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Oscillator strengths for photoabsorption and photoionization processes of feron and NO₂ molecules Zhang, Wenzhu 1991

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OSCILLATOR STRENGTHS FOR PHOTOABSORPTION AND PHOTOIONIZATION PROCESSES OF FREON AND N02 MOLECULES By Wenzhu Zhang B. Sc. (Physics) Tsinghua University, Beijing, China, 1982 A THESIS SUBMITTED IN THE REQUIREMENTS DOCTOR OF PARTIAL FULFILLMENT OF FOR THE DEGREE OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES CHEMISTRY We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September 1991 © Wenzhu Zhang, 1991 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver, Canada DE-6 (2/88) Abstract Absolute photoabsorption differential oscillator strengths (cross sections) for N Is and 0 Is inner shell excitation and ionization of N02 have been derived from the presently obtained high resolution electron energy loss spectra using dipole (e,e) spectroscopy. The N02 inner shell differential oscillator strength spectra are in good agreement with multi channel quantum defect theory calculations in both excitation energies and (differential) osciUator strengths. The N02 spectra were interpreted with the aid of the calculations. A resonance present in both the N02 N Is and 0 Is ionization continua was identified as excitation to an unbound molecular orbital. A consideration of the present spectra for N02 and earlier spectra for other molecules showed that additional prominent structures observed in previously reported N02 inner shell photoabsorption spectra obtained using synchrotron radiation were due to the presence of impurities. Absolute photoabsorption differential oscillator strengths for the valence sheUs of CF4, CF3CI, CF2C12 and CFCI3 have been measured in the equivalent photon energy range up to 200 eV using dipole (e,e) spectroscopy. The present results are in good agreement with earher reported optical measurements and electron impact measurements. The photoionization efficiencies and also the photoion branching ratios have been determined for CF4, CF3CI, CF2C12 and CFCI3 from time of flight mass spectra using dipole (e,e+ion) coincidence spectroscopy at equivalent photon energies ranging up to 80 eV. Absolute partial differential oscillator strength spectra for the molecular and dissociative photoions have been derived. The natures of the dipole induced breakdown pathways of CF4, CF3CI and CF2C12 were investigated by combining the present differential oscillator strength 11 measurements for molecular and dissociative photoionization with photoelectron data obtained in the present thesis work plus previously reported photoelectron branching ratios. On the basis of the present work, a revised set of absolute electronic state partial photoionization differential oscillator strengths for CF4 are presented. Absolute electronic state partial photoionization differential osciUator strength spec tra for CF3CI, CF2C12 and CFCI3 in the photon energy range 41—160 eV have been derived by combining total differential oscillator strength spectra obtained in the present thesis work with photoelectron branching ratios obtained from photoelectron spectra measured using synchrotron radiation. Absolute photoabsorption differential osciUator strengths and for F Is, C Is, and Cl 2p,2s inner shell excitation and ionization of freon molecules CF4, CF3C1, CF2C12, CFCI3 and CCI4 have been derived from the presently obtained high resolution electron energy loss spectra plus previously reported. Tentative assignments of the spectra were obtained using the MO picture and the potential barrier model. iii Table of Contents Abstract ii List of Tables viiList of Figures x List of Abbreviations xiii Acknowledgements xiv 1 Introduction 1 2 Photoabsorption and Electron Energy Loss Spectra 5 2.1 Photoabsorption Cross Section and Differential Oscillator Strength .... 6 2.2 The Bethe-Born Theory of Fast Electron Impact 9 2.3 Spectral Analysis 17 2.3.1 Occupied and Unoccupied Molecular Orbitals 17 2.3.2 Transitions to Rydberg Orbitals 19 2.3.3 Transitions to Virtual Valence Orbitals 21 2.3.4 Transitions to Ionization Continua2.3.4.1 Delayed Onsets of Ionization Continua 22 2.3.4.2 XANES and EXAFS 22.3.4.3 Atomic and Molecular Photoionization at High Photo-electron Energies 23 iv 2.3.5 Photoelectron Spectroscopy and Dipole (e,e-fion) Spectroscopy . . 23 2.3.6 Potential Barrier Effects . . 25 2.3.7 The Equivalent Core (Z + 1) Analogy 26 2.3.8 The Absolute Differential Oscillator Strength Scale 26 3 Experimental Methods 28 3.1 The Dipole (e,e+ion) Spectrometer 23.2 The High Resolution Dipole (e,e) Spectrometer 32 3.3 Energy Calibration 36 3.4 Sample Handling 7 4 Inner Shell Electron Energy Loss Spectra of N02 at High Resolution: Comparison with Multichannel Quantum Defect Calculations of Dipole Oscillator Strengths and Transition Energies 39 4.1 Calculations 34.2 Results and Discussion 41 5 Absolute Differential Oscillator Strengths for the Photoabsorption and the Ionic Photofragmentation of CF4, CF3C1, CF2C12 and CFC13 59 5.1 Electronic Structures 55.2 Photoabsorption Differential Oscillator Strengths for the Valence Shells . 59 5.2.1 The CF4 Photoabsorption Differential Oscillator Strengths .... 80 5.2.2 The CF3C1 Photoabsorption Differential Oscillator Strengths ... 83 5.2.3 The CF2CI2 Photoabsorption Differential Oscillator Strengths . . 86 5.2.4 The CFC13 Photoabsorption Differential Oscillator Strengths ... 90 v 5.2.5 Comparison of the Photoabsorption Differential Oscillator Strengths of CF4, CF3CI, CF2C12 and CFC13 93 5.3 The CF4 Photoabsorption Differential OsciUator Strengths for the C Is and F Is Inner Shells and the Valence SheU Extrapolation 94 5.4 Molecular and Dissociative Photoionization of CF4, CF3CI, CF2C12 and CFCI3 97 5.5 Absolute Electronic State Partial Photoionization Differential OsciUator Strengths for CF4 124 5.6 The Dipole Induced Breakdown 128 5.6.1 The Dipole Induced Breakdown of CF4 129 5.6.2 The Dipole Induced Breakdown of CF3C1 132 5.6.3 The Dipole Induced Breakdown of CF2C12 136 6 Photoelectron Spectroscopy and the Electronic State Partial Differen tial Oscillator Strengths of the Freon Molecules CF3C1, CF2C12 and CFCI3 Using Synchrotron Radiation from 41 to 160 eV 141 6.1 Photoelectron Spectra 142 6.2 Photoelectron Branching Ratios and Partial Photoionization Differential OsciUator Strengths 145 7 Absolute Dipole Differential Oscillator Strengths for Inner Shell Spec tra from High Resolution Electron Energy Loss Studies of the Freon Molecules CF4, CF3C1, CF2C12, CFC13 and CC14 164 7.1 Absolute Differential OsciUator Strengths 167.2 Electronic Configurations and Spectral Assignments 167 7.3 C Is Spectra 170 vi 7.4 F Is Spectra 180 7.5 Cl 2s and 2p Spectra 183 8 Conclusions 190 Bibliography 1 vii List of Tables 3.1 Reference energies of spectral calibration 37 3.2 Sources and purity of samples 38 4.3 Dipole-allowed transitions for N02 42 4.4 Experimental and calculated data for N Is excitation of N02 45 4.5 Experimental and calculated data for 0 Is excitation of N02 55 4.6 Term values for N02 and its Z+l analogue 03 57 5.7 Valence electronic configurations for CF4, CF3C1, CF2C12 and CFC13 . . 60 5.8 Electronic ion states for CF4 61 5.9 Electronic ion states for CF3C1 2 5.10 Electronic ion states for CF2C12 63 5.11 Electronic ion states for CFC13 4 5.12 Differential oscillator strengths for CF4 65 5.13 Differential oscillator strengths for CF3C1 8 5.14 Differential oscillator strengths for CF2C12 71 5.15 Differential oscillator strengths for CFC13 4 5.16 Coefficients of the valence shell extrapolation formulas 79 5.17 Photoion branching ratios for CF4 107 5.18 Photoion branching ratios for CF3C1 9 5.19 Photoion branching ratios for CF2C12 Ill 5.20 Photoion branching ratios for CFCI3 113 viii 5.21 Ion appearance potentials for CF4 120 5.22 Ion appearance potentials for CF3CI 1 5.23 Ion appearance potentials for CF2Cl2 122 5.24 Ion appearance potentials for CFCI3 3 5.25 Electronic state partial differential oscillator strengths for CF4 126 6.26 Ionization energies for CF3C1, CF2C12 and CFC13 144 6.27 Photoelectron branching ratios for CF3C1 146 6.28 Photoelectron branching ratios for CF2C12 147 6.29 Photoelectron branching ratios for CFC13 148 6.30 Electronic state partial differential oscillator strengths for CF3C1 154 6.31 Electronic state partial differential oscillator strengths for CF2CI2 .... 155 6.32 Electronic state partial differential oscillator strengths for CFCI3 156 7.33 Inner shell atomic oscillator strengths for C,F and Cl atoms 166 7.34 Integrated sub-shell oscillator strengths per atom for CF4, CF3C1, CF2C12, CFCI3 and CC14 167.35 Electronic configurations for CF4, CF3C1, CF2C12, CFC13 and CC14 ... 168 7.36 Dipole-allowed transitions for CF4, CF3C1, CF2C12 and CFC13 169 7.37 Experimental data for the inner shell excitations of CF3C1 174 7.38 Experimental data for the inner shell excitations of CF2C12 175 7.39 Experimental data for the inner shell excitations of CFC13 176 7.40 Experimental data for the inner shell excitations of CF4 and CC14 .... 177 ix List of Figures 2.1 Schematic of scattering geometry 10 3.2 Schematic of the dipole (e,e+ion) spectrometer 29 3.3 Schematic of the high resolution dipole (e,e) spectrometer 33 4.4 Calculated quantum defects for N02 40 4.5 ISEELS spectra for N02 N Is excitation in the discrete and continuum regions 43 4.6 ISEELS spectra for N02 N Is excitation in the pre-ionization edge region 44 4.7 N02 sample purity investigation 47 4.8 Comparison of ISEELS spectra with earher optical measurements for N02 49 4.9 ISEELS spectra for N02 0 Is excitation in the discrete and continuum regions 53 4.10 ISEELS spectra for N02 0 Is excitation in the discrete region 54 5.11 Differential oscillator strengths for valence shell photoabsorption of CF4 . 81 5.12 Differential oscillator strengths for valence shell photoabsorption of CF3CI 84 5.13 Differential oscillator strengths for valence shell photoabsorption of CF2C12 87 5.14 Differential oscillator strengths for valence shell photoabsorption of CFCI3 91 5.15 Differential osciUator strengths for valence shell and inner shell photoab sorption of CF4 95 5.16 TOF mass spectrum of CF4 at an equivalent photon energy of 80 eV . . 98 5.17 TOF mass spectrum of CF3CI at an equivalent photon energy of 45 eV . 99 x 5.18 TOF mass spectrum of CF2CI2 at an equivalent photon energy of 50 eV . 100 5.19 TOF mass spectrum of CFCI3 at an equivalent photon energy of 49 eV . 101 5.20 Photoion branching ratios for CF4 103 5.21 Photoion branching ratios for CF3C1 4 5.22 Photoion branching ratios for CF2CI2 105 5.23 Photoion branching ratios for CFCI3 6 5.24 Differential oscillator strengths for dissociative photoionization of CF4 . . 116 5.25 Differential oscillator strengths for molecular and dissociative photoioniza tion of CF3CI 117 5.26 Differential oscillator strengths for dissociative photoionization of CF2C12 118 5.27 Differential oscillator strengths for dissociative photoionization of CFCI3 119 5.28 Electronic state partial photoionization differential oscillator strengths for CF4 127 5.29 Differential oscillator strengths for the dipole induced breakdown scheme ofCF4 130 5.30 Dipole induced breakdown scheme for CF4 131 5.31 Differential oscillator strengths for the dipole induced breakdown scheme of CF3CI 133 5.32 Dipole induced breakdown scheme for CF3C1 134 5.33 Differential oscillator strengths for the dipole induced breakdown scheme ofCF2Cl2 139 5.34 Dipole induced breakdown scheme for CF2CI2 140 6.35 Photoelectron spectra of the freon molecules 143 6.36 Photoelectron branching ratios for CF3C1 149 xi 6.37 Photoelectron branching ratios for CF2CI2 150 6.38 Photoelectron branching ratios for CFCI3 151 6.39 Electronic state partial differential osciUator strengths for CF3CI 157 6.40 Electronic state partial differential osciUator strengths for CF2C12 .... 158 6.41 Electronic state partial differential osciUator strengths for CFC13 159 7.42 C Is differential oscillator strength spectra for CF4, CF3C1, CF2C12, CFC13 and CCI4 in the discrete region 172 7.43 C Is differential oscillator strength spectra for CF4, CF3CI, CF2C12, CFC13 and CCI4 in the discrete and continuum regions 173 7.44 F Is differential osciUator strength spectra for freon molecules in the dis crete region 181 7.45 F Is differential osciUator strength spectra for freon molecules in the dis crete and continuum regions 182 7.46 Cl 2p differential oscillator strength spectra for CF3C1, CF2C12,CFC13 and CC14 in the discrete region 185 7.47 Cl 2p,2s and C Is differential osciUator strength spectra for CF3C1, CF2CI2, CFCI3 and CC14 186 7.48 Cl 2p and 2s oscillator strength distributions per Cl atom for CF3CI, CF2C12, CFCI3 and CC14 molecules and for the Cl atom 187 xii List of Abbreviations EELS electron energy loss spectroscopy EXAFS extended X-ray absorption fine structure FWHM full width at half maximum IP ionization potential ISEELS inner shell electron energy loss spectroscopy MCQD multichannel quantum defect MO molecular orbital MS-Xc* multiple scattering Xa method OS oscillator strength PES photoelectron spectroscopy T term value TOF time of flight TRK Thomas-Reich e-Kuhn VUV vacuum ultraviolet XANES X-ray absorption near edge structure XPS X-ray photoelectron spectroscopy xiii Acknowledgements I should like to express my sincere thanks to Dr. CE. Brion for his interest, assistance, encouragement and supervision throughout the course of my study. I appreciate having had the opportunity to work with him and other members in his research group. Special thanks are due to Dr. G. Cooper, who gave me a lot of help in my research, and also measured the freon photoelectron spectra, to Dr. H.K. Sze, who helped me in the early stages of my work, to Dr. X.M. Tong and Prof. J.M. Li, who performed the multichannel quantum defect calculation on the N02 molecule, to Dr. T. Ibuki, who helped to record the freon photoabsorption and photofragmentation data, to Prof. A.P. Hitchcock, who provided me with the background and Gaussian fitting programs, to Dr. J.H. Scofield, who supplied numerical data of calculated atomic photoionization cross sections, and to Dr. Y.H. Hong and G. Burton, who gave helpful comments and suggestions on the writing of my thesis. For invaluable technical assistance, discussions of things I could not grasp on my own, for advice, for guidance and for a few good references, I am very grateful to: W.F. Chan, S. Clark, M. Coschizza, P. Duffy, B. Greene, X. Guo, B. Hollebone, N. Lermer, B. Todd, E. Zarate, and Y. Zheng. I should also like to gratefully acknowledge a University of British Columbia Graduate Fellowship. The research work was also supported by operating grants from The National Sciences and Engineering Research Council of Canada. Finally, I should like to thank my parents. This thesis is dedicated to them. xiv Chapter 1 Introduction Absolute photoabsorption and photoionization differential oscillator strength (cross sec tion) spectroscopies for molecular valence shell and inner shell excitation in the VUV and soft X-ray regions are of fundamental and applied interest. A quantitative knowl edge of photoabsorption and photoionization processes is very important in understand ing the interaction of molecules with electromagnetic radiation. Detailed information on the transition energies and (differential) oscillator strengths is urgently needed in a large number of scientific contexts, including studies in aeronomy [1], astrophysics [2], planetary sciences [3] and radiation chemistry, physics and biology [4]. However, un til comparatively recently, only limited data were available from optical measurements using discharge lamps or X-ray tubes [5]. In the past decade, an increasing amount of quantitative spectral information over a wide energy range has been obtained with the increasing availability of tunable synchrotron radiation [6,7]. Alternatively, electron en ergy loss spectroscopy (EELS) can also be used to measure optical differential oscillator strengths by utilizing the virtual photon field created by a fast scattered electron at neg ligible momentum transfer. Under such conditions EELS techniques are often referred to as dipole electron impact experiments. A recent review of such techniques and measure ments has been published by Gallagher et al. [8]. Electron energy loss techniques have been used to obtain most of the experimental results reported in the present work. In addition photoelectron branching ratios from synchrotron radiation measurements have 1 Chapter 1. 