/gA C (F)/gB C (F)/gC  1.1(1) 0.9(1) 1.2(1)  0.9(1) 0.7(1)  C (P)/gA C (P)/gB C (P)/gC  2.2(3) 1.5(2) 1.9(2)  aa  bb  cc  aa  bb  cc  OPF  Scheme 1°  Sch eme I P  0.8(1)  1.1(1) 0.9(1) 1.2(1)  0.8(1)  2.6(2) 2.2(1) 2.7(1)  2.0(2) 1.6(2) 1.9(2)  2.6(2) 2.2(1) 2.7(1)  0.9(1) 0.7(1)  Because the spin-rotation coupling constants could not be uniqely assigned, the reduced spin-rotation coupling constants were calculated using both possible assignments: Scheme I: (1)=F, (2)=P; Scheme II: (1)=P (2)=F. a  CHAPTER  7. PHOSPHENOUS  131  FLUORIDE  Table 7.7: Fluorine and phosphorus spin-rotation constants (kHz) and nuclear shielding parameters (ppm) of OPF a  Sch eme I P  Ca a  C'bb Cc C  Sc;heme I I  6  F  6  F  P  103.1(128)  121.0(100)  121.0(100)  103.1(128)  16.1(18) 16.1(18)  23.0(12)  23.0(12) 23.0(12)  16.1(18) 16.1(18)  23.0(12)  C (n) C (n) C (n) aa  -5.4  -7.9  -5.4  -7.9  bb  -2.4  -7.8  -2.4  cc  -3.0  -7.8  -3.0  -7.8 -7.8  C (e) C (e) C (e)  128.9(100) 30.8(12)  126.4(100) 25.4(12)  111.0(128)  bb  108.5(128) 18.5(18)  cc  19.1(18)  30.8(12)  26.0(12)  23.9(18)  ^aa(p)  -1050(124) -809(79)  -538(42) -578(23)  -1224(97) -1110(52)  -463(53) -449(34)  -709(28)  -1388(64)  -608(31)  -1241(71)  -550(41) -487(43)  aa  <76(>(P)  <?cc{p) - 1 0 1 9 ( 9 6 ) ^av(p)  -960(100)  23.9(18)  1013 1067  504 617  1013 1067  504  1119  650  1119  650  (7 (d)  1066  590  1066  590  Vaa  -37(124)  -34(42)  -211(97)  41(53)  Obb  258(79)  38(23)  &CC  100(96)  -59(28)  -43(52) -269(64)  168(34) 100(41)  <7av  107(100)  -18(31)  -174(71)  103(43)  ^aa(d) (d) o- (d) 0-66  cc  av  617  a  O n l y the results for the m a i n isotopomer are presented; those for  b  Because the spin-rotation coupling constants could not be assigned to a p a r t i c u l a r nucelus,  1 8  O P F are s i m i l a r .  the nuclear shielding parameters were calculated using both possible assignments: Scheme I: ( 1 ) = F , ( 2 ) = P ; Scheme II: ( 1 ) = P ( 2 ) = F .  CHAPTER  7. PHOSPHENOUS  132  FLUORIDE  Table 7.8: Comparison of thefluorinenuclear shielding parameters (ppm) of O P F and ONF 16  ONF  OPF Scheme I'  Scheme IP  -538(42) -578(23) -709(28) -608(31)  -463(53) -449(34) -550(41) -487(43)  1  ^aa(p) <7&6(P)  <7 (p) cc  ^av(p) ^aa(d)  CT (d) cr (d) cc  av  Van &bb &CC  a  504 617 650 590  504 617 650 590  -34(42) 38(23) -59(28) -18(31)  41(53) 168(34) 100(41) 103(43)  -638(5) -1145(7) -840(8) -874(7) 483 575 588 549 -155(5 -570(7) -252(8) -325(7)  The spin-rotation constants in Table 7.2 could not be positively assigned; in Scheme I, (1)=F; Scheme II, (2)=F.  a  CHAPTER  7. PHOSPHENOUS  FLUORIDE  133  Table 7.9: Non-zero calculated fluorine paramagnetic shielding proportionalities, cr (ppm) x A£(E ), for OPF and ONF p  fc  ONF  OPF  -16 19 -25 -163 -55 -10 13 -3  -66 12 32 -156 -53 -18 19 1  2A" -4 12A' 1A" -4 12A' 2A" -4 11A' 1A" -4 11A' 10 A' ->3A" 9 A' -*3A" 8A' -•3A" 7 A' -4 3A" 5 A' -4 3A"  -28 36 -48 -148 -4 -54 21 -15 1  13 -30 -49 -2 -5 42 -322 -1 -1  10 A' -4 12A' 9A' -4 12A' SA' -4 12A' 7 A' -4 12A' GA' -4 12A' 10 A' -4 11 A' 9 A' -4 11 A' SA' -4 11A' 7 A' -4 11 A' 6A' -4 11 A' 5 A' -4 11 A' AA' -4 11A'  7 4 1 -29 -1 21 -104 -280 -17 -1 -1 -2  13 -18 -90 522 -59 -2 3 7 -6 -1  <76fe(p)  3A" -4 15A' 2A" -4 15A' 3A" -4 14A' 2A" -4 UA' 12A' -4 4A" 11A' -4 4A" 10 A' -4 4A" 9i4' -4 4A"  <7 (P)  13A' 12A' 11A' 10A' 9 A' 12 A 10 A' BA' 7 A'  -4 15A' -4 15A' -4 15A' -4 15A' -4 15 A' -4 UA' -4 14A' -4 14A' -4 14A'  CC  3A" 2A" 3A" 2A" ISA' 12A' UA' 10 A' 9 A' 7 A'  12A' 12A' 11A' 11 A' 3A" 3A" 3A" 3A"  -4 15A' -4 15 A' -4 14A' -4 14A' -4 4,4" -4 4A" -4 4A" -4 4A" -+ 4A" -4 4A"  C<m(p)  2A" 1A" 2A" 1A" 10A' 9A' SA' 6A'  -4 -4 -4 -4 -4 -4 -4 -4  Appendix A Measured transitions of Nitrosyl Chloride  Table A.l: Measured transitions of nitrosyl chloride  A /kHz with without J ,K -Jk ,K Ka  c  a  F"  c  Ftn  F'  35  5.5 5.5 4.5 4.5 6.5 6.5 3.5 5.5 3.5 4.5 6.5 3.5  4.5 6.5 3.5 5.5 5.5 7.5 2.5 5.5 4.5 4.5 6.5 3.5  5.5 5.5 4.5 4.5 6.5 6.5 3.5 5.5 3.5 4.5 6.5 3.5  C 1  v /MHz  14 16 N  4.5 6.5 3.5 5.5 5.5 7.5 2.5 5.5 4.5 5.5 6.5 3.5  134  X  a  h  Xa  »  0  5417.2445(10) 5 417.6889(10) 5 417.8566(10) 5 418.4626(,10) 5 419.5003(10) 5 419.9340(10) 5419.9608( 10) 5 420.1374(10) 5 420.7340(10) 5 420.7555(10) 5 422.7868(10) 5 423.3002(10)  0.8 0.5 0.2 0.2 0.1 -0.4 -0.5 0.6 0.6 -0.6 0.0 -0.2  1.5 1.2 2.6 2.5 2.4 2.0 -0.5 1.3 0.7 1.6 2.5 -0.2  APPENDIX  A. MEASURED  TRANSITIONS  OF NITROSYL  135  CHLORIDE  Measured transitions of nitrosyl chloride cont'd  A /kHz with without J'LK.-Jl< ,K a  c  61,5 - 6 i ,  7i,6 - 7i,  lo,i  —  0o,o  F&  F"  F  F'  V /MHz  6.5 6.5 5.5 5.5 7.5 7.5 6.5 4.5 5.5 7.5 4.5  5.5 7.5 4.5 6.5 6.5 8.5 6.5 5.5 5.5 7.5 4.5  6.5 6.5 5.5 5.5 7.5 7.5 6.5 4.5 5.5 7.5 4.5  5.5 7.5 4.5 6.5 6.5 8.5 6.5 5.5 5.5 7.5 4.5  7584.5971(10) 7 584.9845(10) 7 585.0954(10) 7 585.6468(10) 7 586.8755(10) 7 587.2614(10) 7 587.5773(10) 7 587.9003(10) 7588.1216(10) 7590.1757(10) 7 590.6225(10)  0.6 -0.1 0.0 -0.2 0.1 -0.5 0.4 -0.6 -0.1 0.7 -1.0  1.4 0.8 5.5 5.0 4.5 4.0 1.4 -0.6 5.0 5.5 -0.9  7.5 7.5 6.5 6.5 8.5 8.5 7.5 5.5 6.5 8.5 5.5  6.5 8.5 5.5 7.5 7.5 9.5 7.5 6.5 6.5 8.5 5.5  7.5 7.5 6.5 6.5 8.5 8.5 7.5 5.5 6.5 8.5 5.5  6.5 8.5 5.5 7.5 6.5 9.5 7.5 6.5 6.5 8.5 5.5  10112.6547(10) 10 112.9924(10) 10 113.0413(10) 10113.5540(10) 10114.9213(10) 10115.2692(10) 10115.6730(10) 10115.8195(10) 10116.1351(10) 10118.2236(10) 10118.6396(10)  -0.2 0.0 0.3 0.3 -0.3 0.3 0.3 0.2 -0.6 -0.1 -0.4  -1.1 -0.8 -24.0 -22.0 -17.9 -17.6 -2.2 0.0 -23.1 -19.4 -0.6  1.5 1.5 1.5 1.5 1.5 1.5  1.5 1.5 1.5 2.5 0.5 0.5  1.5 1.5 1.5 1.5 1.5 1.5  0.5 ' 2.5 > 11104.0086(10) -0.4 1.5 2.5 11 104.2099(10) -0.1 0.5 • 11 104.3668(10) 0.3 1.5  a  Xab  Xab  6  -0.5 -0.2 0.3  A. MEASURED  APPENDIX  TRANSITIONS  OF NITROSYL  CHLORIDE  136  Measured transitions of nitrosyl chloride cont'd  A /kHz with without J'L,K^K ,K a  §0,8  5l,5  —  —  c  Fc\  F"  Ft*  F'  2.5  1.5  1.5  0.5  2.5  1.5  1.5  1.5  2.5  3.5  1.5  2.5  2.5  0.5 0.5  v /MHz  X  a  b  Xa»  11116.3117(10)  0.1  0.2  2.5  11116.4046(10)  0.1  0.2  1.5  1.5  11116.6103(10)  0.1  0.1  0.5  1.5  0.5  0.5  1.5  1.5  11 126.2407(10)  0.1  -0.1  0.5  1.5  1.5  2.5  0.5  1.5  1.5  1.5  11 126.2456(10)  0.3  0.1  8.5  7.5  6.5  6.5  11920.5579(10)  -0.3  17.7  7.5  6.5  6.5  5.5  11 921.5054(10)  0.4  1.8  8.5  7.5  7.5  6.5  11 921.5440(10)  -0.9  17.5  7i,7  8.5  9.5  7.5  8.5  11 921.6456(10)  0.8  19.3  7.5  8.5.  6.5  7.5  11 921.6738(10)  -1.1  0.2  7.5  7.5  6.5  6.5  11 922.9152(10)  -0.1  1.0  8.5  8.5  7.5  7.5  11922.9828(10)  -0.6  19.3  9.5  8.5  8.5  7.5  11 923.1935(10)  0.3  0.7  6.5  5.5  5.5  4.5  11923.2164(10)  0.0  24.6  9.5  10.5  8.5  9.5  11 923.3544(10)  0.7  0.8  6.5  7.5  5.5  6.6  11 923.4485(10)  0.5  24.8  7.5  7.5  7.5  6.5  11923.9019(10)  -0.2  1.3  9.5  9.5  8.5  8.5  11924.7590(10)  0.5  0.7  6.5  6.5  5.5  5.5  11 924.7914(10)  -0.1  22.8  3.5  3.5  4.5  4.5  12 499.5743(10)  -0.1  1.9  6.5  6.5  7.5  7.5  12499.6010(10)  0.0  -0.3  6Q,6  3.5  4.5  4.5  5.5  12 500.8532(10)  -0.1  2.1  6.5  7.5  7.5  8.5  12 501.0112(10)  0.4  0.1  3.5  2.5  4.5  3.5  12 501.1979(10)  -0.4  1.8  6.3  5.5  7.5  6.5  12 501.2210(10)  -0.2  -0.5  5.5  5.5  6.5  6.5  12 502.0320(10)  -0.2  1.4  A. MEASURED  APPENDIX  TRANSITIONS  OF NITROSYL  CHLORIDE  137  Measured transitions of nitrosyl chloride cont'd  A /kHz with without •ft.,*.- *..*. 7  c.  