2 been used to determine some partial differential oscillator strengths. Electron impact experiments are now widely recognized as providing physical infor mation complementary to that obtained in photon impact experiments. In fact one of the earhest demonstrations of quantization was the classic Franck-Hertz experiment [9] in which electrons were used to probe atomic systems. Dipole electron impact techniques have been demonstrated in the past decade to provide a very suitable alternative to VUV and soft X-ray photoabsorption experiments for the measurement of optical quantities such as transition energies and dipole differential osciUator strengths or cross-sections for photoabsorption and photoionization processes [8]. The possibility of studying optical processes by electron impact was in fact pointed out as early as 1930 by Bethe [10]. The use of electron energy loss spectroscopy for optical differential osciUator strength measurements was pioneered by the early experiments of Lassettre [11], Geiger [12] and Van der Wiel [13,14,15]. In particular the direct techniques developed by Van der Wiel and co-workers [13,14,15] and more recent development here at The University of British Columbia have provided versatile methods for the measurement of absolute differential osciUator strengths for photoabsorption and photoionization processes for valence sheU (for examples, see references [16,17,18]) and inner shell (for example, see reference [19]) processes. Some useful reviews on the electron energy loss spectroscopy studies and absolute optical differential oscillator strength measurements are to be found in refer ences [8,20,21,22,23,24,25,26]. In the present work optical (differential) osciUator strengths and transition energies for photoabsorption and photoionization have been obtained for a variety of valence and inner shell processes in N02 (chapter 4) and the freon molecules CF4, CF3C1, CF2C12 and CFC13 (chapters 5 and 7) using the EELS based techniques of dipole (e,e) and dipole (e,e+ion) spectroscopies. In addition partial optical differential oscillator strengths for valence Chapter 1. 3 shell photoionization (electronic states) have been derived for CF3C1, CF2CI2 and CFCI3 (chapter 6) from synchrotron radiation PES measurements and the dipole (e,e) results. The NO2 molecule and the freons were selected because of their fundamental interest and also because of the importance of their interaction with energetic electromagnetic radiation in a number of applications. For example N02 is a toxic gas which is an important link in the chain leading to the production of the atmospheric photochemical smog from air, sunlight, and automobile exhaust. Freons (in particular CF2C12 and CFCI3) have been released to the atmosphere as a result of their widespread use in industry and daily life, for example as refrigerants, foam blowing agents and aerosol propellants. The release of these molecules into the atmosphere has caused major concern as to their role [27,28,29,30,31,32,33] in processes resulting in depletion of the ozone layer which protects us and our planet from the damaging effects of short wavelength solar radiation. Quantitative spectroscopic information for these molecules in the VUV and soft X-ray regions of the electromagnetic spectrum are thus needed due to the presence of such energetic solar radiation in the upper levels of the earth's atmosphere [34]. Prior to the present work very little quantitative spectroscopic information was available for N02 and the freons in the VUV and soft X-ray regions. The results of the work described in this thesis are to be found in the following publications: • W. Zhang, K.H. Sze, CE. Brion, X.M. Tong and J.M. Li, Chem. Phys. 140 (1990) 265. • W. Zhang, G. Cooper, T. Ibuki and CE. Brion, Chem. Phys. 137 (1989) 391. • W. Zhang, G. Cooper, T. Ibuki and CE. Brion, Chem. Phys. 151 (1991) 343. • W. Zhang, G. Cooper, T. Ibuki and CE. Brion, Chem. Phys. 151 (1991) 357. Chapter 1. 4 • W. Zhang, G. Cooper, T. Ibuki and CE. Brion, Chem. Phys. 153 (1991) 491. • G. Cooper, W. Zhang, CE. Brion and K.H. Tan, Chem. Phys. 145 (1990) 117. Chapter 2 Photoabsorption and Electron Energy Loss Spectra The spectroscopic properties of molecular systems can be studied by using either photons or electrons as probes. In a photoabsorption experiment, when a photon of energy E = hv is resonantly absorbed by a target molecule, the process may be represented as Process : hv + AB —• AB* (2.1) Energy of photon : E where AB is the molecule in its initial state and AB* in its final (bound or continuum) state with an energy higher than the initial state by E. In an electron energy loss experiment with the same molecule, if an incident electron e transfers the same amount of energy E to the target molecule, the same final molecular state can be accessed. In this process Process : e + AB —> AB* + e (2.2) Energy of electron : E0 0 — E, in which E0 and (E0 — E) are the electron energies before and after the colhsion respec tively. The energy loss E of the incident electron is analogous to the photon energy E in the photoabsorption experiment. Moreover, a quantitative relation exists between the target transition intensities in the two experiments when the electron impact experiment is performed under the condition that the momentum transfer to the target is neghgibly 5 Chapter 2. 6 small. This parallel between photoabsorption and electron impact experiments is the basis of the major part of this thesis work. 2.1 Photoabsorption Cross Section and Differential Oscillator Strength The probability that a photon of energy E — hu will be absorbed in passing through a target is specified by a cross section o~(E). o~(E) has the dimensions of area and is often given a geometrical interpretation. Imagine that a circle of area o~(E) is centered on each target molecule in the plane perpendicular to the incident photon beam. The circular area cr(E) has the property that any photon of energy E entering o~{E) is absorbed by the target [35]. Consider an incident photon flux N (N = number of photons per unit area per unit time) impinging on the target and passing through it with a path length dL. If no circles are hidden behind others within the distance dL, when viewed from the direction of the incident photon beam, the change in the photon flux is then dN = -Na(E)m dL (2.3) where ra is the target density (i.e. the number of target molecules per unit volume). The corresponding attenuation of the incident hght intensity (I = Nhv) is accordingly given by dl = -Icr{E)m dL. (2.4) The condition corresponding to the requirement for the vahdity of the above linear rela tionships is a(E)m dL « 1,, - (2.5) in which the cr(E)mdL is the total area of circles centered on molecules contained in a slab with thickness dL and unit area surface, on which the photon beam is incident. Chapter 2. 7 This correspondence can be understood since, the smaller cr(E)mdL is compared with one (unit area), the smaller the chance that the circles are hidden behind others. An equivalent of condition 2.5 is that the probabihty (—dN/N) of a given photon being absorbed in passing a distance dL through the target is much smaller than one. In the language of electron scattering, this is also the condition for a single coUision in an electron impact experiment (see the following section). In the situation where condition 2.5 is not valid for a path length L, equation 2.4 may be integrated over the path length and the Lambert-Beer Law is obtained, that is I = J0 e-°{E)mL (2.6) where IQ and I are the light intensities before and after passing through the target. The quantum mechanical expression for the cross section for a process in which a molecule having Z electrons with coordinates {r,}, whose components in the direction of the electric field of the electromagnetic radiation are {XJ}, undergoes a transition from an initial state u0 to a bound, final state un, upon resonantly absorbing a photon of energy E, is (in atomic units) <r(E) = — fnS(E) (2.7) c with fn = 2E = 2£|(:r)n|2 (2.8) where c is the speed of light, (x)n is the dipole moment matrix element, /„ is the dimen-sionless photoabsorption (dipole) oscillator strength, and S(E) is the lineshape function (/ S(E)dE = 1) [36]. By integrating equation 2.7 on both sides over the linewidth, the Chapter 2. 8 integrated cross section for the transition is obtained as 2TT2 o-n = — /„. (2.9) c If the photon energy E is sufficiently large, ionization can occur and the cross section for a transition from an initial state u0 to a continuum final state UE is given by [25] and * = 2E dE J u£(Fi, • "i?z)Y^ x3uo(nr ••,rz)dr1--- drz 3 2E\(x)E\2 (2.11) where df /dE is the photoionization differential oscillator strength. df/dE has the dimen sions of 1/energy. The oscillator strength /„ and differential oscillator strength df/dE have a useful property known as the Thomas-Reiche-Kuhn (TRK) sum rule [25,37], namely ^fn + JdEdE = Z- (2-12) The TRK sum rule states that the sum of oscillator strengths over all possible transitions from an initial state to bound and continuum states is equal to Z, the total number of electrons in the target. This is a very general rule which rigorously holds for any atomic and molecular system [37]. In practice, an approximate partial sum rule has been used in spectral normalization. According to the partial sum rule, the sum of the oscillator strengths for transitions of a single electron (which is assumed to be in a fixed potential) from its initial state to all other states, which include both bound and continuous, occupied and unoccupied, is unity [38]. This approximation permits a separation of the valence and inner shell oscillator strengths (see section 2.3.8). Chapter 2. 9 The transition probability for a photoionization process can be described by either the cross section or the differential osciUator strength. The relation between the values of these two quantities is given by a (Mb) = 109.75 df / dE(eV~l) [25], where 1 Mb = 106 barn = 10~18 cm2. When cross section is chosen to be the scale of the transition intensity in a photoabsorption spectrum, it is used for energy regions both below and above the ionization hmit. In contrast, in the differential osciUator strength spectrum, the spectral intensity for transitions to ionization continua is df/dE, while the intensity of a feature which corresponds to a transition to a bound state is fnS(E), at a given photon energy E. To obtain the oscillator strength /„ for a discrete transition, the spectral intensity must be integrated over the linewidth of the spectral feature. 2.2 The Bethe-Born Theory of Fast Electron Impact Consider a process in which a fast, but non-relativistic, electron colhdes with a target molecule. The influence of the incident electron on the molecule may be regarded as a sudden and small perturbation [26,39]. In the Born approximation, this perturbation could produce a sudden transfer of energy and momentum to target electrons [26] and the target molecule would undergo a transition from an initial state UQ to a final state un, while the incident electron described by a plane wave would be deflected into a scattered wave which can also be approximated by a plane wave. The differential electron scattering cross section dan/d^l for such a process can be expressed as [26] do~n 1 k' AT2 k 2 rz)Vu0(ri,- • • ,fz) dfi - • • dfzdf (2.13) in which K = k- k' (2.14) Chapter 2. 10 k Figure 2.1: Schematic of scattering geometry, k and k' are the momenta of the electron before and after the collision, K is the momentum transfer and 6 is the scattering angle. as is shown in fig. 2.1, or K2 = k2 + k'2 - 2kk'cos9 (2.15) —* —* where r is the position of the incident electron, k and k' are the momenta of the electron before and after the collision respectively, K is the momentum transfer from the incident electron to the target molecule, 9 is the scattering angle, the u's are the wavefunctions in the coordinates {fj} of the Z molecular electrons, and V is the Coulombic interaction between the incident electron and the target molecule, namely M zpt2 2 e2  V = "p?i|f-4| +j£|r-r>| (2-16) where M is the number of atoms associated with atomic number zp. Bethe showed [26] that equation 2.13 can be reduced to where en(K) is a matrix element for the initial and final states, en(K) = / <(ri, •••,r*)E ^f'uQ{ru • • •, rz) <*ri • • • dfz. (2.18) J 3=1 Chapter 2. 11 The cross section expressed in equation 2.17, for a process in which a fast electron trans fers a given amount of energy and momentum, consists of two distinct factors, namely 4(k'/k)(l/K4) and \en(K)\2. The quantity 4(k'/k)(l/K4) may be evaluated from the measurable quantities k, k' and 8, which concern the incoming and outgoing electrons only, and it is therefore a purely kinematic factor. The second quantity |e„(.fY)|2, as shown in equation 2.18, is target dependent and it determines the conditional probabil ity of a transition in the target from state u0 to state un upon receiving a momentum transfer K. The conditional probabihty is because there is no unique correspondence between momentum transfer and energy transfer. The quantity |en(./iT)|2 is referred to as a dynamic factor [26]. The differential cross section in equation 2.17 can be also written as £f=!iik-<*> <>•»> where the generalized oscillator strength fn(K) = j^MK)\2 (2-20) is introduced as a straightforward generalization of the optical oscillator strength defined in equation 2.8 [26]. The relationship between the electron scattering process, in which a small momen tum is transferred, with the photoabsorption process can be revealed by considering the following: The term exK'r> in equation 2.18 can be expanded in a power series of K ei&*i = eiK*t = ! + iKx. + ilE^L + ... + (infill + ... (2.21) assuming that the momentum transfer vector is in the x direction. With this expansion, and considering the orthogonahty of the wavefunctions u0 and «„, equation 2.18 becomes ' en(K) = (iK)ex + (iK)2e2 + • • • + {iK)*et + ••• (2.22) Chapter 2. 