F"  F^  F'  v /MHz  4.5 4.5 5.5 4.5 5.5  4.5 5.5 6.5 3.5 4.5  5.5 5.5 6.5 5.5 6.5  5.5 6.5 7.5 4.5 5.5  12 502.0575(10) 12 503.2041(10) 12 503.3117(10) 12 503.4216(10) 12 503.4562(10)  0.0 0.1 0.4 0.1 -0.1  -0.3 -0.1 1.8 -0.1 1.4  8.5 8.5 7.5 7.5 9.5 6.5 9.5 8.5 6.5 7.5 9.5 6.5  7.5 9.5 6.5 8.5 8.5 5.5 10.5 8.5 7.5 7.5 9.5 6.5  8.5 8.5 7.5 7.5 9.5 6.5 9.5 8.5 6.5 7.5 9.5 6.5  7.5 9.5 6.5 8.5 8.5 5.5 1 10.5 J 8.5 7.5 7.5 9.5 6.5  13001.1143(10) 13 001.4061(10) 13 001.4523(10) 13 001.9383(10) 13003.3953(10)  -0.4 0.0 -0.1 -0.5 -0.1  -0.3 0.2 -4.1 -3.9 -2.7  13003.7100(20)  0.2  -1.5  13 004.1407(10) 13 004.1642(10) 13 004.5792(10) 13 006.6993(10) 13 007.0521(10)  0.1 0.0 0.0 -0.2 0.5  -0.2 -0.1 -3.7 -3.0 0.5  16 249.5741( 10) 16 249.8206( 10) 16 249.8525( 10) 16 250.3352(10) 16 251.8485(10) 16 252.1238(10) 16 252.1369(10) 16 252.5258(10) 16 252.5769(10) 16 252.9927(10) 16255.1510( 10) 16 255.4608(10)  0.2 0.0 -1.2 0.3 0.3 0.8 -0.6 0.4 -0.1 -0.1 0.3 0.2  0.3 0.2 -3.4 -1.4 -1.0 0.7 -1.9 0.3 -0.4 -2.2 -1.1 0.2  F  9.5 8.5 9.5 9.5 10.5 9.5 8.5 7.5 8.5 8.5 9.5 8.5 10.5 9.5 10.5 7.5 6.5 7.5 10.5 11.5 10.5 7.5 8.5 7.5 9.5 9.5 9.5 8.5 8.5 8.5 10.5 10.5 10.5 7.5 7.5 7.5  8.5 10.5 7.5 9.5 9.5 6.5 11.5 8.5 9.5 8.5 10.5 7.5  X a b  X a b  APPENDIX  A. MEASURED  TRANSITIONS  OF NITROSYL  CHLORIDE  138  Measured transitions of nitrosyl chloride cont'd  A /kHz with without J'LK^ ,K Ka  c  F&  F"  F'  v /MHz  2.5  2.5  2.5  3.5  1.5  1.5  21855.9366(10)  0.0  3.8  1.5  2.5  21857.5229(10)  0.0  3.8  2.5  1.5  1.5  0.5  21858.3329(10)  0.3  3.7  1.5  2.5  1.5  1.5  21859.9066(10)  0.6  0.9  1.5  1.5  1.5  1.5  21860.0352(10)  0.6  0.8  2.5  2.5  1.5  1.5  21855.9366(10)  0.0  3.8  2.5  3.5  1.5  2.5  21 857.5229(10)  0.0  3.8  0.5  21858.3329(10)  0.3  3.7  21859.9066(10)  0.6  0.9  X a b  X a b  2i,2 —  2.5  1.5  1.5  1.5  2.5  1.5  1.5  1.5  1.5  1.5 1.5  21860.0352(10)  0.6  0.8  1.5  2.5  1.5  2.5  21 860.9912(10)  0.6  1.0  2.5  1.5  2.5  1.5  21 863.9711(10)  -0.5  2.8  2.5  3.5  2.5  3.5  21864.3830(10)  -0.1  3.5  2.5  2.5  2.5  2.5  21864.9720(10)  -0.3  0.1  0.5  0.5  1.5  1.5  21864.9830(10)  -2.1  3.4  3.5  4.5  2.5  3.5  21869.6081(10)  0.0  -2.8  3.5  3.5  2.5  2.5  21 869.6795(10)  0.4  7.5  1.5  0.5  0.5  0.5  21 873.8525(10)  -0.7  8.1  1.5  1.5  0.5  0.5  21 874.1917(10)  0.3  -0.8  1.5  2.5  0.5  1.5  21874.2853(10)  -1.1  0.7  0.5  1.5  0.5  0.5  21 879.0352(10)  -0.5  -0.6  0.5  1.5  0.5  1.5  21879.2584(10)  -0.8  -1.1  0.5  0.5  0.5  1.5  21 879.3661(10)  0.7  -1.4  1.5  0.5  0.5  0.5 '  1.5  2.5  0.5  1.5  22 214.3549(20)  -0.7  -0.9  1.5  1.5  0.5  1.5  2.5  2.5  2.5  2.5  22215.3194(10)  -0.3  -0.5  2.5  3.5  2.5  3.5  22 215.4270(10)  -0.7  -0.9  2.5  1.5  2.5  1.5  22 215.4672(10)  0.0  -0.2  . t  APPENDIX  A. MEASURED  TRANSITIONS  OF NITROSYL  CHLORIDE  139  Measured transitions of nitrosyl chloride cont'd  A /kHz with without J ,K -Jk K Ka  c  ai  F"  F  F'  v /MHz  1.5 1.5 0.5 0.5 0.5 1.5 1.5 1.5 0.5 0.5  1.5 2.5 0.5 1.5 1.5 2.5 2.5 1.5 0.5 1.5  2.5 2.5 0.5 0.5 0.5 1.5 1.5 1.5 1.5 1.5  2.5 3.5 1.5 1.5 0.5 2.5 1.5 1.5 0.5 2.5  22 223.9935(10) 22 224.1963(10)  0.1 0.2  -0.4 -0.7  22 226.6037(20)  - 0.2  -0.5  22 236.3912(10) 22 236.5915(10) 22 236.5954(10) 22 248.4817(10) 22 248.6381(10)  0.2 0.6 0.7 0.8 0.2  -0.1 -0.8 0.6 0.3 -0.2  2.5 2.5 2.5 2.5 1.5 1.5 2.5 1.5 2.5 1.5 1.5 3.5 3.5 3.5 1.5 1.5 0.5 0.5 0.5  1.5 3.5 2.5 3.5 0.5 1.5 2.5 2.5 3.5 2.5 1.5 4.5 2.5 3.5 1.5 2.5 1.5 1.5 0.5  1.5 1.5 1.5 2.5 1.5 1.5 2.5 1.5 2.5 1.5 1.5 2.5 2.5 2.5 0.5 0.5 0.5 0.5 0.5  0.5 2.5 1.5 2.5 0.5 0.5 2.5 2.5 3.5 1.5 1.5 3.5 1.5 2.5 0.5 1.5 0.5 1.5 1.5  22 578.9705(10) 22 579.9180(10) 22 580.9266(10)  0.1 0.2 0.1  -0.5 -0.6 -0.4  22 584.4884(20)  - 0.5  -0.2  22 584.8304(10) 22 584.8630(10) 22 585.1455(10) 22 585.1967(10) 22 585.7798(10) 22 586.0072(10) 22 592.3642(10) 22 592.5089(10) 22 592.9815(10) 22 594.5582(10) 22 594.6119(10) 22 601.7763(10) 22 602.0585(10) 22 602.1752(10)  0.7 