12 where the tth order multipole matrix element et (t = 1 is electric dipole, t = 2 is electric quadrupole, etc) is given by 1 / z  et = If / <(rir",rz)£x$u0(7V",rz) dr1---drz. (2.23) The relationship between the optical and the generalized oscillator strength is obtained by combining equations 2.8 and 2.22, and is given by fn(K) = 2E[e21-r(el-2e1e3)K2 + (el + 2e1e5-2e2e4)K4 + ---] = fn + AK2 + BK4 + •••. (2.24) Thus in the limit of zero momentum transfer, the generahzed oscillator strength becomes equal to the optical oscillator strength, that is lim UK) = fn, (2.25) A2—>0 and therefore equation 2.19 becomes, in the limit of K2 —> 0, do-n 2 k' 1 = ElKif- (2'26) This is the Bethe-Born equation which gives the quantitative relationship between the process in which an electron is scattered at neghgible momentum transfer and the pho toabsorption process. This is the basis of dipole (e,e) and dipole (e,e+ion) spectroscopies. For an ionization process in which the target molecule undergoes a transition from the initial state UQ to a final continuum state ug, the differential electron scattering cross section corresponding to equation 2.13 is d2a 1 k' i ' - 2 dttdE 4TT2 k \J e,^'r«£(fi, • • •,rz)Vu0(fir .., j^) dfi • • • drzdr (2.27) Chapter 2. 13 and the parallel of equation 2.19 is <Pa _ 2 k' 1 df(K) dVtdE E k K2 dE (2'28^ where the generalized differential osciUator strength df(K)_2E -JE~-T^E{K)U (2-29) and t z -eE(K) = J ^(n, • • •, fz)£ e'KrJuo(?i, • • • Sz) dn • • • dfz. (2.30) Similarly, in the limit of zero momentum transfer, the generalized differential oscillator strength is equal to the optical differential osciUator strength, that is and the Bethe-Born equation which relates the differential electron scattering cross sec tion and optical differential osciUator strength is d2a 2 k! 1 df dVldE ~ EJlOdE' ^2'32) The fact that the molecule undergoes dipole transitions in response to the distur bance induced by a fast, neghgibly deflected incident electron can be understood as follows [20,21,25]. Classically, when a fast electron passes at a large distance from a molecule (i.e. a large impact parameter), the molecule experiences an induced electric field which is rather uniform in space and sharply varying in time. If the field pulse is regarded as infinitely sharp in time (i.e. a delta function), its Fourier components of all frequencies have equal intensity. Thus the molecule experiences a virtual photon field which causes the molecule to undergo dipole aUowed transitions. The large impact pa rameter corresponds to the small momentum transfer condition in the previous quantum Chapter 2. 14 analysis. Therefore, at negligible momentum transfer the electron scattering differential cross section is quantitatively related to the optical (differential) oscillator strength by the kinematic Bethe-Born factor (2/E)(k'/k)(l/K2). The Bethe-Born theory has been used in the past to evaluate optical oscillator strengths of atoms and molecules using electron impact experiments. To obtain the required experimental conditions under which momentum transfer is very small, K2 can be expressed as a function of incident electron energy EQ, energy loss E, and scattering angle 0 [20]. By substituting k2 = 2E0, k'2 = 2(E0 - E) into equation 2.15, K2 = 2E0 + 2{E0 - E) - 2^2E^2{E0 - E)cos9 = 2E0(2- (2.33) It can be proved, by using the above equation, that K2 —> 0 if and only if both E/E0 and 0 approach zero. Earlier electron impact experiments were based on the above considerations by measuring the generalized oscillator strength for a fixed transition as a function of K2 and extrapolating to K2 = 0 to obtain the optical oscillator strength. For example, Lassettre et al. [23,24,40] measured the generalized oscillator strength for a particular transition (fixed E) as a function of the scattering angle 9 at a fixed impact energy E0. Alternatively, Hertel and Ross [41,42] obtained the generahzed oscillator strength for a particular transition (fixed E) at zero scattering angle, while varying the impact energy E0. However, the extrapolating procedures used were tedious and involved considerable uncertainty in the resulting optical oscillator strength in some cases due to the long extrapolation needed under the experimental conditions employed. A more direct approach was employed by Geiger et al. [12] and by Van der Wiel et al. [13,14,15]. To this end, a very small K2 in equation 2.33 can be approximated in terms of the first Chapter 2. 15 order of x2 = (E/2E0)2 and 62 as [20] 2E0(x2 + 62). (2.34) With this expression for small K2 and integrating equations 2.26 and 2.32 over the small scattering angle, it is found that where 9Q is the half angle of acceptance of the scattered electrons [20]. Therefore, under experimental conditions of high impact energy (smaU x) and small scattering acceptance angle about zero degrees (small 60), the momentum transfer K is small, and therefore the electron scattering signal (which is proportional to the scattering cross section as discussed below) can be related to the optical oscillator strength through the Bethe-Born factor. This latter approach of direct measurements at negligible momentum transfer has been developed for a routine measurement procedure for oscillator strengths for various optical processes [8]. This direct method is preferable and has therefore been used in the present work. The scattered electron signal is recorded as a function of energy loss E and this electron energy loss spectrum is then converted to a relative optical spectrum by a Bethe-Born factor. An absolute optical differential oscillator strength scale is then established for the spectra by using a normalization method as described in section 2.3.8. To convert an electron energy loss spectrum to a relative optical spectrum, the Bethe-Born factor in equations 2.35 and 2.36 can be evaluated from the scattering kinematics and the spectrometer geometry as has been done with the dipole (e,e+ion) spectrometer described in section 3.1. A simpler approach is to approximate equations 2.35 and 2.36 (2.35) and (2.36) Chapter 2. 16 as [20,43] dan = aE bf, n (2.37) and d*L = aE~b^L dE dE (2.38) where a and b are constants depending on the values of the impact energy of the incident electrons and the acceptance angle of the scattering electrons. In an actual experimental situation, it is found that 2 < b < 3 [44]. The above equations are useful for Bethe-Born conversion over a limited energy range, and have been used to obtain approximate optical differential oscillator strength spectra in section- 5.3 and chapter 7 using the high resolution dipole (e,e) spectrometer which is described in section 3.2. In the presently described electron energy loss experiments the gas pressure in the collision chamber is adjusted so that the length of chamber is much smaller than the mean free path of the molecules to ensure that only single collision events occur when the incident electrons pass through the gas sample. This can be checked by estimating the value of the mean free path in the present experiments, and also by seeing that peaks corresponding to multiple scattering processes are absent in the spectra obtained in the lower electron energy loss region (i.e. in valence shell spectra). Under this condition, which in fact corresponds to condition 2.5 (since ami — 1 [45], where a and I are the cross section and the mean free path for the forward scattering, and m is the target density), a linear relationship exists between the electron scattering signal and the corresponding electron scattering cross section, similar to that for light intensity attenuation given in equation 2.4. Therefore, the intensity of the electron energy loss spectrum is related to the photoabsorption differential oscillator strength as indicated in equations 2.35 and 2.36 or in the approximate equations 2.37 and 2.38. For this reason, the scattered electron Chapter 2. 17 signal in a dipole electron scattering experiment drops off ~ E b times as quickly as does the corresponding photoabsorption intensity. 2.3 Spectral Analysis The profile and features of a photoabsorption differential oscillator strength spectrum are determined by the molecular wavefunctions before and after the transition as shown in equations 2.8 and 2.11. To assign these features to particular transitions accurately, reliable theoretical calculations of both transition energies and oscillator strengths are needed. In chapter 4, such a high quality calculation for N02 based on multichannel quantum defect theory [46] has been used to provide the spectral assignments. How ever, such calculations are often not available, especially for larger polyatomic molecules, due to computational difficulties and the cost of computation. Therefore it is neces sary to have an alternative method to analyze spectra with the aid of simple qualitative and semi-quantitative principles without involving extensive calculations. The qualita tive principles concern general characteristic of various molecular orbitals, and of cor responding transition processes. Regarding the semi-quantitative analysis, term values and quantum defects have proved to be useful concepts for providing tentative spectral assignments in electron energy loss and photoabsorption studies [47,48,49]. In addition, relatively simple calculations such as GAUSSIAN 76 [50] are sometimes also helpful for spectral assignment. 2.3.1 Occupied and Unoccupied Molecular Orbitals In the molecular orbital (MO) theory, the state of an electron in the molecule is described by a one-electron wavefunction, which is also referred to as a molecular orbital. The molecular orbitals can be conveniently classified into occupied inner shell (core) orbitals, Chapter 2. 18 occupied valence orbitals, unoccupied (virtual) valence orbitals and unoccupied Rydberg orbitals [47]. An inner shell orbital closely surrounds a particular atomic site and orbital character is therefore dominantly atomic-like and non-bonding. The ionization energy of an inner shell electron (or binding energy of inner shell orbital) is close to the corre sponding value for the isolated atom, differing only by a small chemical shift which is due to molecular effects. In contrast, occupied and unoccupied valence shell orbitals extend over the molecular framework, and they can be bonding, anti-bonding, or non-bonding. These molecular orbitals are therefore responsible for the formation and chemical prop erties of the molecule. The ionization energies of electrons in occupied valence orbitals are generally in the energy range ~ 10-45 eV. As for Rydberg orbitals, they are large and diffuse, extending well beyond the spatial bounds of the ground state molecule. If an electron is excited to a Rydberg orbital, it does not distinguish the detailed spatial charge distribution of the molecular ion core and sees the ion core essentially as a point charge. A Rydberg orbital is therefore atomic-like and non-bonding. In addition to the bound states involving the above types of orbitals, the molecule may alteratively be in an ionized (continuum) state in which case the electron is unbound. The present study provides an examination of the differential oscillator strength spec trum resulting from excitations of electrons from the occupied valence shell or inner shell orbitals in the ground state molecule to the unoccupied Rydberg and virtual valence or bitals as well as for ionization to continuum states. The term value T is a useful quantity in the spectral analysis. For a particular transition feature in the spectrum, T is defined as [47] T = IP-E (2.39) where IP is the ionization potential of the electron in the initial state and E is the transition energy between the initial and final states. T can therefore be thought of as the Chapter 2. 19 ionization energy of the excited, final state. The term values corresponding to the same final state, but different initial states, have been found to be related. In particular, since an electron in a Rydberg state is mostly located far away from the molecular ion core, the hole location has little effect on its orbital energy. Therefore, Rydberg transitions associated with the same final state have similar term values. This is often referred to by saying that the Rydberg term value is transferable. In contrast, virtual valence orbitals are normally delocahzed over the framework of the molecule and their energies are sensitive to the hole location. Hence the virtual valence term value is not expected to be transferable [51,52,53]. In addition to the term value of a feature, its transition intensity is another important consideration in spectral analysis. The intensity of a transition induced by photons (or electrons under the conditions of neghgible momentum transfer) depends on the dipole moment matrix element for the initial and final states as shown in equation 2.8. Such transitions which obey dipole selection rules are called dipole allowed transitions. Given a dipole aUowed transition, another necessary condition for appreciable transition probability is that the two wavefunctions involved have significant spatial overlap. In the absence of a detailed oscillator strength calculation for a molecule a qualitative argument which is often used is that the intensity of a transition is expected to increase with the degree of spatial overlap. 2.3.2 Transitions to Rydberg Orbitals Since Rydberg orbitals in a molecule are atomic-like, the term values for Rydberg tran sitions can be fitted into the Rydberg formula [47] T = R (2.40) (n - s,y Chapter 2. 20 where R is the Rydberg energy (13.605 eV), n is a quantum number, and Si is the di-mensionless quantum defect of the s, p, d etc. type of Rydberg orbital labeled according to the angular momentum quantum number /. The quantum defect reflects the degree of penetration of the Rydberg orbital into the molecular ion core. The deeper the pene tration, the larger the Si value (i.e. larger T). For molecules containing second and third row atoms, the typical range of quantum defects Si is 0.8-1.3 for s Rydberg series, 0.4-0.8 for p Rydberg series and 0-0.2 for d Rydberg series [47]. The typical magnitudes of term values for the lowest members of Rydberg series are in the range 2.8-5.0 eV for the lowest ns member, 2.0-2.8 for the lowest np member and 1.5-1.8 for the lowest nd member [47]. Since both the inner sheU orbitals and Rydberg orbitals are essentially non-bonding, the excitation of an inner shell electron to a Rydberg state does not cause any appreciable change in internuclear distance. At room temperature the ground state molecules are populated mostly in the lowest vibrational level, and the Franck-Condon region [54] of the transition will mainly contain the lowest vibrational level of the Rydberg state. Therefore Rydberg features in inner shell spectra are generally expected to be sharper than those features associated with transitions to the virtual valence orbitals which are mostly anti-bonding. Since Rydberg orbitals are large and have low probability density in the molecular ion core region, where the inner shell orbital resides, the intensities of Rydberg transitions are usuaUy weak compared to transitions to virtual valence orbitals. As the quantum number n increases, the higher Rydberg orbitals have even less spatial overlap with the initial state orbital, and the transition intensities become smaller [55]. These properties of shape and intensity are useful for identifying Rydberg transition features in inner shell spectra. Chapter 2. 21 2.3.3 Transitions to Virtual Valence Orbitals The orbitals which have spatial distributions most delocalized over the framework of molecule are valence orbitals and may be occupied or unoccupied by electrons. The vir tual valence (unoccupied) states can either be located below (T > 0) or above (T < 0) the ionization hmit. The latter situation is due to potential barrier effects (see section 2.3.6 below). Since the initial orbital generally has better spatial overlap with virtual valence orbitals than with Rydberg orbitals, transitions to virtual valence states are expected to have larger intensities than those to Rydberg states. Unlike Rydberg orbitals, which are essentially non-bonding, virtual valence orbitals are mostly antibonding in character, and the excitation of an electron to these virtual valence orbitals will lead to a significant change in internuclear distance. According to the Franck-Condon principle, the features for transition to these states are expected to be vibrationally broadened, particularly in inner shell spectra. Thus the virtual valence features in inner shell spectra are usually more intense and broader than those features associated with Rydberg states. 2.3.4 Transitions to Ionization Continua For the hydrogen atom, the photoionization differential oscillator strength is a maximum at ionization threshold and monotonically decreases at higher energies [25,56]. Such a hydrogenic profile in the atomic photoionization differential oscillator strength is also observed for many-electron atoms when an electron in a sufficiently deep inner shell is ionized [25,57]. Centrifugal effects and molecular field effects have been observed in the photoionization differential oscillator strength spectra of molecules, and such effects lead to the various types of non-hydrogenic spectral behavior discussed below. Chapter 2. 22 2.3.4.1 Delayed Onsets of Ionization Continua A delayed onset in the spectral distribution occurs when the photoionization intensity is depressed near the ionization threshold and then increases to a maximum at an energy above the threshold. This phenomenon, which may be explained in terms of centrifugal effects [25,56], has been observed for some photoionization processes in many-electron atoms and molecules, for example the 2p —> ed transition in Ne (e represents a continuum state), the 3d —> ef transition in Kr [25] and the Cl 2p continua in the freon molecules studied in the present work (see figure 7.47). When an electron is ionized to a continuum state of higher angular momentum the centrifugal repulsion prevents the ionized electron from approaching close to the ion core and thereby reduces its wavefunction overlap with the initial state. Hence the photoabsorption is depressed near the ionization threshold by centrifugal effects which become more significant with increasing angular momentum. An absorption maximum occurs when the photoelectron energy has increased sufficiently to overcome centrifugal effects. 2.3.4.2 XANES and EXAFS Inner shell photoionization spectra are also called "above edge X-ray absorption spec tra". The spectra can be divided into two regions. The spectral structures in the high photoelectron energy region are referred to as extended X-ray absorption fine structure (EXAFS) and this has been interpreted as being due to scattering processes where the high kinetic energy photoelectron emitted by an atom is weakly scattered by only one neighboring atom in a single scattering process [58]. In contrast, the X-ray absorption near edge structure (XANES) located in the low photoelectron energy region is explained in terms of multiple scattering of the low kinetic energy photoelectron by neighboring Chapter 2. 23 atoms in the molecule [58]. The shape resonances (see section 2.3.6 below) in the inner shell spectra are actually special cases of XANES [58]. A photoelectron energy of ~40 eV has been used, somewhat arbitrarily, to divide the spectra XANES and EXAFS [58]. 2.3.4.3 Atomic and Molecular Photoionization at High Photoelectron Energies A theoretical study of the N Is photoionization of N2 molecule by Dehmer and Dill [59] showed that in the high energy continuum the total molecular ionization cross section is close to twice the atomic cross section in magnitude. This is because the initial core state has an atomic-hke charge distribution and also because the escape of the energetic photoelectron is not significantly altered relative to the free atom case (i.e. the final orbital is also atomic-hke). Thus, to a first approximation, the molecular inner shell photoionization differential oscillator strength for high photoelectron energies is equal to the sum of the corresponding differential oscillator strengths for the constituent atoms. Molecular effects, including EXAFS discussed in the previous section 2.3.4.2, are weak modulations on the sum of the atomic differential osciUator strengths. This relationship between molecular and atomic photoionization is the basis for the inner shell spectral normalization procedures used in the present study (see section 2.3.8) and also by others [44,60]. 2.3.5 Photoelectron Spectroscopy and Dipole (e,e-f-ion) Spectroscopy When a photon excites a molecule to a state above its first ionization threshold, ionization may occur where an electron is ejected, but this need not occur 100% of the time [56]. The ratio of the number of photo-ejected electrons to the number of photons absorbed is the photoionization efficiency [8]. Chapter 2. 24 In a photoionization process where a particular electron in an orbital is ejected, the molecular ion is left in a corresponding electronic ion state. Subsequently the molecular ion relaxes and may remain as a stable molecular ion or dissociate into fragments (charged and/or neutral). The photoelectron spectrum indicates the intensity of the ejected pho-toelectrons at a given photon energy as a function of electron kinetic energy. By using Einstein's photoelectric equation, the scale can be converted from electron kinetic en ergy into orbital binding energy. In this spectrum, to a first approximation, each peak corresponds to the ejection of an electron from a particular orbital or more precisely, to the production of the molecular ion in a particular electronic state. The probability for a molecule to produce a molecular ion in a particular electronic state upon absorbing a photon can be expressed by the electronic state branching ratio which is the ratio of the corresponding peak area to the area of aU peaks in the photoelectron spectrum. Accu rate branching ratios are only obtained in an experiment if the variation of the analyzer transmission efficiency with electron kinetic energy is taken into account. The photofragmentation processes following the electron photo-ejection can be studied by photoionization mass spectrometry or the equivalent electron impact technique of dipole (e,e+ion) coincidence spectroscopy [8]. In the dipole (e,e+ion) experiment, the photoions are detected in coincidence with the energy loss electrons as a function of mass-to-charge ratio. Similar to the electronic state branching ratio, the photoion branching ratio is obtained as the ratio of the area of one ion peak to the area of all ion peaks in the mass spectrum. The partial photoionization differential oscillator strengths for production of the elec tronic states and photoions can be obtained by taking the triple product of the total photoabsorption differential oscillator strengths and the photoionization efficiencies with the branching ratios for producing the electronic states and the photoions, respectively. Chapter 2. 25 Furthermore, the dipole induced breakdown pathways can be investigated by appropriate combination of the two kinds of partial photoionization differential oscillator strengths (see chapter 5). 2.3.6 Potential Barrier Effects Originally studied for many-electron atoms where potential barriers are formed due to the presence of centrifugal potentials [25], potential barrier effects have also been investigated for many molecules (for examples, see references [59,61,62,63,64]). Such effects have been found to occur in the inner shell spectra of N02 (chapter 4) and the freon molecules (chap ter 7). The potential barrier effects are manifested in inner shell photoabsorption and electron energy loss spectra by intense resonance features (shape resonances) accompa nied by a suppressed ionization continuum and/or Rydberg structures. The mechanism of the effects has been studied earlier [61,62,65]. Briefly, if a double well potential exists in a molecule, with a potential barrier on the perimeter of the molecule, it is possible that the spatial distribution of a particular wavefunction is mostly within the inner well or the outer well. An inner well wavefunction, which can be at an energy either above or below the ionization energy of the molecule, has a large spatial overlap with the initial state wavefunction which resides mainly in the inner well and this results in strongly enhanced spectral features [65]. In contrast, the outer well wavefunctions have small am plitudes in the inner well region, and this leads to very low intensities for transitions to the outer well states [65]. Rydberg states belong to the outer well manifold of states [65]. The causes of potential barriers have been studied theoreticaUy and experimentally. For example, centrifugal effects have been assigned as the cause of the shape resonances in the inner shell spectra of the N2 molecule [59]. The presence of electronegative hgands surrounding a central atom in a molecule is also believed to cause a potential barrier. Chapter 2. 26 Such an explanation was used to account for the inner shell spectra of molecules such as SF6, SeF6, TeF6 and C1F3 [62,63,64]. 2.3.7 The Equivalent Core (Z + 1) Analogy Inner shell spectra can also be analyzed using the (Z + 1) equivalent core model [66,67]. Consider an inner shell electron, bound to a particular atomic site with atomic number Z, which is excited to an unoccupied virtual valence or Rydberg orbital. Since, in the final state, there is one less electron in the core to shield the nucleus, the promoted electron will see the atom as having an effective atomic number of (Z + 1) so that the term values for the inner shell transitions will be approximated by those for valence excitations in the (Z + l) core analogous species. For example, the term values for the N02 N Is transitions are expected to be comparable with those for the valence transitions for the (Z + 1) core analogous species 03 as discussed in chapter 4. 2.3.8 The Absolute Differential Oscillator Strength Scale Since in general only relative intensities are obtained for both photoabsorption and Bethe-Born converted EELS spectra, calibration (normalization) procedures are required in order to estabhsh an absolute differential osciUator strength scale. Normalization may be achieved using several different approaches: 1. Normalization at a single photon energy to a pubhshed absolute measurement or calculation for the molecule. 2. Normalization using the partial TRK sum rule. For example, in chapter 5, the partial TRK sum rule (see section 2.1) has been used to normahze valence sheU Bethe-Born converted EELS spectra so that the area under the normahzed valence Chapter 2. 27 shell differential oscillator strength spectrum, as a function of photon energy (eV), is equal to the number of valence shell electrons plus a small correction corresponding to Pauh excluded transitions [38]. Similarly, in chapter 7 the partial TRK sum rule has been used to verify the differential oscillator strength scale estabhshed using atomic differential osciUator strengths (see method 3 below). 3. Normalization of inner sheU spectra in the high photoelectron energy region to atomic differential osciUator strengths (see section 2.3.4.3). The atomic differential osciUator strengths (cross sections) can be obtained either from calculations [57, 68,69] or from recommended semi-empirical values [70]. This approach has been used in the normalization of inner shell Bethe-Born converted EELS spectra in section 5.3 and chapter 7. Chapter 3 Experimental Methods The results reported in this thesis were obtained using dipole (e,e+ion) and dipole (e,e) spectroscopies. The dipole (e,e+ion) spectrometer was used to obtain the valence shell photoabsorption, photoionization and photofragmentation differential oscillator strength spectra and photoionization mass spectra for the freon molecules discussed in chapters 5. The inner shell photoabsorption and photoionization differential oscillator strength spec tra for NO2 in chapter 4 and for the freon molecules in chapter 7 were derived from electron energy loss spectra measured using the high resolution dipole (e,e) spectrometer. The photoelectron branching ratios and partial electronic state photoionization differen tial oscillator strengths for the freon molecules discussed in chapter 6 were obtained from photoelectron spectroscopy measurements made at the Canadian Synchrotron Radiation Facility at the University of Wisconsin by Dr. G. Cooper. 3.1 The Dipole (e,e+ion) Spectrometer The dipole (e,e+ion) spectrometer was originally built and operated at the FOM insti tute in Amsterdam [13,14,15,71,72,73,74,75]. In 1980 this instrument was moved to the University of British Columbia where it has been modified [76,77]. Details of the con struction of the apparatus and its operation have been described in references [13,14,15, 71,72,73,74,75,76,77]. The form of the spectrometer as used for the work discussed in this thesis is shown in figure 3.2. 28 (e,e +jon) SPECTROMETER ELECTRON GUN COLLISION CHAMBER ANGULAR SELECTION EINZEL LENSES DECELERATING LENS TIME OF FLIGHT MASS SPECTROMETER AND ION LENSES PRIMARY BEAM DUMP DELAYS ELECTRON ANALYSER PRINTER PLOTTER DISC DRIVES ENERGY LOSS PDP 11-03 ION TAC Figure 3.2: Schematic of the dipole (e,e+ion) spectrometer. Legend: TAC—time to amplitude convertor PDP 11-03—computer Chapter 3. 30 A narrow (1 mm diameter) beam of fast electrons (8 keV) is produced from a black and white television electron gun with an indirectly heated oxide cathode (Philips 6AW59). The incident electrons interact with target molecules in the collision chamber. In the scattered channel the electrons in a small cone of 1.4 x 10-4 steradians about the zero scattering angle pass through an angular selection aperture and are transported and decelerated by the Einzel lenses and the decelerating lens as shown in figure 3.2. The electrons then are energy analyzed by the hemispherical electron analyzer (~1 eV FWHM resolution) and are detected by a channel electron multiplier (Mullard B419AL). The positive ions produced in the collision chamber are extracted at 90 degrees to the incident electron beam into the time-of-flight (TOF) drift tube and are then detected by the ion multiplier (Johnston MM1-1SG). A homogeneous electric field (400 Vcm-1) across the colhsion chamber and an accelerating lens system ensure uniform collection of ions with up to ~20 eV excess kinetic energy of fragmentation, independent of the initial direction of dissociation [73,74,77]. The length of the drift tube and the final ion kinetic energy are such that mass spectra with a mass resolving power (ra/Am) of 50 can be obtained from a time-of-flight analysis. Magnetic shielding is achieved with Helmholtz coils and high permeability mumetal shields. The spectrometer is evacuated with turbo molecular pumps to provide the clean vacuum environment desirable for quantitative ion and electron spectroscopy. Two modes of operation of the spectrometer are possible: 1. Photoabsorption differential oscillator strengths. According to the Bethe-Born theory discussed in section 2.2, the small momentum transfer (K) condition is to be satisfied to ensure that the collected scattered elec trons are associated with dipole transitions in the target molecule. In the present Chapter 3. 