0.3 0.3 0.3 1.0 0.3 0.1 0.4 0.0 0.3 0.0 0.2 0.2 0.2  1.1 0.2 0.4 0.3 1.8 0.9 0.4 -0.2 0.2 0.6 0.4 -1.1 -1.0 -1.0  c  a  X  a  b  Xa . b  2i,i — li,i  A. MEASURED  APPENDIX  TRANSITIONS  OF NITROSYL  CHLORIDE  140  Measured transitions of nitrosyl chloride cont'd  A /kHz with without Jh,K -Jk ,K c  a  c  FZ  F"  2.5 5.5 2.5 5.5 5.5 3.5 4.5 3.5 4.5 3.5 4.5  2.5 5.5 3.5 6.5 4.5 3.5 4.5 4.5 5.5 2.5 3.5  X  F>  3.5 6.5 3.5 6.5 6.5 4.5 5.5 4.5 5.5 4.5 5.5  3.5 6.5 4.5 7.5 5.5 4.5 5.5 5.5 6.5 3.5 4.5 37  5l,4  —  ujMHz  C 1  14 16 N  *  a  b  Xab  24 476.9545(10) 24477.0303(10) 24478.1298(10) 24 478.4288(10) 24 478.6777(10) 24 480.0922(10) 24 480.1254(10) 24 481.1097(10) 24481.3270(10) 24 481.3482(10) 24 481.4908(10)  0.0 -0.2 -0.8 0.2 0.7 -0.5 0.1 0.1 0.3 0.2 -0.2  0.6 -0.7 0.0 -0.3 0.2 -1.5 0.9 -0.9 1.0 -0.7 0.4  5175.9905 [10) 5176.3766 ;io) 5176.7934(;io) 5 176.8264(;io) 5177.4673(10) 5178.1271( 10) 5 178.4538(10) 5 178.5568(10) 5179.2042( 10) 5179.2296( 10) 5179.6962( 10) 5 180.9290(10) 5181.4105( 10)  0.4 0.2 0.5 0.1 0.9 0.4 0.4 0.8 0.0 0.9 -0.3 0.1 0.2  0.5 0.6 1.0 1.5 2.2 1.7 0.5 2.1 0.5 0.9 0.9 1.7 1.7  0  5i,5  5.5 5.5 5.5 4.5 4.5 6.5 3.5 6.5 5.5 3.5 4.5 4.5 6.5  5.5 4.5 6.5 3.5 5.5 5.5 2.5 7.5 5.5 4.5 4.5 4.5 6.5  4.5 5.5 5.5 4.5 4.5 6.5 3.5 6.5 5.5 3.5 4.5 5.5 6.5  5.5 4.5 6.5 3.5 5.5 5.5 2.5 7.5 5.5 4.5 4.5 4.5 6.5  APPENDIX  A. MEASURED  TRANSITIONS  OF NITROSYL  CHLORIDE  141  Measured transitions of nitrosyl chloride cont'd  A /kHz with without JK ,K^k ,K a  a  6l,5 ~ 6 i ,  30,8  F"  P  a  F'  v /MHz  3.5  3.5  3.5  3.5  5181.7945(10)  0.1  6.5  5.5  5.5  5.5  7 246.4065(10)  0.3  0.4  6.5  6.5  5.5  6.5  7 247.2206(10)  0.4  0.8  6.5  5.5  6.5  5.5  7 247.3003(10)  0.5  0.9  5.5  4.5  5.5  4.5  6.5  7.5  6.5  7.5  7 247.6513(20)  0.5 0.5  1.8  5.5  6.5  5.5  6.5  7 248.2515(10)  0.3  2.7  c  X  a  b  X  a  b  0.1  6  7.5  6.5  7.5  6.5  7 249.0627(10)  0.6  2.9  4.5  3.5  4.5  3.5  7 249.3498(10)  0.3  -0.3  7.5  8.5  7.5  8.5  7 249.4452(10)  0.1  2.4  4.5  5.5  4.5  5.5  7 249.9808(10)  0.2  -0.2  6.5  6.5  6.5  6.5  7 250.1926(10)  0.4  1.1  5.5  5.5  5.5  5.5  7 250.6397(10)  0.7  3.3  5.5  6.5  6.5  6.5  7 251.2229(10)  0.3  2.5  5.5  5.5  6.5  5.5  7 251.5332(10)  0.6  3.4  7.5  7.5  7.5  7.5  7 252.3599(10)  0.2  2.3  0.6  0.7  1.6  -1598.9  4.5  4.5  4.5  4.5  7 252.7038(10)  6.5  5.5  5.5  4.5  9 638.0202(10)  7l,7 7.5  6.5  6.5  5.5  9 638.2287(10)  1.5  -62.8  6.5  7.5  5.5  6.5  9 638.2941(10)  0.1  -1556.6  7.5  8.5  6.5  7.5  9 638.4054(10)  1.7  -52.5  9 639.6164(20)  0.0  -20.3  7.5  7.5  6.5  6.5  9.5  8.5  8.5  7.5  9.5  10.5  8.5  9.5  9 639.7862(10)  0.7  -0.6  6.5  6.5  5.5  5.5  9 639.8515(10)  0.2  -1348.2  9.5  9.5  8.5  8.5  9 641.1895(10)  0.8  -6.4  7.5  6.5  6.5  6.5  2.4  64.8  7.5  6.5  7.5  6.5  2.3  65.1  7l,6 — 7i,7  APPENDIX  A. MEASURED  TRANSITIONS  OF NITROSYL  142  CHLORIDE  Measured transitions of nitrosyl chloride cont'd  A /kHz with without J'K ,K -Jk ,K a  c  a  c  F&  F"  F'  7.5 6.5 5.5 6.5 5.5 7.5 6.5 6.5 5.5  8.5 5.5 4.5 7.5 6.5 7.5 6.5 6.5 5.5  7.5 6.5 5.5 6.5 5.5 7.5 6.5 7.5 5.5  8.5 5.5 4.5 7.5 6.5 7.5 6.5 6.5 5.5  1.5 1.5 1.5 1.5 1.5 1.5 2.5 2.5 2.5 2.5 0.5 0.5  1.5 1.5 1.5 2.5 0.5 0.5 1.5 1.5 3.5 2.5 1.5 1.5  1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5  0.5 2.5 1.5 2.5 0.5 1.5 0.5 1.5 2.5 1.5 2.5 1.5  8.5 8.5 7.5 8.5 8.5 7.5 9.5 6.5  7.5 7.5 6.5 8.5 9.5 8.5 8.5 5.5  7.5 8.5 7.5 7.5 8.5 7.5 9.5 6.5  v /MHz  X  a  b  X  a  b  9 663.2581(10) 9 664.7540(10) 9 664.9198(10) 9 665.1968(10) 9 665.4651(10) 9 665.9739(10) 9 667.5495(10) 9 668.2026(10) 9 668.2886(10)  -2.3 -0.3 -0.2 -0.1 -0.7 -1.3 -0.3 -0.4 0.0  61.4 1580.7 -0.2 1435.5 13.9 173.0 1330.9 1330.9 16.5  10 849.2647(10)  0.7  0.6  10 849.4667(10)  -0.4  -0.5  > 10 849.6249(10)  