31 studies for which the energy loss E < 200 eV, this condition is met by choos ing the scattering kinematics of the spectrometer: high electron impact energy (Eo = 8 keV) and small half scattering acceptance angle (9Q = 6.7 x 10-3 radians) about zero degrees. The electron energy loss spectrum can be converted to a rela tive optical spectrum by using equations 2.35 and 2.36 through a Bethe-Born factor which can be readily obtained from the E,EQ,80 values. The absolute differential oscillator strength scale for the optical spectrum can then be estabhshed using the partial TRK sum-rule (section 2.12). 2. Time of flight mass spectra and ionic photofragmentation differential oscillator strengths. TOF mass spectra at a fixed energy loss (i.e. photon energy) can be obtained in an electron-ion coincidence measurement with the aid of a time to amphtude converter (TAC). The TAC is started by a pulse signal from an electron of a given energy loss and stopped by a pulse from the ion signal. The TAC generates an output pulse with an amphtude proportional to the time between the start and stop pulses. This time is proportional to ^/m/e, a characteristic quantity for a specific ion which has mass ra and positive charge e. A TOF mass spectrum is then constituted from the pulse height distribution measured using a PDP-11/03 computer via an analogue to digital converter and software routines. As has been discussed in section 2.3.5, the ionic photofragmentation branching ratios at a fixed energy loss for a particular ion are obtained from the ratio of the area under the corresponding peak to the area under all ion peaks. The photoionization efficiency is measured as the number of ions produced by each energy loss electron. The photofragmentation differential osciUator strength for a particular ion can then be obtained by taking the triple Chapter 3. 32 product of the absolute photoabsorption differential oscillator strength (derived from the non-coincident energy loss measurement described in the measurement mode above), the photofragmentation branching ratio, and the photoionization efficiency. 3.2 The High Resolution Dipole (e,e) Spectrometer The high resolution dipole (e,e) spectrometer was built in this laboratory in the early 1980s. Fig. 3.3 shows a schematic diagram of the instrument. The design and con structional details have been described in detail in reference [78] and hence only a brief description will be given here. Electrons are produced from a direct current heated thoriated tungsten filament located within an externally adjustable mount in an oscilloscope electron gun body (Cliftronics CE5AH). The voltage for the filament cathode (C), grid (G), anode (A) and the second element of the focussing Einzel lens F are all floated at the negative of the impact energy (typically in the range 2-3.7 keV in the present work) with respect to the grounded first and third elements of the focusing lens F. The electron gun provides a nar row (1 mm diameter) electron beam. The beam is then retarded by the two element lens Li at the monochromator entrance to the required pass energy of the monochromator, which is a hemispherical electron energy analyzer. The monochromated beam then exits through a virtual slit formed by the accelerating lens L2 (ratio 1:20) and is brought into focus at the entrance (P4) of the stainless steel reaction chamber after passing through a second accelerating lens L3 (ratio 1:5). The beam is then transported to the collision chamber (CC) by the Einzel lens L4 to collide with the molecules under study. The exiting main beam and scattered electron beam then pass through a zoom (energy-add on) lens L5, retarding lenses L6 (ratio 5:1) and L7 (ratio 20:1) to a virtual slit formed MONOCHROMATOR DETECTOR ELECTRON GUN pTTc"T Til—HjT Wn ANALYSER U L7 TURBO PUMP r 360 L/S 0 SCALE llXllllJllll}. ' I" " ' 10 20 cm TURBO PUMP 450 L/S 8 •8 Co TURBO PUMP 360 L/S WHIM/MA Figure 3.3: Schematic of the high resolution dipole (e,e) spectrometer. Legend: A anode G grid Pi~Ps apertures C cathode GAS gas inlet Q1-Q9 deflectors CC collision chamber HV high voltage T tube D decoupling transformer L1-L7 lenses V valve F forcusing lens L/S liter per second co co Chapter 3. 34 at the analyzer entrance. The half angle of acceptance (0Q) of the scattered electrons is 3.0 x 10-3 radians about zero degrees. Following energy analysis, the scattered electrons are detected by a channeltron electron multiplier (Mullard B419AL) mounted behind the analyzer exit aperture. The channeltron is operated at high voltage of 3.5 keV and the signal is decoupled using a ferrite core transformer. Magnetic shielding of the various regions of the spectrometer is provided by hydrogen-annealed mumetal enclosures, exte rior to the vacuum housing. Turbo molecular pumps are used to provide a clean vacuum environment. High resolution, high sensitivity, and high stabihty are achieved by this spectrometer due to the following features [78]: 1. Separate differential pumping of the four vacuum chambers of the spectrometer has alleviated the problems of surface contamination, retuning and frequent cleaning that occur with single chamber instruments. This ensures long term stabihty and maintains high sensitivity and good resolution. In addition, thermal stability of the hot filament is not affected when the sample is introduced into the spectrometer. 2. The advanced electron optics allow transmission of large beam currents and also minimize the effects of scattering of the beam from slit edges and the surfaces of the analyzer into the detector. This design also permits operation at zero degree scattering angle since the main (unscattered) primary electron bean is strongly suppressed due to the high energy selectivity of the zoom lenses. 3. The large hemispherical electron energy analyzers (mean radius RQ = 19 cm = 7.5 in) chosen provide high transmission and high resolution for a relatively high pass energy. This also permits a high impact energy, which is necessary for optical differential oscillator strength measurements, while still retaining reasonable lens Chapter 3. 35 ratios. The primary (unscattered) electron beam is used to tune up the spectrometer by steering the beam with analyzer deflection voltages, lens voltages and the deflectors (Qx to Qg). Each of the deflectors consist of two pairs of electrostatic plates. The colhmation and direction of the electron beam can be monitored with electrometers connected to the apertures (P1 to P8) and to the cone of the channeltron. The small currents on the channeltron cone are measured with a floated vibrating reed electrometer (Cary, model 401). To obtain an energy loss spectrum, a voltage equal to the energy loss corresponding to the inelastic scattering is added on top of the voltages already applied to the analyzer system, from the lens L5 onward. Thus by regaining their energy loss, the scattered electrons are transmitted through the analyzer system to the channeltron and an energy loss spectrum is obtained by using a suitable offset energy loss voltage and scanning the energy loss region of interest. The channeltron signals are processed by high gain pre-amplifier and amplifier-/discriminator units (PRA models 1762 and 1763 respectively). The spectrum is recorded by using a PDP 11/023 computer, and/or a Nicolet 1071 signal averager operated in a multichannel scaling mode where the channel address is stepped synchronously with the voltage on L5 and the analyzer. The spectrum is monitored on-line via a VT105 graphics terminal. The energy resolution, which can be defined as the full width at half maximum height (FWHM) of the electron beam at the analyzer exit, depends on the pass energies selected for the monochromator (EM) and analyzer (EA)- The theoretical resolution for this spectrometer has been derived to be [78] AEFWHM = 0.003 y7^ + E\. Chapter 3. 36 In practice, the experimental resolution achieved is shghtly better than the above theo retical value. The energy resolutions specified in the spectra reported in the present work were obtained by measuring the profile of the primary electron beam, and were within the range 0.030—0.3 eV FWHM. The choice of the resolution to be used is determined by the spectral region of interest as well as natural hnewidth considerations. For exam ple, when structures in the pre-ionization edge region of a molecule are to be examined, high resolution is chosen; when a spectrum over a long energy range, including both pre-ionization edge and continuum regions, is to be scanned, a lower energy resolution is used. The length of time need to collect an inner shell spectrum ranges from a few hours to several days, depending on the primary beam current and the intensities of the transitions involved. 3.3 Energy Calibration To calibrate the energy loss scale of the electron energy loss spectrum measured using the high resolution dipole (e,e) spectrometer, the sample and a suitable reference gas were introduced simultaneously into the spectrometer, and the spectrum of the mixture was measured to avoid any problems of chemical-dependent energy shifts and contact potentials. The absolute energy scale was then estabhshed by calibrating a prominent spectral feature due to the sample with respect to a known feature of the reference gas. Sodhi and Brion have carefully measured the energy of a number of selected inner shell atomic and molecular transitions for calibrating energy loss spectra [51]. The particular calibration energies used in this work are hsted in table 3.1. The cahbration corrections have been found to be very small (<0.03 eV) due to the efficient differential pumping of the different regions of the spectrometer (see section 3.2). The energies of the various spectral features were visually determined with the aid of computer software. Chapter 3. 37 The energy loss scale for the dipole (e,e+ion) spectrometer has been calibrated using one of the following methods: 1. Using a prominent feature of known energy from previously published high resolu tion spectrum of the sample molecule. 2. Using the reported appearance potential for production of a particular ion in the mass spectrum of the sample molecule. 3.4 Sample Handling The samples studied were introduced to the reaction chambers of the respective spec trometers through gas inlet systems including Granville-Phillips series 203 stainless steel leak valves. Appropriate gas regulators were used for the respective gaseous samples depending on the type of gas in the gas cylinder. In case of CFCI3 the liquid sample was degassed by freeze, pump and thaw cycles before the sample was allowed to evaporate into the spectrometer via the leak valve. Cylinders of commercially available NO2 were found to contain various amounts of NO impurity. The NO was removed by cooling and pumping the cyhnder prior to use. No dimers (i.e. N2O4) were expected to be present [79] at the low pressures employed in the presently reported experiment. Table 3.1: Reference energies for inner shell spectra0 Inner shell transition Transition energy b (eV) SF6 S 2Pl/2 —»t2g 184.54(5) N2 N Is —> n*(v = 1) 401.10(2) CO C Is—>TV'(V = 0) 287.40(2) "Reference energies are taken from ref. [51]. ^Uncertainties are shown in brackets, e.g. 184.54(5) means 184.54 ± 0.05 eV. Chapter 3. 38 All the samples studied in the work presented in this thesis were obtained commer cially and their stated purities are listed in table 3.2. Table 3.2: Source and purity of samples Sample Source Purity(%) N02 Matheson 99.5 CF4 Matheson 99.7 CF3C1 Matheson 99.0 CF2C12 Matheson 99.0 CFCI3 PCR 99.0 Chapter 4 Inner Shell Electron Energy Loss Spectra of N02 at High Resolution: Comparison with Multichannel Quantum Defect Calculations of Dipole Oscillator Strengths and Transition Energies The N02 inner shell EELS spectra reported in this chapter were measured using the high resolution dipole (e,e) spectrometer described in section 3.2. 4.1 Calculations The multichannel quantum defect (MCQD) theory calculations were carried out by Tong and Li [80] and the details of the calculations are similar to those reported earlier for SO2 [53]. Fig. 4.4 shows the calculated quantum defects for ai, &i, b2 and a2 symmetries. The calculated term values (IP-E) are obtained from the (state-dependent) quantum defects. The calculated (electronic) oscillator strengths /'s for discrete transitions are represented (see figs. 4.5a and 4.9a below) as //A, where the width A (FWHM) is estimated from the experimental spectra (~0.9 eV for the 6a!, 2fel5 and 7a1 final states, 3 eV for 5b2 and ~0.5 eV for the lower Rydberg states). The representation of oscillator strength in the discrete transition region has been discussed in section 2.1. Oscillator strengths for the higher Rydberg states and in the ionization continuum are represented as differential oscillator strengths, df/dE. 39 Chapter 4. 40 < Z> O 2.0 1.0 0.0 10 0 4 3-1 r m = N02 — pbi — fibi -1 ; i »3t>1 1 , 45 P" Pt>2 |/ 'f"3b2 |/ f-ib2 4 p db2 1 , •10 10 0 TERM VALUE (eV) 10 IL —f°2 4 J ca2 1 , Figure 4.4: Calculated quantum defects for excitations of NO2. Chapter 4. 41 4.2 Results and Discussion The NO2 molecule is of C2v symmetry, and the ground state, independent particle, elec tron configuration, including the unoccupied (virtual) valence orbitals, may be written as [81,82,83] (162)2(laQ2(2^^^ O Is N Is valence orbitals (261)°(7a1)0(562)° ; 2AX. unoccupied (virtual) valence orbitals As a result of the unpaired electron in the half-filled 6ai valence orbital, any transition from the core orbitals to any other final orbital results in a pair of doublet final excited states, depending on the coupling of electron spins [82]. Similarly, core ionization leads to the 3Ai and xAi states of NOj [84,85]. The sphtting caused by interaction between the two 0 Is orbitals (lfe2 and lcii) is expected to be negligibly small due to their essentially atomic-like nature. The dipole-allowed transitions for N02 are shown in table 4.3. Fig. 4.5 shows the measured low-resolution (0.14 eV FWHM) ISEELS and MCQD calculated N Is excitation spectra of N02 in the discrete (pre-ionization edge) and ion ization continuum regions. The absolute differential oscillator strength scale was estab lished using procedures described below. The N02 sample was purified as explained in section 3.4 above (see also further discussion below), but a very small amount of residual NO is still present. Fig. 4.6 shows the high-resolution (0.090 eV FWHM) N Is ISEELS spectrum of the pre-ionization edge region for an N02 sample of higher purity, together with the MCQD calculation. The MCQD calculated oscillator strengths are presented in the discrete and continuum transition regions, as discussed in section 4.1. The measured energies and oscillator strengths together with the calculated oscillator strengths and Chapter 4. 