0.2  0.2  -  10 858.9841(10)  1.2  1.3  10859.0765(10) 10 859.2836(10)  0.1 -0.1  0.2 0.0  10 866.8581(10)  0.2  0.0  7.5 12 422.4296(10) 7.5 12 422.9216(10) 6.5 12 423.1114(10) 8.5 ' > 12 423.1448(20) 9.5 8.5 12423.7173(10) 8.5 12 424.6551(10) 5.5 12 424.8859(10)  0.4 0.2 1.2  0.3 0.2 -1.7  -0.2  -0.5  0.3 -0.2 -0.1  -1.5 -2.1 -0.1  ' , ' '  ' j  •  j  A. MEASURED  APPENDIX  TRANSITIONS  OF NITROSYL  143  CHLORIDE  Measured transitions of nitrosyl chloride cont'd  A /kHz with without Jk ,K-Jk J< a  a  c  F&  F"  FQ  F'  V /MHz  9.5 10.5 6.5 7.5 8.5 8.5 7.5 7.5 7.5 8.5 7.5 7.5 9.5 9.5 6.5 6.5  9.5 6.5 8.5 7.5 8.5 8.5 9.5 6.5  10.5 7.5 8.5 7.5 8.5 7.5 9.5 6.5  12 424.9689(10) 12 425.3445(10) 12 425.7608(10) 12 426.1705(10) 12 426.3345(10) 12 426.6630(10) 12 427.9597(10) 12 428.2325(10)  -0.1 0.1 0.8 -0.2 0.3 0.1 0.3 0.0  -2.0 0.0 -0.2 -2.8 -1.2 -2.5 -1.8 -0.1  3.5 6.5 3.5 6.5 3.5 6.5 5.5 4.5 4.5 5.5 5.5 4.5  4.5 7.5 4.5 7.5 4.5 7.5 6.5 5.5 5.5 6.5 6.5 5.5  4.5 7.5 5.5 8.5 3.5 6.5 6.5 5.5 6.5 7.5 5.5 4.5  14177.8741(10) 14177.8804(10) 14179.1524(10) 14179.2928(10) 14 179.4975(10) 14 179.5047(10) 14179.8165(10) 14 179.9021(10) 14 181.0200(10) 14 181.1020(10) 14 181.2120(10) 14181.2297(10)  1.0 -0.7 -0.0 0.0 1.1 -0.3 -0.0 0.1 0.3 -0.2 -0.4 -0.1  2.0 -0.9 1.1 -0.2 2.3 -0.5 0.9 -0.2 0.1 0.6 0.4 -0.2  8.5 7.5 8.5 9.5 10.5 9.5 8.5 9.5 8.5 10.5 9.5 10.5 7.5 6.5 7.5 10.5 11.5 10.5 7.5 8.5 7.5 9.5 9.5 9.5 8.5 8.5 9.5  7.5 10.5 9.5 9.5 6.5 11.5 8.5 9.5 8.5  15 527.0966(10) 15 527.1362(10) 15 527.2272(10) 15 528.6832(10) 15 528.8883(10) 15 528.9703(10) 15 529.2909(10) 15 530.2433(10) 15 530.5427(10)  0.3 0.2 -0.1 0.3 0.7 -0.2 0.0 0.1 -0.6  -1.3 0.3 -1.0 -0.6 0.6 -1.1 -0.1 -0.3 -2.0  3.5 6.5 4.5 7.5 2.5 5.5 5.5 4.5 5.5 6.5 4.5 3.5  X  X  a6  Xa6  APPENDIX  A. MEASURED  TRANSITIONS  OF NITROSYL  CHLORIDE  144  Measured transitions of nitrosyl chloride cont'd  A /kHz with without 1"  2l,2  -V  F"  F'  v /MHz  Xab  10.5 10.5 10.5 7.5 7.5 7.5  10.5 7.5  15 531.9863(10) 15 532.2269(10)  0.4 -0.2  -0.6. -0.3  21360.2912(10) 21361.9308(10) 21 362.7101(10) 21364.6803(10) 21 366.3692(10) 21 367.2834(10) 21 367.8742(10) 21 371.4641(10) 21 371.4716(10) 21 371.5659(10) 21375.2752(10) 21378.9349(10) 21379.2004(10) 21379.3392(10)  0.2 0.2 0.1 0.5 -1.0 -0.6 -0.4 -0.3 1.3 0.4 -0.6 -0.1 -0.3 -0.0  1.5 1.5 1.3 0.7 0.4 0.7 0.9 2.6 4.0 3.3 -0.4 -0.4 -0.7 -0.4  21 703.4284(20)  0.3  0.2  21 704.2833(10) 21704.3222(10)  -0.2 -0.2  -0.3 -0.4  21 713.0994(10)  0.2  0.0  21713.6809(10) 21713.9376(10) 21 713.9525(10) 21 713.9958(10) 21 714.1927(10) 21 720.8196(10) 21 721.0272(10)  0.2 -0.6 -0.3 0.1 -0.7 0.1 0.6  0.2 -0.6 -0.3 0.1 -0.7 -0.0 0.5  Xab  —  2.5 2.5 2.5 1.5 2.5 2.5 2.5 3.5 3.5 3.5 1.5 0.5 0.5 0.5  2.5 3.5 1.5 2.5 2.5 3.5 2.5 4.5 2.5 3.5 2.5 1.5 1.5 0.5  1.5 1.5 1.5 1.5 2.5 2.5 2.5 2.5 2.5 2.5 0.5 0.5 0.5 0.5  1.5 2.5 0.5 2.5 1.5 3.5 2.5 3.5 1.5 2.5 1.5 0.5 1.5 1.5  1.5 1.5 2.5 2.5 0.5 0.5 2.5 3.5 3.5 3.5 2.5 1.5 1.5  0.5 2.5 3.5 1.5 1.5 0.5 1.5 4.5 2.5 3.5 2.5 2.5 1.5  0.5 0.5 2.5 2.5 0.5 0.5 1.5 2.5 2.5 2.5 1.5 1.5 1.5  0.5 \ 1.5 J 3.5 1.5 1.5 1 1.5 J 0.5 3.5 1.5 2.5 1.5 2.5 1.5  2o,2 lo,i —  APPENDIX  A. MEASURED  TRANSITIONS  OF NITROSYL  CHLORIDE  145  Measured transitions of nitrosyl chloride cont'd  Jk ,K -Jk K a  c  a<  c  F&  F"  F*  F'  2.5 2.5 1.5 2.5 1.5 2.5 2.5 3.5 3.5 3.5 1.5 1.5 0.5 0.5 0.5  3.5 2.5 1.5 2.5 2.5 1.5 3.5 4.5 2.5 3.5 1.5 2.5 1.5 1.5 0.5  1.5 1.5 1.5 2.5 1.5 2.5 2.5 2.5 2.5 2.5 0.5 0.5 0.5 0.5 0.5  2.5 1.5 0.5 2.5 2.5 \ 1.5 J 3.5 3.5 1.5 2.5 0.5 1.5 0.5 1.5 1.5  2.5 5.5 2.5 5.5 2.5 5.5 4.5 3.5 3.5 4.5 3.5 4.5  2.5 5.5 3.5 6.5 1.5 4.5 4.5 3.5 4.5 5.5 2.5 3.5  3.5 6.5 3.5 6.5 3.5 6.5 5.5 4.5 4.5 5.5 4.5 5.5  3.5 6.5 4.5 7.5 2.5 5.5 5.5 4.5 5.5 6.5 3.5 4.5  a  „/MHz  A /kHz with without a» Xab X  2i,i — l i , o  22 052.1267 ;io) 22 053.0697 ;io) 22 055.9960 ;io) 22 056.0310 ;io)  0.2 0.2 0.3 0.0  -0.1 0.2 0.5 -0.1  22 056.2232 ;20)  -0.2  0.1  22 056.3821 ;io) 22 062.0175 ;io) 22 062.22181;io) 22 062.660K;io) 22 063.8332(;io) 22 063.8880(10) 22 069.5127(10) 22 069.8726(10) 22 070.0219( 10)  0.2 -0.1 -0.2 -0.1 -0.1 0.2 -0.3 0.3 -0.2  0.2 0.1 -0.1 0.1 0.1 0.5 -0.8 -0.2 -0.7  25 861.6332( 10) 25 861.6667( 10) 25 862.8072( 10) 25 863.0651( 10) 25 863.2556( 10) 25 863.3159( 10) 25 864.1317( 10) 25 864.1798( 10) 25 865.1705( 10) 25 865.3404( 10) 25 865.3973( 10) 25 865.4707( 10)  -0.9 -0.0 -0.0 -0.1 0.4 -0.6 0.5 0.0 0.1 0.6 0.4 -0.9  -0.6 -0.4 0.3 -0.5 0.8 -1.0 0.9 -0.8 -0.7 1.0 -0.3 -0.6  A. MEASURED  APPENDIX  TRANSITIONS  OF NITROSYL  CHLORIDE  146  Measured transitions of nitrosyl chloride cont'd  A /kHz with without T" J  K  a  -V  , I < c  J  K a , K c  F&  F"  Fc,  u /MHz  F'  Xab  X.ab  35 15 16Q C 1  6l,5 - 6 i ,  5l,5  7l,6  lo,i  —  —  —  N  6  6.5  7  6.5  7  6.5  6  6.5  6  5.5  6  5.5  6  5.5  5  5.5  5  7.5  8  7.5  8  7.5  7  7.5  7  4.5  5  4.5  5  4.5  4  4.5  4  6.5  7  7.5  8  6.5  6  7.5  7  4.5  5  5.5  6  9156.2175(10)  1.1  1.0  4.5  4  5.5  5  9 156.2218(10)  -0.6  -0.8  7.5  8  7.5  8  7.5  7  7.5  7  10 396.5264(20)  -0.2  -0.2  6.5  7  6.5  7  6.5  6  6.5  6  10 396.9996(20)  0.4  -8.6  8.5  9  8.5  9  8.5  8  8.5  8  10 398.9562(20)  -0.4  -6.9  5.5  6  5.5  6  5.5  5  5.5  5  10 399.4218(20)  0.5  0.5  1.5  2  1.5  2  1.5  1  1.5  1  11006.3278(20)  -0.4  -0.5  2.5  3  1.5  2  2.5  2  1.5  1  11018.6844(20)  0.0  0.1  7 797.8279(20)  -0.3  0.6  7 798.3981(20)  -0.2  8.3  7 800.2692(20)  -0.2  6.8  7 800.8049(20)  0.2  0.2  9153.9255(10)  0.1  -0.2  9153.9314(10)  -0.6  -0.8  60,6  7l,7  0o,o  APPENDIX  A.  MEASURED  TRANSITIONS  OF NITROSYL  147  CHLORIDE  Measured transitions of nitrosyl chloride cont'd  A /kHz with without Jk ,K ~Jk ,K a  a  c  4l,4  2o,2  F&  F"  F  0.5  1  1.5  2  0.5  1  1.5  1  5.5  6  6.5  5.5  5  2.5 2.5  C1  F'  v /MHz  X  a  b  X  a  b  11028.5323(10)  -0.1  -0.3  7  21054.9262(40)  -1.3  -1.7  6.5  6  21054.9376(40)  1.2  0.7  3  1.5  2  2  1.5  1  21651.6264(20)  0.9  52.5  1.5  2  1.5  2  1.5  1  1.5  1  21655.0902(20)  0.9  0.8  2.5  2  2.5  2  21658.9427(10)  0.1  51.6  2.5  3  2.5  3  21658.9575(10)  0.1  51.5  3.5  3  2.5  2  21663.9774(20)  -2.6  88.9  3.5  4  2.5  3  21663.9921(20)  1.8  93.3  5o,5  —  2l,2  c  —  —  1.5  2  0.5  1  21668.3999(10)  -0.1  0.0  1.5  1  0.5  0  21668.4371(10)  -0.7  -0.7  1.5  2  0.5  1  1.5  1  0.5  0  22 0 1 8 . 5 9 1 0 ( 2 0 )  -0.4  -0.5  2.5  3  2.5  3  2.5  2  2.5  2  22 0 1 9 . 6 4 0 3 ( 2 0 )  -0.0  -0.3  1.5  2  2.5  3  22 028.4395(10)  0.5  0.1  0.5  1  0.5  1  0.5  1  0.5  0  22 030.9112(20)  -0.2  -0.5  0.5  0  0.5  1  2.5  3  1.5  2 22 0 3 1 . 9 9 6 9 ( 2 0 )  -0.8  -0.8  22 040.7954(20)  -0.0  -0.3  lo,i  3.5  4  2.5  3  2.5  2  1.5  1  3.5  3  2.5  2  1.5  2  1.5  2  1.5  1  1.5  1  APPENDIX  A. MEASURED  TRANSITIONS  OF NITROSYL  148  CHLORIDE  Measured transitions of nitrosyl chloride cont'd  JL,K -J'K.,K C  C\  F"  2.5 2.5 2.5 2.5 1.5 1.5 3.5 3.5 1.5 1.5 0.5 0.5 0.5  3 2 2 3 2 1 3 4 2 1 1 1 0  F C  F'  iz/MHz  A /kHz with without Xab  X a b  2i,i — li,o 1.5 1.5 2.5 2.5 1.5 1.5 2.5 2.5 0.5 0.5 0.5 0.5 0.5  2 1 2 3 2 1 2 3 1 0 1 0 1  37  C 1  15 16 N  22 394.7338(20)  0.5  0.1  22 399.6222(10) 22 399.6374(10)  -0.7 0.1  -0.7 0.0  22 399.9757(20)  -0.9  -0.2  22 407.0492(10) 22 407.0617(10) 22 408.9260(10) 22 408.9652(10) 22416.2919(10)  -1.2 1.6 0.1 0.2 0.5  -0.9 1.9 0.5 0.6 -0.4  22 416.3129(20)  -0.4  -1.3  10 749.8150(20)  -0.0  -0.1  10 759.5703(20)  0.1  0.2  10 767.3449(20)  -0.1  -0.2  21 153.1646(20)  0.3  4.8  21 155.9308(20)  0.9  0.8  0  lo,i - 0,0,0  2i, - 1 1,1  1.5 1.5 2.5 2.5 0.5 0.5  