42 Table 4.3: Dipole-allowed transitions in N02 from the 2AX ground state for C21, symmetry Final configuration Dipole-allowed core hole occupied final state orbital virtual MO ax \2AX,22AX a ax 12B1,22B1 a ai b2 l2B2,22B2a a2 12B2,22B2 a2 b2 l2B1,22Bl h ai l2B1,22B1 a h bi l2Au22Ai b2 ai l2B2,22B2a b2 b2 \2Ai,22Ax ai continuum 3AU1A1 continuum 3A2,M2 h continuum *Bi?Bx h continuum 3B2* B2 "Only one doublet state will result from transitions to final states in which the 6ai orbital is doubly occupied or empty. term values are shown in table 4.4. Also shown are the assignments based on a consider ation of the MCQD calculations. The energies of the 3Ai and 1Ai N Is ionization edges are assigned according to XPS measurements [84,85,86] using the triplet-singlet sphtting of 0.70 eV reported by Davis et al. [84]. The energies of features 1 and 2 are close to the values reported for the two largest peaks in the N Is photoabsorption spectrum (see fig. 4.8b below) of N02 from ref. [82], but peak 1 is much less intense relative to peak 2 in the ISEELS spectrum. The smaU peak, just below 400 eV, barely visible in fig. 4.5b but present to a much larger extent in the photoabsorption spectrum [82], is clearly due to the presence of a small amount of an NO impurity (see discussion below) which has Chapter 4. 43 ^15H T > © 10-CM 5H o ui cn f— Dl o o (a) MCQD Calculation 3Ai edge 2bi 6ai 7a 4pai N02 N1s |5b2 I5.0 5.0 -5.0 -15.0 TERM VALUE (eV) (b) 2bi ISEELS Experiment cn 5H OH AT edge 0=0" E0=3700eV AE=0.14eV i—r i 2 ftN1s edges" l in in i 34 914 16 400 4I0 420 430 440 ENERGY LOSS (eV) 450 Figure 4.5: (a) MCQD calculation and (b) low-resolution N Is ISEELS spectrum of NO2 in the discrete and continuum regions. Spectrum (b) as shown is not Bethe-Born corrected. Chapter 4. 44 > 0) CM I o X r-o ui Dl I— CO OH o o CO o rr Ul (a) MCQD Calculation 10- 2bi 5-6ai 0-Aiedge lPbl7Ql A 4p°1m 4sai n, LH K5D ' £0" TERM VALUE (eV) 0.0 10-(b) ISEELS Experiment 2b 0=0* E0=3000eV AE=0.090eV 5-0 x3 N1s edges 1—I I I llllll II T 3 4 5 678101214 15 • • 9"'? 400 410 ENERGY LOSS (eV) Figure 4.6: (a) MCQD calculation and (b) high-resolution N lfi ISEELS spectrum of NO2 in the pre-ionization edge region. Spectrum (b) as shown is not Bethe-Born corrected. Chapter 4. 45 Table 4.4: Experimental and calculated data" for N Is excitation of N02 Experimental [this work MCQD calculation feature energy term value oscillator6 term oscillator assignment (eV) strength value0 strength final orbital 3AX 1Ald (xlO"2) (eV) (xlO"2) (to 3Ai limit)d 1 401.04 11.56 2.7 13.12 2.10 6ax 2 403.28 9.32 8.9 10.62 8.26 3 ~ 408 ~ 5 4.80 0.20 4sai 4 408.92 3.68 3.22 0.60 4pbx 5 409.48 3.12 (3.82) 3.05 0.38 4pax 6 410.08 2.52 (3.22) 2.40 0.02 4pb2 7 410.48 2.12 (2.82) 1.98 0.06 5sai 8 410.68 1.92 (2.62) 1.89 1.46 7ai(aJ) 9 410.84 1.76 (2.46) 1.70 0.04 ZdW 10 411.04 1.56 (2.26) 1.50 0.72 3d2ai 1.44 0.18 5pbi 11 411.28 1.32 ' (2.02) 1.39 0.14 5pai 12 411.52 1.08 (1.78) 0.96 0.02 4dbx 0.89 0.30 4do<2i 13 411.76 0.84 (1.54) 0.82 0.08 6p&i 0.80 0.06 6pax 0.78 0.10 4ii2ai 0.60 0.02 5dW 14 411.96 0.64 (1.34) 0.57 0.12 5c?ofli 0.53 0.04 lpbx 0.52 0.02 1pax 0.51 0.02 5d2a,i 0.40 0.06 6c?oai 0.36 0.02 6d2ai 0.29 0.04 7dodi IP(3AX) 412.66 0 0 — oo 15 412.72 (0.58) IP^Ai) 413.306 0 16 416.16 -3.56 7.3 -2.45 9 562(6$) "See fig. 4.5 and 4.6. ''A kinematic Bethe-Born conversion of E2,5 has been applied. cWith respect to the 3Ai limit. dNote assignment for 1J4i term value must be interpolated since MCQD calculation is shown for 3Ai terms only. ^AiMi, IPs from XPS [84,85,86]. Chapter 4. 46 an intense N Is —> n* band at 399.7 eV [51,87,88,89]. Much larger contributions from NO were found in spectra produced from gas samples taken directly from commercially supphed gas bottles of N02 without any further purification. The NO contribution in the N02 could be diminished to an almost negligible level (as shown in figs. 4.6b and 4.7a) by repeated freezing, pumping and thawing cycles of the gas cylinder. The presence of impurities may be the reason for the significant differences between the spectral features observed in the present ISEELS N Is and 0 Is spectra of N02 and those shown in the previously published photoabsorption results [82]. Therefore a careful study has been made of spectra obtained from commercial cylinders of N02 before and after fractionation. In addition, comparisons are made with the known ISEELS spectra of possible impurities. The results of these investigations are shown in fig. 4.7. The peak at 399.5 eV observed in fig. 4.5b is clearly shown to be due to an NO impurity by the vibrational structure present in a high-resolution (0.068 eV FWHM) ISEELS spectrum obtained using a sample from an unfractionated commercial N02 cyhn der (fig. 4.7b). This vibrational structure is identical in profile and energy position to that observed in an earlier reported high-resolution ISEELS spectrum of NO [88], which is shown as an insert in fig. 4.7b. A further possible impurity that could complicate N02 N Is spectra is N2, since peak 1 (N Is —> 6ax) of the N Is spectrum of N02 (see fig. 4.5b and table 4.4) is at 401.04 eV, whereas the intense Is —» n*(v = 1) peak of N2 is known to be at 401.10 eV [51]. This is clearly shown by the spectra in fig. 4.7c. in which comparable amounts of N2 and N02 were admitted simultaneously (see comparison of spectra 4.7c and 4.7d with 4.7a). The familiar pattern [21,51,89,90] of the vibrationally resolved N Is —• TT* transition of N2 can clearly be seen, superimposed on the N02 (N Is —> 6ai) band at ~401 eV. Fig. 4.7d shows the spectrum when the relative contribution of N2 is greatly increased. Fig. 4.7a shows the same spectral region for an N02 sample Chapter 4. 47 in LU cn N02 samples HR ISEELS (a) NO ISEELS -ref [88] (c) (d) ^ /N02 • 0=0* E0=3000eV AE=0.090eV Purified Cylinder Sample N02 Commercial Cylinder NO + N02 Addition of N2 to cylinder sample NO + N2 + N02 •MO excess - NO + N2 + N02 398 400 402 404 406 ENERGY LOSS (eV) 408 Figure 4.7: Investigation of sample purity in N02 cylinders'by high resolution ISEELS measurements in the N Is region: (a) purified N02; (b cyhnder N02 (unpurified) showing NO impurity and the high resolution NO spectrum of Tronic et al. [88]; (c) Addition of N2 to cyhnder N02; (d) same as (c) but with excess N2. Chapter 4. 48 that has been purified by repeated freezing, pumping and thawing of the cylinder. The earlier pubhshed photoabsorption results [82] show a prominent peak at ~400 eV in the N Is spectrum and also a number of other significant differences from the present N Is (figs. 4.5 and 4.6) and 0 Is (see figs. 4.9 and 4.10 below) ISEELS spectra of N02. We have therefore digitized the previously pubhshed N Is and 0 Is photoabsorption spectra attributed to N02 [82] and transposed them from a wavelength (A) to an energy scale (eV). The respective photoabsorption results (figs. 4.8b and 4.8f) are compared on the same energy scales with similar resolution N Is ISEELS spectra of pure N02 (this work), N2 [89], and NO [87] in figs. 4.8a-4.8d, and with 0 Is ISEELS spectra of N02 (this work), 02 [89], NO [87], and H20 [91] in figs. 4.8e-4.8i. It should be noted that some differences in relative intensities may occur since the photoabsorption spectral intensities were presumably derived [82] from a photoplate. It can be concluded from a consideration of the data in figs. 4.7 and 4.8 that both the discrete and continuum regions of the inner-shell photoabsorption spectra 1 of ref. [82] contain appreciable contributions from impurities that probably include NO and N2 in the case of N Is, and 02, NO, and H20 in the case of 0 Is. This implies that peaks attributed to double excitation in the photoabsorption spectra [82] are in fact due to impurity gases. In view of these considerations, no further comparison between the present ISEELS measurements and the experimental photoabsorption results of ref. [82] will be made for either the N Is or O Is spectra. That the experimental N Is ISEELS spectra obtained in the present work are of the NO molecule and contain no significant contributions from impurities is further confirmed by the MCQD calculations, which predict features that correspond extremely well with 1In comparing the various spectra, it should be noted that the uncertainties in the energy (wavelength) scales of the photoabsorption spectra [82] were stated to be to ± 0.4 eV (N Is and ± 1 eV (0 Is). In the present ISEELS work the energy scales are considered to have an uncertainty of ± 0.02 eV. Chapter 4. 49 400 410 420 430 530 540 550 560 ENERGY LOSS (eV) Figure 4.8: Comparison of N Is and 0 Is ISEELS spectra of N02 (a) and (e) with photoabsorption measurements (b) and (f) from ref. [82]. Also shown ((c) and (d)) are N Is ISEELS spectra of N2 [89] and NO [87], as well as O Is ISEELS spectra of H20 [91], 02 [89] and NO [87] ((g) and (i), respectively). Chapter 4. 50 the present experiment (but not the photoabsorption spectra [82]) with regard to both transition energies and relative intensities (see table 4.4 and figs. 4.5 and 4.6). The MCQD calculations are therefore used for the spectral assignments (see table 4.4 and figs. 4.5 and 4.6). There is a small difference between experimental and calculated energies for the N Is to 6ai and N Is to 2b\ virtual-valence excitations, but agreement is quite good for the higher valence (7ai(a^) and 562(&2)) and Rydberg excitations. It should be noted that the 7a! peak is both predicted and observed in the discrete portion of the spectrum. This is contrary to the conclusions of Schwarz et al. [82]. When an inner-shell electron in the open-shell molecule NO2 is excited to an orbital above the (singly occupied) 6a! orbital there will be three unpaired electrons and the final states accessible according to dipole selection rules are in two doublet series (12B!, and 22Bi, for example [82]). Following Slater's treatment of three unpaired electrons [92,93], the wavefunctions of the two doublet states can be represented as linear combinations of the Slater determinants for the spin degenerate states. The coefficient of the hnear combinations are determined by the interactions (exchange integrals) among the electrons and the relative intensities for the transitions to the two doublet states can be calculated accordingly. Two situations involving different couplings can be envisaged. In the first case, if one electron is far away from the other two electrons (i.e. the situation for higher Rydbergs or ionization) the two doublet states would result from weak coupling of the remote Rydberg (or ionized) electron with the two more strongly coupled electrons (in the core and 6ax orbitals, respectively) and these states would be associated with the 3Ai and xAi ionization limits. In this situation the relative intensities of the doublet states would be [94] approximately 3 : 1, as observed in XPS measurements [84]. The second type of situation occurs when the three electrons are much closer together and this corresponds to excitation to the normally unoccupied virtual valence orbitals, which are of course quite Chapter 4. 51 localized. In this situation all interactions between the three electrons are important and a consideration of the various couphngs leads to relative intensities for transitions to the two doublet states leading to the 3AX and xAi ion states of p : 1 (where 1 < p < 3, depending on the interactions) with the lower-lying doublet state being the more intense. The unsymmetrical profiles of peaks 2 and 16 in the N Is spectra (figs. 4.5b and 4.6b) and peaks 2 and 10 in the 0 Is spectra (figs. 4.9b and 4.10b) of N02 are consistent with these considerations. Thus two doublet series are expected throughout the ISEELS spectra. However, the linewidths and densities of states, together with the lower relative intensity expected for those states leading to the higher energy 1A1 limit, result in only the lower energy, higher intensity doublet series being clearly identifiable in the present work. The asymmetry of peaks 16 (N Is, fig. 4.5) and 10 (0 Is, fig. 4.9) may alternatively be due to the inherent nature of continuum resonance line shapes, as discussed in refs. [96,97]. The MCQD calculation (table 4.4) predicts a relatively low intensity for the 4s(a!) Rydberg state, which is at best rather weak (feature 3) on the low-energy side of fea ture 4 (see also the discussion below for the situation in the 0 Is spectrum) in the measured spectrum (figs. 4.5b and 4.6b), in keeping with the fact that on the basis of a purely atomic-hke selection rule a Is —> 4s transition would be formally dipole for bidden. Such atomic-hke selection rules have generally been found to be a reasonable guide for interpreting intensities of core-to-Rydberg molecular transitions, given the es sential atomic-like character of both the initial and final orbitals [20]. In general, the predicted overall distribution of Rydberg intensity compares quite favorably with the high-resolution experimental spectrum (fig. 4.6). In the continuum (fig. 4.5) the position and intensity of the N Is to 5&2(&2) resonance is fairly accurately predicted (table 4.4), as is the intensity of the underlying continuum relative to the discrete structure below the ionization edge (see fig. 4.5). A width of 3 eV has been assigned to the fe2 resonance, Chapter 4. 52 as indicated by the measured spectrum. The presently obtained N Is and 0 Is inner-shell excitation spectra of N02 (see figs. 4.5b, 4.6b, 4.9b and 4.10b) have each been placed on an approximate absolute dipole (i.e. optical) differential oscillator strength scale, according to the normalization principles discussed in sections 2.3.4.3 and 2.3.8. The normalization procedures used were as follows. Firstly a straight-line extrapolation of the pre-ionization edge region below the respective 6a! excited states was used to estimate a baseline for the respective inner-shell spectra. The lower resolution N Is (fig. 4.5b) and 0 Is (fig. 4.9b) spectra were then respectively normalized to the known atomic nitrogen Is and twice the atomic oxygen Is photoionization differential oscillator strengths [57,68,70], at 25 eV above the respective ionization edges. No kinematic Bethe-Born conversions (equations 2.35 and 2.36) were apphed to the spectra shown in figs. 4.5b, 4.6b, 4.9b and 4.10b. While such conversions are of the order of ~ Eb (3 > b > 2) as approximated in equations 2.37 and 2.37, their effect in the N Is and 0 Is inner-shell region will be small (only about 20% and 15% variation, respectively) over the energy loss (E) ranges of the spectra shown in figs. 4.5b and 4.9b. The slightly higher resolution spectra (figs. 4.6b and 4.10b) were then normahzed to the respective lower resolution spectra (figs. 4.6b and 4.9b). Despite the approximations and uncertainties in the procedure outlined above, it can be seen (figs. 4.5, 4.6, 4.9 and 4.10) that quite good agreement exists between the differential oscillator strength spectra obtained for the normahzed experimental spectra and those derived from the MCQD calculations. The experimental optical oscillator strengths for transitions to the 6ai, 2b\ and 562 orbitals as shown in table 4.4 have been obtained by integrating the respective peak areas in figs. 4.5 and 4.6 and then applying an estimated Bethe-Born conversion factor of E2'5. Good quantitative agreement exists between the measured and calculated values. Chapter 4. 