2 1 3 2 0 1  1.5 1.5 1.5 1.5 1.5 1.5  2 1 2 1 1 2  2.5 2.5 1.5 1.5  3 2 2 1  1.5 1.5 1.5 1.5  2 1 2 1  2  APPENDIX  A. MEASURED  TRANSITIONS  OF NITROSYL  149  CHLORIDE  Measured transitions of nitrosyl chloride cont'd  A /kHz with without J'k j< -J'K ,K a  c  2 ,2 0  a  F"  c  - 10,1  F  F'  a  2.5 2.5 3.5 3.5 1.5 1.5 1.5 0.5 0.5 0.5  2 3 3 4 2 1 1 1 0 1  2.5 2.5 2.5 2.5 0.5 0.5 0.5 0.5 0.5 0.5  2 3 2 3 1 1 0 1 1 0  1.5 1.5 1.5 2.5 2.5 0.5 0.5 0.5 2.5 3.5 2.5 3.5 1.5 1.5 0.5 0.5  2 1 1 3 2 1 1 0 3 4 2 3 2 1 1 0  0.5 0.5 0.5 2.5 2.5 0.5 0.5 0.5 1.5 2.5 1.5 2.5 1.5 1.5 1.5 1.5  1 1 0 3 2 1 0 1 2 3 1 2 2 1 2 1  2.5 2.5 2.5  3 2 2  1.5 1.5 2.5  2 1 2  v/MKz  21 21 21 21 21 21 21 21  a  X  b  Xa  b  158.9428(10) 158.9613(10) 162.8866(10) 162.9013(10) 166.4506(10) 166.4677(10) 166.4876(10) 170.3468(10)  -1.3 1.1 -1.6 1.8 1.2 -0.5 -1.8 1.2  3.0 5.4 7.0 0.3 1.2 -0.4 -1.8 0.8  21 170.3673(20)  -0.8  -1.2  21504.1297(10)  -0.0  -0.2  21 504.9577(20)  -0.5  -0.7  21513.8574(20)  0.1  -0.2  21514.7157(20)  1.4  1.4  21521.6599(20)  0.2  -0.0  21531.3868(20)  -0.7  -1.0  21862.7125(20)  0.5  0.3  21866.5592(10)  -1.5  -1.5  2i,i — li,o  APPENDIX  A. MEASURED  TRANSITIONS  OF NITROSYL  CHLORIDE  150  Measured transitions of nitrosyl chloride cont'd  A /kHz with without J'LK^K^  4l,4  —  F&  F"  2.5  3  F  I//MHZ  2.5  3  21 866.5776(10)  1.1  1.1  21 866.8546(20)  -0.7  -0.2  0 l l  Xa  b  1.5  2  1.5  2  1.5  1  1.5  1  3.5  3  2.5  2  21872.4327(10)  -1.1  -0.9  3.5  4  2.5  3  21872.4459(10)  1.1  1.3  0.5  1  1.5  2  21872.6768(10)  0.7  0.3  1.5  2  0.5  1  21873.9073(10)  0.2  0.6  0.5  1  0.5  1  21879.7285(10)  -0.1  -0.7  0.5  1  0.5  0  0.5  0  0.5  1  21879.7497(20)  -1.7  -2.3  2.5  3  3.5  4  22 4 5 3 . 6 4 2 4 ( 4 0 )  -1.9  -1.2  2.5  2  3.5  3  22 4 5 3 . 6 5 3 8 ( 4 0 )  -0.8  -0.2  5.5  6  6.5  7  22 4 5 3 . 8 0 8 9 ( 4 0 )  -1.2  -1.6  5.5  5  6.5  6  22 453.8222(40)  1.5  1.1  3.5  4  4.5  5  22 456.0388(40)  1.5  0.9  3.5  3  4.5  4  22 456.0486(40)  1.4  1.1  4.5  5  5.5  6  22 456.2097(40)  -1.1  -0.6  4.5  4  5.5  5  22 456.2211(40)  0.4  0.9  10 532.7072(10)  -0.2  10 532.8996(10)  -0.2  10 533.0499(10)  0.3  5 ,5 0  35  l  a0  X  C  1  14  N  18  0  - 00,0 1.5  1.5  1.5  0.5  1.5  1.5  1.5  2.5  1.5  1.5  1.5  1.5  1.5  2.5  1.5  2.5  1.5  0.5  1.5  0.5  1.5  0.5  1.5  1.5  APPENDIX  A. MEASURED  TRANSITIONS  OF NITROSYL  151  CHLORIDE  Measured transitions of nitrosyl chloride cont'd  A /kHz  with F"  Jk ,K -Jk ,K a  c  a  c  F'  2.5 2.5 2.5 2.5 0.5 0.5 0.5 0.5  1.5 1.5 3.5 2.5 0.5 0.5 1.5 1.5  1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5  0.5 1.5 2.5 1.5 0.5 1.5 2.5 1.5  2.5 2.5 1.5 2.5 1.5  2.5 3.5 2.5 3.5 2.5  1.5 1.5 1.5 2.5 0.5  1.5 2.5 2.5 3.5 1.5  1.5 1.5 1.5 2.5 0.5 0.5 2.5 2.5 3.5 3.5 3.5 2.5 2.5 1.5 1.5 1.5  0.5 2.5 1.5 3.5 0.5 1.5 1.5 3.5 4.5 2.5 3.5 1.5 2.5 2.5 2.5 1.5  0.5 0.5 0.5 2.5 0.5 0.5 1.5 1.5 2.5 2.5 2.5 1.5 1.5 1.5 1.5 1.5  0.5 1.5 1.5 3.5 1.5 1.5 0.5 2.5 3.5 1.5 2.5 1.5 1.5 2.5 1.5 1.5  WMHz  a„  X  10 544.8326(10)  0.2  10 544.9212(10) 10 545.1185(10)  -0.1 0.1  10 554.6171(10)  -0.2  10 554.6217(10)  0.1  20 738.1541(10) 20 739.7333(10) 20 743.2033(10) 20 746.4242(10) 20 756.1866(10)  0.3 0.7 -0.5 -0.1 -0.3  21071.7745(20)  0.1  21072.8307(10)  0.4  21083.8490(20)  1.9  21084.6513(10) 21084.8516(10) 21084.8964(20) 21084.9065(20) 21084.9499(10) 21084.9936(10) 21085.1374(10) 21093.4970(10)  0.2 -0.3 0.4 -1.5 -0.7 0.2 -0.5 0.6  21093.6902(20)  -0.3  without X  a  »  APPENDIX  A. MEASURED  TRANSITIONS  OF NITROSYL  152  CHLORIDE  Measured transitions of nitrosyl chloride cont'd  A /kHz with without Jk ,K^k ,K a  a  c  F&  F"  F  F'  I//MHZ  Xa  2.5 2.5 2.5 1.5 2.5 3.5 3.5 3.5 1.5  3.5 3.5 2.5 2.5 3.5 4.5 2.5 3.5 2.5  1.5 2.5 2.5 1.5 2.5 2.5 2.5 2.5 0.5  2.5 2.5 2.5 2.5 3.5 3.5 1.5 2.5 1.5  21412.2011(10) 21416.7705(10) 21 417.1417(10) 21 417.3023(10) 21417.4805(10) 21424.4736(10) 21424.6243(10) 21425.0803(10) 21426.7653(10)  -0.4 0.0 0.1 -0.2 -0.3 -0.1 0.3 0.7 -0.1  a  b  2i,i — li,o  Xa  b  Appendix B Measured transitions of Sulphur Difluoride  Table B.l: Transitions of sulphur difluoride Jk,K -Jk.jc c  c  This work: 5, 61,6 —  2 3  -4  32,1  M  2o,2 —  22,0  3i,3  — 3 ,2 ll.o -lo.l  4l,3  2i,i  2  —  2Q,2  I" F" F  F'  v /MHz  1 1 1 1 1 1 0 0 0 1  1 1 1 1 1 1 0 0 0 1  4 5 6 5 4 3 1 3 3 2  5 500.1578(50) 5 500.2176(50) 5 500.2917(50) 5934.7779(10) 5 934.8352(10) 5 934.8706(10) 14175.9558(10) 15 979.0300(20) 18 727.7059(10) 20 084.3027(10)  -5.9 -6.6 -6.9 -0.7 -0.2 -0.6 0.0 0.1 -0.9 -1.0  1 0 1 1 1 1 0 2 0  !  20 084.3376(10)  1.3  22 672.1355(10)  0.2  5 6 7 4 3 2 2 2 4 2  2  Ref 95: 22,0 2i,i 2l,2 fo,i  53 372.52(3) 47 468.04(1) 50 843.68(2) 63 931.79(20) 31 725.57(10)  —  —  32,1  —  3i,2  32,2 ~~ 3i,3  3o,3  2 4 ,2 - 4i, —  li2  2  4o,4  —  33,0  —  48 531.28(2)  3  49 356.29(1) 30574.90(10)  31,3 42,3  153  A /kHz  -40 50 -20 -90 -10 -30 20 -10  APPENDIX  B. MEASURED  TRANSITIONS  OF SULPHUR  DIFLUORIDE  Transitions of sulphur difluoride cont'd  TI  Til J  K  a  , I < c  K  J  5j,4  52,3  —  44,0  —  ^3,3  44,1  —  5,  61,5 62,5 62,4 7  2,5  , K c  a  3 2  -  60,6 61,6 61,5  7l,6  —  65,1 ~ ^4,4 65,2  —  ^4,3  82,6  —  81,7  82,7 8 ,6  73,4  —  73,5  —  2  9 ,7 - 9 2  li8  92,8 83,5 —  93,6  —  84,5  85,3  —  94,6  10 ,7 - 9 ,6 3  4  112,9  12  —  lil2  123,10 H4,7 117,4 126,7 117,5 ~ 126,6 —  —  132,12  —  123,9  134,10 125,7 134,9 125,8 127,5 136,8 127,6 136,7 —  —  —  —  14 ,n - 13 , 4  5 8  145,10 136,7 13 ,5 - 14 , —  7 8  8  13 - 14 , 8i6  7 7  155,10 166,11 166,10  —  183,16  —  —  —  146,9 157,8 157,9 174,13  v /MHz  47175.57(1) 50 967.20(20) 50 607.46(35) 53 243.12(10) 82 714.08(20) 47 452.06(1) 49 896.43(1) 55 882.37(10) 55 779.28(10) 54911.76(2) 22211.41(5) 58 024.02(20) 62 764.65(10) 30 324.25(20) 24 228.48(10) 22 273.96(10) 46 681.81(15) 44 515.86(20) 53 754.47(20) 48 879.05(25) 48 858.43(35) 25.287.22(50) 44 925.53(20) 57394.37(20) 31 830.16(15) 31 774.72(15) 60 520.62(20) 25 190.53(15) 53 741.29(20) 53 736.24(20) 47150.74(20) 20 591.22(15) 21 258.97(15) 48 293.34(20)  A /kHz 0 0 90 110 200 .0 10 90 40 -20 50 140 40 100 40 -30 140 500 -190 -80 -10 -50 20 0 -30 -40 -100 10 -140 -90 0 30 80 60  APPENDIX  B. MEASURED  TRANSITIONS  OF SULPHUR  DIFLUORIDE  Transitions of sulphur difluoride cont'd  T"  V  v  17g,8 — 188,11 17g,9 — 188,10  20  - 19 ,n — 19s,12  7)14  8  2O743  19io,9  2O942  —  19io,io  2O941  22s,i4 —  2I9J3  —  23 2i 22io,i2 23g,i4 — 22io,i3 22i2,n — 23n,i2 244, i 235,18 24i2,i2 25n,i5 24i2,i3 25n,i4 26i4,i3 — 27i3,i4 275,22 28,25 28n,i8 27i ,i5 224,1s 23945  —  3|  —  —  2  —  —  —  4  —  2  28n,i7 —  305,26  —  27i2,i6  296,23  29i3,i6 29i3,i7  30i2,l9 — 30i2,18  —  32i ,21 — 3113,18 2  32i2,20  —  3113,19  33i6,i7 34 o 33i7,i6 — 34i ,i9 34i7,is — 35i6,19 —  152  6  35i7,i8 — 36i6,21 35i8,17 36i7,20 37i5,2 — 36i6,21 —  2  37is,19  —  38i7,22  39l6,23 — 38i7,22 43i7,26 — 42is,25  /MHz  24 345.49(15) 24 336.89(15) 51642.91(10) 52 415.70(20) 29 185.13(16) 29183.02(16) 46 628.74(10) 49 768.04(15) 23 289.53(10) 23 316.19(10) 55 809.15(20) 51 429.83(15) 21522.98(15) 21 522.68(15) 65 075.18(10) 42 519.45(10) 30 934.31(15) 30 937.96(15) 43 967.09(15) 25 939.68(15) 25 940.55(15) 61470.80(10) 61 474.80(10) 23 068.04(10) 61 638.47(10) 44 673.70(20) 27 633.05(15) 66 033.10(20) 28 784.50(15) 32131.31(15) 23 993.48(15) 53 973.05(30)  A /kHz 10 20 130 -10 10 -20 60 -520 -20 -10 30 -160 -60 -70 30 100 -40 -30 80 0 -10 110 -70 60 80 -20 0 -110 -70 -200 -40 -20  Bibliography  [1] C. 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