53 > 0) CM I o X I-o 2 Ui OH h-Ul OH O O o OH Ul 10H 5" 0-5H 0 (a) MCQD Calculation AT edge 6ai 2b' 7a, 4pb, 4pa! 4sa! \ —P JlJrJkl N02 01s :5b2 15.0 5.0 -5.0 -15.0 TERM VALUE (eV) (b) ISEELS Experiment 2bi Aied9e 6 = 0' E0=3700eV AE=0.14eV r—i 1 l l l 12 34 89 J L_ 10 520 530 540 550 560 570 ENERGY LOSS (eV) 580 Figure 4.9: (a) MCQD calculation and (b) low-resolution 0 Is ISEELS spectrum of N02 in the discrete and continuum regions. Spectrum (b) as shown is not Bethe-Born corrected. Chapter 4. V to o Cr ion i > 0) CN I - 5H o Ld cr r— LO cr O 0 10H 5H OH (a) MCQD Calculation N02 01s 2bi 6a-7a-4pbi 4sa1^pai JO Aiedge I Jlk I0.0 5.0 TERM VALUE (eV) 0.0 (b) ISEELS Experiment 6a-2b-/ 0=0' E0=3700eV AE=0.090eV 4sa id, , i 01s edges i r I 2 i i i II—r 45 678 9 __i I— Figure discrete 530 540 ENERGY LOSS (eV) 4.10: (a) MCQD calculation and (b) high-resolution O Is ISEELS spectrum of N02 in region. Spectrum (b) as shown is not Bethe-Born corrected. Chapter 4. 55 Table 4.5: Experimental and calculated data" for 0 Is excitation of N02 Experimental this work feature energy (eV) term value oscillatorb strength (xlO-2) MCQD calculation term value0 (eV) oscillator strength (xlO"2) assignment final orbital (to 3AX limit)1* 1 2 3 4 5 6 7 8 530.32 532.36 536.34 537.76 538.20 538.82 539.18 539.6 IP^Ax) 541.3e IP^Ai) 541.97e 10 547.18 10.98 8.94 4.96 3.54 3.10 2.48 2.12 1.7 4.1 8.1 (4.21) (3.77) (3.15) (2.79) (2.37) 540.52 0.78 (1.45) -5.88 4.3 13.12 10.62 4.80 3.22 3.05 2.40 1.98 1.89 1.70 1.50 1.49 1.48 1.44 1.39 0.96 0.89 0.84 0.83 0.82 0.80 0.78 0.60 0.57 0.54 0.53 0.52 0.52 0.51 0.40 0.37 0.37 0.36 0.29 0 -2.45 3.68 5.84 0.54 0.52 0.40 0.06 0.20 3.06 0.08 1.06 0.06 0.06 0.08 0.06 0.02 0.40 0.04 0.04 0.02 0.02 0.24 0.02 0.14 0.02 0.02 0.02 0.02 0.08 0.06 0.02 0.02 0.04 0.04 6ax 26i(ftf) Asa,! 4pbx 4pax 4pb2 5sax 7ax(a*) 3dbx 3d2ax 3db2 3da2 5p6i 5pax 4dbx 4doax 4db2 4da2 6pbx 6pax 4d2ax 5dbx 5doai 5db2 5da2 7PW 7pax 5d2ax 6^0^! 6db2 6da2 6d2ax IdQd-y oo "See fig. 4.9 and 4.10. *A kinematic Bethe-Born conversion of E2,5 has been applied. cWith respect to the 3AX limit. dNote assignment for 1A\ term value must be interpolated since MCQD calculation is shown for 3AX terms only. ^AtMi, IPs from XPS [84,85,86]. Chapter 4. 56 Figs. 4.9a and 4.9b show the measured ISEELS 0 Is spectra of N02 at low resolution (0.14 eV FWHM), together with the MCQD calculation. Fig. 4.10 shows the high-resolution experimental 0 Is spectrum and the MCQD calculation in the below-edge region in somewhat greater detail. The approximate differential oscillator strength scale for the experimental spectra as shown in figs. 4.9 and 4.10 was estabhshed as described above. The measured energies and oscillator strengths together with calculated oscillator strengths and term values, are shown in table 4.5. Also shown are the assignments based on a consideration of the MCQD calculations. The values of the experimental oscillator strengths for transitions to the 6ai, 2bx and 562 orbitals reported in table 4.5 include apphcation of an estimated Bethe-Born conversion of E25 to the peak areas in the spectra. The energies of the 0 Is 3AX and XAX ionization edges are assigned according to XPS measurements [84,85,86] using the singlet-triplet splitting of 0.67 eV reported by Davis et al. [84]. As has already been discussed with reference to fig. 4.8 the earlier reported O Is photoabsorption spectrum of N02 contains major contributions from impurities, and thus no effective comparison with the present work can be made. While the MCQD calculation is in quite good quantitative agreement with respect to the transition energies and also the relative intensities observed in the present ISEELS work the differences with experiment are greater than in the case of the N Is excitation (compare figs. 4.5 and 4.6 with figs. 4.9 and 4.10). These differences, particularly noticeable for the 6oti and 2&i states probably arise from the fact that the present calculations use C2v symmetry for the 0 Is excited and ionized states of N02 and thus do not take account of the broken symmetry caused by a localized Is hole in one of the O atoms. It can be seen that the 4sGt! Rydberg state is clearly visible (feature 3) in figs. 4.9b and 4.10b in contrast to the situation in the N Is spectrum where the corresponding transition is extremely weak. The greater intensity of the 4sai peak in the 0 Is spectrum reflects a further relaxation Chapter 4. 57 Table 4.6: Term values for N Is and 0 Is excitation of N02 Transition Measured term value (eV) a Estimated term value (eV) 3AX limit XAX limit from (Z -f 1) analogue 6ai 11.6 12.3 11.4 2&i 9.3 10.0 8.7 7ai 1.9 2.6 4 562 -3.6 -2.9 -6ax 11.0 11.7 -26i 8.9 9.6 -7ai 1.7 2.4 -5fc2 -5.9 -5.2 -N Is N Is N Is N Is 0 Is 0 Is O Is O Is "This work, from N02 ISEELS; see tables 4.4 and 4.5 'from data for valence-shell excitation of O3 using geometry and exchange correction—see ref. [82]. of the atomic-like (s —> s) selection rule due to the broken symmetry. The below-edge lax (°i) final state (peak 8) is quite prominent, as is the above-edge fe2 (&2) resonance. The MCQD calculation reproduces these features as well as the rest of the spectrum, quite well both for transition energies and oscillator strengths. In accord with the equivalent core model discussed in section 2.3.7, the term values of the N Is core excitations in N02 would be expected to be similar to those for the corresponding valence-shell excitations of the (Z + 1) analogue, O3, if geometry and exchange corrections are taken into account [82]. This situation for core-excited N02 and valence-excited O3 has been discussed in some detail by Schwarz et al. [82]. The term values of the O3 valence excitation obtained from extensive CI calculations were adapted [82] to the N02 geometry and allowance was made for exchange effects (since core-excited N02 is open-shell). Table 4.6 shows the adapted 03 valence-shell term values [82] in comparison with the presently measured N Is term values for several transitions. A quite reasonable correspondence exists, given the various approximations Chapter 4. 58 involved [82] in obtaining the estimated term values of O3 valence excitation. In a similar fashion the term values for the 0 Is excitations of NO (see table 4.6) could be used to obtain estimates of the valence-shell excitation energies of the species NOF. A consideration of the data in tables 4.4-4.6 shows that the term values for given core-to-virtual-valence transitions show systematic differences, with the 0 Is values being consistently lower than those for N Is. In contrast, and as expected (see discussed in section 2.3.1), the term values for Rydberg transitions to the same final orbitals are almost identical for N Is and 0 Is excitation. In conclusion, the present work demonstrates the use of high quahty MCQD calcula tions of transition energies and osciUator strengths to provide definitive interpretations of high resolution inner-shell electronic excitation spectra for the NO2 molecule. Chapter 5 Absolute Differential Oscillator Strengths for the Photoabsorption and the Ionic Photofragmentation of CF4, CF3C1, CF2C12 and CFC13 The relative photoabsorption spectra and time of flight (TOF) mass spectra used to derive absolute differential oscillator strengths (total and partial) for CF4, CF3C1, CF2C12 and CFCI3 were obtained using the dipole (e,e+ion) spectrometer described in section 3.1. 5.1 Electronic Structures The point group symmetries for CF4, CF3C1 and CFC13, and CF2C12 are T<j, C3t, and C2„ respectively. The electronic state configurations of the ground states of CF4, CF3CI, CF2C12 and CFCI3 are shown in table 5.7. The electronic states produced by ionizing cor responding outer and inner valence orbitals of corresponding vertical ionization energies are summarized in tables 5.8-5.11. In addition, the carbon K and fluorine K-edges of CF4 have been measured to be at 301.8 eV and 695.2 eV respectively by X-ray photoelectron spectroscopy [86]. 5.2 Photoabsorption Differential Oscillator Strengths for the Valence Shells The absolute photoabsorption differential oscillator strengths obtained in the present work for the valence shells of CF4, CF3C1, CF2C12 and CFCI3 are presented respectively in tables 5.12, 5.13, 5.14 and 5.15. They are shown diagrammatically in fig. 5.11a (12-100 eV), fig. 5.11b (70-200 eV) and (on an expanded scale) in fig. 5.11c (12-25 eV) 59 Chapter 5. 60 Table 5.7: Valence electronic configurations for the CF4, CF3C1, CF2C12 and CFC13 Molecule Inner valence orbitals Outer valence orbitals CF4 la2 1*2 2al 2t\ le4 Zt% lt\ CF3C1 lal le4 2al Za\ 2e4 4a2 3e4 4e4 la\ 5a2 5e4 CF2C12 lal lbl 2a\ lbl 3a2 2b\ 4a{ 2b2x 5a2 la2 362 362 6a2 2a2 462 462 CFCI3 lal 2al le4 3a2 4a2 2e4 3e4 5a2 4e4 5e4 la2 Chapter 5. 61 Table 5.8: Electronic ion states produced by photoionizing valence electrons from the CF4 ground state (Mi) Electronic ion states X2TX A2T2 B2E C2T2 B2AX Outer valence orbitals l*i 3t2 le 2t2 2ai Vertical IPs (eV)a 16.20 17.40 18.50 22.12 25.12 Electronic ion states E2T2 F2A2 Inner valence orbitals 1*2 Vertical IPs (eV)b 40.3 43.3 "IPs of outer valence are from He I and He II PES measurement [99]. 'IPs of inner valence are from PES measurement [86]. Chapter 5. 62 Table 5.9: Electronic ion states produced by photoionizing valence electrons from the CF3C1 ground state (Mi) Electronic ion states X2E A2AX B2A2 C2E D2E E2AX F2E &A\ Outer valence orbitals 5e 5ax la2 4e 3e 4ai 2e 3ai Vertical IPs (eV)a 13.08 15.20 15.80 16.72 17.71 20.20 21.8 23.8 Electronic ion states H2AX I2E PAX Inner valence orbitals 2ai le lai Vertical IPs (eV)b 26.9 40.0 42.5 "IPs of outer valence are from He I and He II PES measurement [100]. fcIPs of inner valence are from PES measurement presented in chapter 6. Chapter 5. 63 Table 5.10: Electronic ion states produced by photoionizing valence electrons from the CF2C12 ground state (MX) Electronic ion states X2B2 A2BX B2A2 CMi D2B1 F?BX Outer valence orbitals 462 46i 2a2 6ai 3b2 3fei Vertical IPs (eV)a 12.26 12.53 13.11 13.45 14.36 15.9 Electronic ion states F2A2 GMi H2BX + /Mi J2B2 K2AX Outer valence orbitals la2 5<zi 26i,4ai 2b2 3ai Vertical IPs (eV)a 16.30 16.9 19.3 20.4 22.4 Electronic ion states ~L2BX + M2AX N2BX OMx Inner valence orbitals 162,2ai 16i lai Vertical IPs (eV)b 27.2 38.6 41.1 "IPs of outer valence are from He I and He II PES measurement [100]. 'IPs of inner valence are from PES measurement presented in chapter 6. Chapter 5. 64 Table 5.11: Electronic ion states produced by photoionizing valence electrons from the CFC13 ground state (Mi) Electronic ion states iMi A2E B2E CMi D2E E2E F2A1 GMi Outer valence orbitals la2 be 4e 5ax 3e 2e 4ai 3ai Vertical IPs (eV)a 11.73 12.13 12.97 13.45 15.05 18.0 18.4 21.5 Electronic ion states H2E /Ma JMi Inner valence orbitals le 2ai lax Vertical IPs (eV)b 25.3 27.6 40.0 "IPs of outer valence are from He I and He II PES measurement [100]. *IPs of inner valence are from PES measurement presented in chapter 6. Chapter 5. 65 Table 5.12: Absolute differential oscillator strengths for the total photoabsorption and the dissociative photoionization of CF4 Photon Differential osciUator strength (10" -2eV-l) a Ionization energy Photo CF+ CF+ CF+ 'F+ C+ CF2+ efficiency (eV) absorption Vi • 12.0 0.91 12.5 2.38 13.0 10.50 13.5 22.25 14.0 21.38 14.5 13.83 15.0 14.58 15.5 23.92 0.81 0.03 16.0 26.28 3.64 0.14 16.5 27.95 7.80 0.28 17.0 29.99 14.95 0.50 17.5 32.89 22.47 0.68 18.0 35.57 29.85 0.84 18.5 36.69 34.22 0.93 19.0 39.64 37.48 0.95 19.5 40.89 39.69 0.97 20.0 42.11 42.11 1.00 6 20.5 45.70 45.64 0.06 21.0 48.61 48.49 0.12 21.5 50.61 49.86 0.75 22.0 52.36 50.19 2.17 22.5 52.27 48.13 4.14 23.0 51.39 46.24 5.15 23.5 49.15 43.83 5.31 24.0 48.17 42.95 5.22 24.5 46.91 42.18 4.73 25.0 45.11 41.01 4.11 continued on next page V(Mb) = 1.0975 x 102(d//d£;)(eV-1). ''The photoionization efficiency is constant and therefore assumed to be unity above 20.0 eV, see section 5.4 and the insert to fig. 5.11a for details. Chapter 5. 66 Table 5.12: (continued) Photon Differential oscillator strength (10 ^V"1) a energy Photo CF+ CF+ CF+ F+ C+ CF2+ (eV) absorption 25.5 42.37 38.72 3.65 26.0 40.83 37.82 3.01 26.5 40.19 37.60 3.59 27.0 39.57 37.19 2.38 27.5 39.02 37.00 2.02 28.0 39.03 37.25 1.78 28.5 38.71 37.00 1.71 29.0 38.91 37.29 1.62 29.5 38.95 37.24 1.64 0.07 30.0 38.91 37.15 1.65 0.12 31.0 38.78 36.86 1.67 0.26 32.0 38.59 36.30 1.73 0.56 33.0 39.42 36.63 1.90 0.89 34.0 39.79 36.56 1.98 1.24 35.0 39.55 35.58 2.14 1.70 0.07 0.06 36.0 39.42 34.95 2.13 1.99 0.15 0.21 37.0 38.76 33.68 2.15 2.19 0.28 0.45 38.0 39.39 33.59 2.22 2.34 0.46 0.78 39.0 39.21 32.61 2.27 2.49 0.65 1.20 40.0 38.99 31.77 2.37 2.34 0.86 1.66 41.0 38.65 31.09 2.37 2.04 1.12 2.03 42.0 37.08 30.07 2.24 1.81 1.15 1.82 43.0 35.24 28.59 2.24 1.50 1.23 1.68 44.0 33.38 27.10 2.12 1.27 1.23 1.61 0.05 45.0 31.37 25.61 2.07 1.14 1.24 1.27 0.04 46.0 30.01 24.64 1.92 1.09 1.14 1.12 0.09 47.0 29.05 23.75 1.91 1.01 1.21 1.06 0.12 48.0 27.99 22.96 1.78 0.99 1.16 0.99 0.12 49.0 27.07 22.00 1.69 1.01 1.15 1.05 0.17 50.0 26.37 21.48 1.54 0.94 1.26 1.02 0.13 55.0 23.92 18.39 1.48 1.07 1.60 1.22 0.15 Ionization efficiency Vi continued on next page V(Mb) = 1.0975 x 10a(d//dJS)(eV-1). Chapter 5. 67 Table 5.12: (continued) Photon Differential oscillator strength (10" -2eV-x) a Ionization energy Photo- CF+ CFt CF+ F+ C+ CF|+ efficiency (eV) absorption 60.0 22.45 16.69 1.43 1.13 1.79 1.17 0.23 65.0 19.83 14.40 1.34 1.08 1.79 1.02 0.20 70.0 18.09 12.84 1.24 0.98 1.89 0.94 0.20 75.0 16.39 11.33 1.07 1.00 1.88 0.93 0.19 80.0 15.02 10.11 0.96 0.97 1.88 0.93 0.17 85.0 13.71 86.0 13.23 87.0 13.28 88.0 12.73 89.0 12.58 90.0 12.56 91.0 12.02 92.0 11.76 93.0 11.57 94.0 11.55 95.0 11.27 96.0 11.08 97.0 10.89 98.0 10.73 99.0 10.59 100.0 10.39 110.0 8.93 120.0 7.63 130.0 6.53 140.0 5.63 150.0 4.88 160.0 4.39 170.0 3.64 180.0 3.12 190.0 3.18 200.0 2.61 V(Mb) = 1.0975 x 102(d//d.E)(eV-1). Chapter 5. 68 Table 5.13: Absolute differential oscillator strengths for the total photoabsorption and the dissociative photoionization of CF3C1  Photon Differential oscillator strength (10-2eV-1)a Ionization energy Photo- CF3C1+ CF2C1+ CF+ CFC1+ CFj CC1+ C1+ CF+ F+ C+ CF2C12+ efficiency (eV) absorption 7.5 0.44 8.0 0.34 8.5 0.40 9.0 4.42 9.5 9.93 10.0 9.35 10.5 11.14 11.0 20.75 11.5 28.45 12.0 30.60 12.5 36.14 0.25 2.99 0.09 13.0 42.04 0.35 14.73 0.36 13.5 42.16 0.39 21.45 0.52 14.0 40.71 0.47 23.57 0.07 0.59 14.5 37.25 0.34 0.23 21.37 0.09 0.59 15.0 36.41 0.28 0.65 19.44 0.05 0.56 15.5 39.91 0.24 2.16 21.96 0.04 0.61 16.0 47.21 0.31 5.51 28.38 0.03 0.72 16.5 50.72 0.26 10.30 30.66 0.06 0.81 17.0 53.06 0.26 14.48 32.61 0.07 0.89 17.5 54.26 0.32 17.25 32.30 0.08 0.92 18.0 56.10 0.30 19.16 33.72 0.10 0.95 18.5 57.44 0.24 20.35 34.53 0.09 0.96 19.0 57.30 0.34 21.16 35.10 0.06 0.24 0.99 19.5 56.29 0.19 20.63 32.88 0.08 0.72 0.39 0.98 20.0 56.15 0.18 18.97 30.92 0.05 1.29 1.20 0.94 20.5 56.50 0.30 18.21 30.87 0.10 2.45 2.34 0.96 21.0 56.48 0.21 16.20 28.43 0.09 5.09 3.78 0.95 21.5 56.38 0.24 15.04 26.78 0.17 6.88 4.14 0.94 22.0 57.39 0.24 15.78 27.18 0.24 8.15 4.69 0.98 22.5 57.04 0.22 16.18 26.92 0.30 8.72 4.70 1.00 continued on next page V(Mb) = 1.0975 x 102(d//d£:)(eV-:l). Chapter 5. 69 Table 5.13: (continued) Photon Differential oscillator strength (10_2eV-1)° Ionization energy Photo- CF3C1+ CF2C1+ CF+ CFC1+ CF+ CC1+ C1+ CF+ F+ C+ CF2C12+ efficiency (eV) absorption 23.0 55.58 0.24 16.03 25.49 0.30 8.42 4.47 0.35 0.99 23.5 55.12 0.22 16.27 25.35 0.30 8.36 4.22 0.41 1.006 24.0 53.38 0.14 16.25 24.09 0.28 7.95 4.21 0.46 24.5 51.02 0.14 15.74 22.84 0.25 7.40 4.01 0.64 25.0 49.98 0.21 15.81 21.76 0.27 7.11 4.05 0.77 25.5 48.77 0.18 15.86 20.98 0.23 6.60 3.97 0.94 26.0 47.07 0.20 15.50 19.86 0.21 6.13 4.05 1.11 26.5 45.64 0.10 15.37 18.93 0.20 5.79 3.91 1.33 27.0 44.39 0.13 15.40 17.96 0.16 5.47 3.80 1.48 27.5 42.25 0.11 14.83 16.92 0.14 5.12 3.50 1.64 28.0 40.95 0.06 14.72 15.80 0.16 4.90 0.03 3.64 1.64 28.5 40.04 0.12 14.55 15.15 0.16 4.74 0.07 3.47 1.78 29.0 39.36 0.08 14.64 14.40 0.12 4.62 0.09 3.51 1.89 29.5 38.37 0.08 14.23 13.67 0.12 4.52 0.13 3.61 2.01 30.0 37.66 0.06 14.22 13.09 0.13 4.46 0.15 3.57 1.98 31.0 35.06 0.06 13.61 11.68 0.12 4.21 0.24 3.24 1.88 32.0 33.67 0.04 13.33 10.57 0.08 4.08 0.29 3.32 1.96 33.0 31.84 0.02 12.98 9.39 0.10 3.86 0.31 3.30 1.85 0.03 34.0 31.59 0.02 12.83 8.70 0.09 4.10 0.43 3.36 1.86 0.06 0.15 35.0 30.28 0.02 12.40 7.80 0.09 4.08 0.43 3.38 1.80 0.07 0.22 36.0 29.35 0.02 11.95 7.14 0.12 4.05 0.46 3.47 1.71 0.10 0.33 37.0 29.57 0.00 11.64 6.93 0.10 4.27 0.47 3.75 1.75 0.19 0.48 38.0 29.44 0.00 11.47 6.47 0.10 4.35 0.52 3.88 1.73 0.24 0.62 0.05 39.0 29.55 0.00 11.29 6.31 0.11 4.55 0.47 4.08 1.66 0.28 0.70 0.07 40.0 28.70 0.00 10.62 6.05 0.10 4.55 0.42 4.23 1.56 0.32 0.75 0.09 continued on next page acr(Mb) = 1.0975 x 102(d//d£:)(eV-1). 6The photoionization efficiency is constant and therefore assumed to be unity above 23.5 eV, see section 5.4 and the insert to fig. 5.12a for details. Chapter 5. 70 Table 5.13: (continued)  Photon Differential oscillator strength (10_2eV_1)° Ionization energy Photo- CF3C1+ CF2C1+ CF+ CFC1+ CF+ CC1+ C1+ CF+ F+ C+ CF2C12+ efficiency (eV) absorption 77,-41.0 28.00 0.00 10.25 5.78 0.10 4.46 0.37 4.39 1.48 0.34 0.74 0.08 42.0 26.54 0.00 9.59 5.51 0.10 4.31 0.32 4.09 1.44 0.37 0.71 0.08 43.0 25.71 0.00 9.30 5.31 0.08 4.20 0.30 4.07 1.42 0.36 0.58 0.09 44.0 24.48 0.00 8.81 5.11 0.11 3.96 0.25 3.88 1.36 0.36 0.56 0.09 45.0 23.44 0.00 8.29 4.94 0.09 3.82 0.21 3.86 1.35 0.33 0.47 0.08 46.0 22.17 0.00 7.89 4.75 0.08 3.59 0.20 3.54 1.29 0.32 0.41 0.10 47.0 22.07 0.00 7.76 4.67 0.08 3.51 0.21 3.59 1.36 0.34 0.45 0.10 48.0 20.98 0.00 7.33 4.50 0.07 3.27 0.20 3.40 1.32 0.35 0.44 0.09 49.0 20.73 0.00 7.18 4.40 0.06 3.22 0.21 3.46 1.36 0.35 0.41 0.08 50.0 19.95 0.00 6.92 4.21 0.07 3.02 0.19 3.32 1.36 0.37 0.40 0.08 55.0 17.83 0.00 5.61 3.94 0.06 2.83 0.16 2.93 1.38 0.40 0.40 0.11 60.0 16.28 0.00 4.95 3.36 0.02 2.59 0.15 2.81 1.37 0.49 0.45 0.08 65.0 14.59 0.00 4.29 2.94 0.03 2.27 0.14 2.65 1.24 0.50 0.45 0.08 70.0 13.19 0.00 3.85 2.64 0.05 2.07 0.12 2.32 1.11 0.50 0.43 0.09 75.0 11.89 0.00 3.35 2.29 0.03 1.90 0.11 2.18 1.00 0.54 0.43 0.05 80.0 11.03 0.00 3.06 2.10 0.02 1.64 0.11 2.08 0.95 0.59 0.41 0.07 85.0 10.23 90.0 8.96 95.0 8.24 100.0 7.95 110.0 6.55 120.0 5.63 130.0 5.04 140.0 4.29 150.0 3.82 160.0 3.55 170.0 3.15 180.0 2.82 190.0 2.70 200.0 2.55 °<r(Mb) = 1.0975 x 102(d//d£)(eV_1). Chapter 5. 71 Table 5.14: Absolute differential oscillator strengths for the total photoabsorption and the dissociative photoionization of CF2CI2  Photon Differential oscillator strength (10_2eV_1)a Ionization energy Photo- CFClJ CF2C1+ CCl£ CFC1+ CF+ CC1+ C1+ CF+ F+ C+ CF2C12+ efficiency (eV) absorption 77,-8.5 0.17 9.0 6.08 9.5 19.22 10.0 26.20 10.5 30.45 11.0 38.00 11.5 42.48 8.33 0.20 12.0 46.44 20.84 0.45 12.5 52.02 32.09 0.62 13.0 55.32 39.06 0.71 13.5 53.68 39.32 0.73 14.0 56.98 0.14 49.20 0.87 14.5 63.48 0.62 55.84 0.89 15.0 66.49 1.05 59.70 0.91 15.5 68.95 2.47 62.66 0.94 16.0 71.20 4.81 65.83 0.99 16.5 72.36 6.66 64.16 0.98 17.0 72.47 7.98 63.80 0.99 17.5 74.37 8.93 65.12 0.32 1.0 6 18.0 76.63 10.10 65.52 1.01 18.5 79.73 10.32 66.72 0.34 2.36 19.0 81.06 10.19 65.39 0.88 4.59 19.5 81.55 9.82 63.33 1.47 6.93 20.0 80.31 9.41 59.31 2.33 8.50 0.31 0.45 continued on next page V(Mb) = 1.0975 x 102(d//d^)(eV_1). *The photoionization efficiency is constant and therefore assumed to be unity above 17.5 eV, see section 5.2.3 and the insert to fig. 5.13a for details. Chapter 5. 72 Table 5.14: (continued) Photon Differential oscillator strength (10 eV ) Ionization energy Photo- CFClJ CF2C1+ CClJ CFC1+ CFj CC1+ C1+ CF+ F+ C+ CF2C12+ efficiency (eV) absorption 20.5 77.94 8.67 56.46 2.87 8.72 0.44 0.79 21.0 75.44 8.18 53.74 3.16 8.69 0.70 0.97 21.5 73.03 8.16 50.78 3.36 8.90 0.69 1.14 22.0 71.08 7.82 48.02 3.67 8.90 0.95 1.72 22.5 69.58 7.44 46.18 , 3.73 8.84 1.08 2.32 23.0 68.21 7.14 44.43 3.84 9.16 0.95 2.68 23.5 66.63 6.94 42.18 4.01 9.04 1.09 3.37 24.0 65.08 6.79 40.07 4.00 8.85 0.21 1.33 3.82 24.5 63.23 6.52 38.45 3.99 8.64 0.20 1.25 4.19 25.0 61.86 6.64 37.02 3.53 8.35 0.35 1.15 4.82 25.5 59.95 6.61 35.53 3.27 7.94 0.50 1.35 4.75 26.0 57.02 6.60 33.23 2.95 7.53 0.64 1.45 4.61 26.5 54.65 6.68 31.42 2.79 7.14 0.63 1.58 4.42 27.0 52.10 6.41 29.48 2.55 6.89 0.78 1.66 4.32 27.5 49.61 6.34 27.50 2.45 6.42 0.86 1.81 4.24 28.0 47.39 6.30 25.92 2.20 6.61 0.91 1.97 3.97 28.5 45.25 6.36 24.09 2.20 5.72 0.93 2.10 3.87 29.0 43.28 6.21 22.54 2.04 5.72 1.05 2.08 3.64 29.5 40.16 5.93 20.49 1.83 5.32 1.00 2.15 3.44 30.0 39.60 6.06 19.81 1.85 5.21 1.01 2.18 3.49 31.0 35.26 5.82 16.55 1.77 4.79 1.05 2.17 3.02 0.09 32.0 32.82 5.54 14.74 1.61 4.58 1.05 2.24 2.83 0.23 33.0 29.71 5.34 12.62 1.49 4.30 1.03 2.26 2.45 0.24 34.0 27.11 4.99 10.71 1.53 3.99 0.89 2.34 2.30 0.36 35.0 25.86 4.85 9.63 1.49 3.88 0.85 2.54 2.21 0.40 36.0 24.68 4.61 8.71 1.42 3.73 0.83 2.70 2.09 0.15 0.45 37.0 24.81 4.58 8.23 1.59 3.77 0.80 3.03 2.17 0.14 0.51 38.0 23.71 4.42 7.49 1.54 3.60 0.71 3.10 2.07 0.16 0.57 0.05 continued on next page V(Mb) = 1.0975 x 102(d//dS)(eV-1). Chapter 5. 73 Table 5.14: (continued) Photon Differential oscillator strength (10 eV )° Ionization energy Photo- CFC1+ CF2C1+ CC1+ CFC1+ CF+ CC1+ C1+ CF+ F+ C+ CF2C12+ efficiency (eV) absorption 77,-39.0 22.84 40.0 22.27 42.0 21.20 44.0 19.84 46.0 18.49 48.0 17.36 50.0 16.73 55.0 14.91 60.0 13.83 65.0 12.97 70.0 11.75 75.0 10.51 80.0 9.94 85.0 8.92 90.0 8.32 95.0 7.71 100.0 6.91 110.0 6.22 120.0 5.41 130.0 4.70 140.0 4.07 150.0 3.60 160.0 3.25 170.0 2.76 180.0 2.63 190.0 2.32 200.0 4.08 4.30 7.03 1.50 3.51 0.70 3.16 1.96 0.14 0.51 0.04 4.04 6.59 1.62 3.43 0.59 3.26 2.01 0.17 0.47 0.08 3.78 6.07 1.56 3.23 0.56 3.21 2.14 0.19 0.37 0.09 3.38 5.49 1.48 3.06 0.55 3.15 2.14 0.18 0.33 0.09 3.04 5.12 0.02 1.35 2.77 0.52 3.00 2.10 0.17 0.30 0.09 2.81 4.79 0.00 1.25 2.62 0.52 2.84 1.99 0.18 0.25 0.10 2.63 4.66 0.02 1.19 2.54 0.55 2.74 1.87 0.20 0.26 0.08 2.21 4.00 0.01 0.93 2.21 0.53 2.69 1.69 0.21 0.34 0.09 1.85 3.69 0.02 0.90 2.04 0.50 2.73 1.52 0.23 0.30 0.05 1.71 3.31 0.02 0.80 1.91 0.46 2.67 1.39 0.28 0.36 0.06 1.54 2.95 0.02 0.72 1.66 0.44 2.42 1.25 0.31 0.34 0.09 °<r(Mb) = 1.0975 x 102(d//d£;)(eV-1). Chapter 5. 74 Table 5.15: Absolute differential oscillator strengths for the total photoabsorption and the dissociative photoionization of CFC13  Photon Differential oscillator strength (10" -2eV-i)a Ionization energy Photo- CC1+ CFCLt CC1+ CFC1+ CC1+ C1+ CF+ F+ C+ efficiency (eV) absorption Vi 6.0 0.39 6.5 0.57 7.0 1.14 7.5 1.60 8.0 3.03 8.5 8.05 9.0 25.57 9.5 42.97 10.0 48.32 10.5 47.07 11.0 48.04 11.5 49.81 3.14 0.06 12.0 52.49 17.81 0.34 12.5 57.03 31.61 0.55 13.0 65.10 50.73 0.78 13.5 74.42 65.98 0.89 14.0 83.81 0.44 82.96 0.99 14.5 93.08 1.11 91.97 1.06 15.0 93.57 1.51 92.06 15.5 93.74 2.10 91.64 16.0 90.87 2.31 88.57 16.5 93.26 2.71 90.00 0.55 17.0 95.39 3.00 91.23 1.16 17.5 95.88 2.22 89.83 0.44 3.39 18.0 94.85 1.76 85.35 1.06 6.21 0.47 18.5 93.93 1.90 79.72 2.01 9.55 0.21 0.53 continued on next page V(Mb) = 1.0975 x 102(d//dJE;)(eV-1). *The photoionization efficiency is constant and therefore assumed to be unity above 14.5 eV, see section 5.4 and the insert to fig. 5.14a for details. Chapter 5. 75 Table 5.15: (continued) Photon Differential oscillator strength (10 -2eV-i)a Ionization energy Photo- CC1+ CFClJ CC1+ CFC1+ CC1+ C1+ CF+ F+ C+ efficiency (eV) absorption Vi 19.0 92.48 1.59 75.05 2.75 11.62 0.33 1.13 19.5 90.09 1.72 71.27 3.09 12.06 0.36 1.58 20.0 90.26 1.45 69.77 3.37 12.62 0.53 2.52 20.5 89.08 1.45 68.42 3.43 12.19 0.51 3.08 21.0 88.64 1.27 66.78 3.75 12.38 0.24 0.47 3.74 21.5 87.65 1.45 65.06 3.70 12.02 0.77 0.39 4.25 22.0 86.05 1.40 63.14 3.74 11.73 1.17 0.63 4.23 22.5 84.75 1.32 61.33 3.98 11.06 1.64 0.67 4.75 23.0 78.88 1.23 55.55 3.65 10.34 2.48 0.69 4.94 23.5 78.07 1.28 54.47 3.14 10.12 2.99 0.97 5.11 24.0 73.61 1.14 51.16 3.20 8.80 3.42 1.09 4.80 24.5 71.98 1.26 49.10 2.95 8.51 4.04 1.36 4.75 25.0 68.33 1.14 46.14 2.73 7.92 4.24 1.87 4.30 25.5 64.11 1.10 42.47 2.44 7.49 4.30 2.15 4.16 26.0 61.75 1.02 40.91 2.23 7.25 4.37 2.33 3.64 26.5 58.31 1.01 37.62 2.36 6.51 4.75 2.64 3.43 27.0 55.14 0.98 35.11 2.00 6.39 4.59 2.79 3.28 27.5 51.82 1.01 32.20 2.21 6.07 4.31 2.79 3.23 28.0 50.19 0.96 30.48 2.16 6.07 4.46 2.88 3.19 28.5 46.80 0.97 28.20 1.92 5.83 4.16 2.92 2.79 29.0 43.74 0.85 25.81 1.90 5.48 3.91 2.80 2.80 0.19 29.5 41.30 0.85 23.86 1.96 5.61 3.63 2.70 2.48 0.22 30.0 37.54 0.83 21.37 1.77 4.87 3.25 2.84 2.32 0.29 31.0 33.75 0.70 16.82 1.66 4.98 3.14 3.71 2.24 0.50 32.0 29.07 0.68 13.79 1.53 4.49 2.64 3.60 1.80 0.53 33.0 25.69 0.57 11.52 1.39 4.01 2.35 3.51 1.81 0.54 34.0 22.12 0.44 9.51 1.27 3.59 2.01 3.24 1.57 0.47 35.0 19.92 0.45 8.32 1.13 3.29 1.81 3.16 1.40 0.36 continued on next page V(Mb) = 1.0975 x 102(d//d^)(eV_1). Chapter 5. 76 Table 5.15: (continued) Photon energy Photo-(eV) absorption Differential oscillator strength (10 2eV 1)a Ionization CC# CFClJ CCll CFC1+ CC1+ C1+ CF+ F+ C+ efficiency Vi 36.0 37.0 38.0 39.0 40.0 41.0 43.0 45.0 47.0 49.0 50.0 52.0 54.0 56.0 58.0 60.0 62.0 64.0 66.0 68.0 70.0 72.0 74.0 76.0 78.0 80.0 82.0 84.0 17.53 17.57 15.69 15.09 14.72 14.22 13.52 12.92 12.44 11.59 11.77 11.19 10.96 10.93 10.33 10.17 9.91 9.60 9.95 9.47 9.27 8.83 8.47 8.16 7.71 7.75 7.33 7.54 0.37 6.68 1.00 3.13 1.49 3.14 1.31 0.40 0.38 6.25 1.22 3.23 1.48 3.28 1.39 0.35 0.34 5.38 0.94 2.99 1.37 3.11 1.24 0.01 0.31 0.32 5.14 1.03 2.75 1.34 2.99 1.18 0.03 0.30 0.30 4.89 0.99 2.55 1.28 3.07 1.35 0.03 0.27 0.31 4.52 0.98 2.60 1.28 2.97 1.26 0.03 0.26 0.30 4.08 0.90 2.49 1.31 2.89 1.29 0.04 0.23 0.26 3.83 0.85 2.27 1.29 2.90 1.26 0.04 0.23 0.25 3.66 0.82 2.16 1.28 2.83 1.19 0.04 0.20 0.21 3.46 0.73 1.93 1.20 2.70 1.11 0.03 0.20 continued on next page V(Mb) = 1.0975 x 102(d//d£;)(eV-1). Chapter 5. 77 Table 5.15: (continued) Photon Differential oscillator strength (10 2eV 1)a Ionization energy Photo- CCL+ CFCit CCLt CFC1+ CC1+ C1+ CF+ F+ C+ efficiency (eV) absorption Vi 86.0 7.10 88.0 7.08 90.0 6.98 92.0 6.17 94.0 6.02 96.0 6.10 : 98.0 6.10 100.0 6.02 105.0 5.62 110.0 5.13 115.0 4.98 120.0 4.65 125.0 4.34 130.0 4.07 135.0 3.77 140.0 3.54 145.0 3.34 150.0 3.10 155.0 3.01 160.0 2.79 165.0 2.73 170.0 2.57 175.0 2.46 180.0 2.37 185.0 2.21 190.0 2.04 195.0 2.16 200.0 ' 3.31 V(Mb) = 1.0975 x 102(d//d£7)(eV_1). Chapter 5. 78 for CF4; in fig. 5.12a (7.5-100 eV), fig. 5.12b (70-200 eV) and fig. 5.12c (7.5-35 eV) for CF3C1; in fig. 5.13a (8.5-100 eV), fig. 5.13b (70-200 eV) and fig. 5.13c (8.5-36 eV) for CF2C12; and in fig. 5.14a (6-100 eV), fig. 5.14b (65-200 eV) and fig. 5.14c (6-38 eV) for CFCI3. The absolute photoabsorption values for CF4, CF3C1, CF2C12 and CFCI3 were ob tained in the present work using the partial TRK sum-rule as discussed in sections 2.1 and 2.3.8. The total areas under the relative photoabsorption spectra (i.e. the Bethe-Born converted electron energy loss spectra) were normalized to total integrated oscilla tor strengths of 33.18, 33.18, 33.17 and 33.17 respectively. These sums correspond to 32 valence electrons for each of the four molecules CF4, CF3C1, CF2C12 and CFC13 plus estimated contributions of 1.18, 1.18, 1.17 and 1.17 respectively for the Pauh excluded transitions from the inner shells to the already occupied valence shell orbitals [112]. The fractions of the areas above 200 eV for CF4 and CF3C1, and above 190 eV and 195 eV for CF2C12 and CFC13 respectively were estimated from extrapolation by fitting a curve of the form: % = AE'1-5 + BE'25 + CE'35 (5.41) dE to the experimental data over the energy ranges 70-200 eV for CF4 and CF3C1, 70-190 eV for CF2C12 and 65-195 eV for CFCI3, and then integrating the respective equations from the upper energy limit of the above fitting ranges to infinity (df/dE is the differential oscillator strength, E is the excitation energy and A, B and C are constants). A similar approach has been used by Dillon and Inokuti to fit an analytical function to measured differential oscillator strengths [113]. The presently used procedure has been found to provide a very good fit to experimental data in a series of other measurements [16,114, 115]. The best fit (see figs. 5.11b, 5.12b, 5.13b and 5.14b) was determined by the method of least squares using a computer program written by Dr. G. Cooper for the purpose. Chapter 5. 79 Table 5.16: The coefficients of the extrapolating formula (equation 5.41) for CF4, CF3CI, CF2C12 and CFC13  Molecules Fitting coefficients A B C CF4 18.439 1.4625 x 104 -5.9640 x 105 CF3CI 49.004 4.7303 x 103 -1.9156 x 105 CF2C12 38.348 5.9654 x 103 -2.6863 x 105 CFCI3 43.662 3.6390 x 103 -2.1182 x 105 For the present data the so obtained best fit coefficients A, B and C for each of CF4, CF3CI, CF2CI2 and CFCI3 are summarized in table 5.16. The extrapolated portions of oscillator strength with respect to the total oscillator strengths are 17.0% and 23.8% respectively for CF4 and CF3C1 from 200 eV to infinity, 20.7% for CF2C12 from 190 eV to infinity, and 21.0% for CFCI3 from 195 eV to infinity. The accuracy of the absolute differential oscillator strength scales is estimated to be better than ±5%. An indication of the random errors is given by the smoothness of the data in various continuum regions. When comparing the present results with other work in the following sections, it should be noted that the dipole (e,e) technique has constant energy resolution (1 eV FWHM) at all photon energies, whereas the photoabsorption techniques have an energy resolution (i.e. AA/A2) which becomes broader with increasing photon energy [20,75]. Another feature of the present work that should be remembered in comparing and as sessing the various data sets is that the present dipole (e,e) measurements, unlike the other determinations, have the advantage of an absolute scale determined by the partial TRK sum rule and thus they are further constrained by the requirements of the total oscillator strength sum. Chapter 5. 80 5.2.1 The CF4 Photoabsorption Differential Oscillator Strengths The presently reported measurements on CF4 are compared with previously reported photoabsorption [101,102] as well as photoionization data (sum of (X+A-\-B-\-C-\-D) states only, without including the inner valence states E and F) [105] obtained using tunable light sources in fig. 5.11a. In fig. 5.11c, photoabsorption data obtained in the low photon energy region with the Hopfield He II continuum as a radiation source [103] and also data derived from small momentum transfer electron impact measurements [104] are shown on an expanded scale. The only pre-ionization edge structure clearly observed is a peak at 13.5 eV which has been assigned as the Rydberg transition ltx —* 3p [116], while the other Rydberg transi tions heavily overlap each other. A maximum at 22 eV and a broad feature at ~40 eV are observed. The data of Lee et al. [101] shows the same maximum and broad feature. In the region 33-69 eV, the agreement between our data and that of Lee et al. [101] is quite good. However, in the 16-36 eV energy region, the data of Lee et al. is higher than the present results. Similar discrepancies in this same energy region (16-24 eV) have also been observed in the comparisons between our results (figs. 5.12 and 5.13) and those of Lee et al. [101] and Wu et al. [110] for the molecules CF3C1 and CF2C12. We note that in the experiments of refs. [101,110] photoabsorption cross sections were measured with a Sn film in the region 16-24 eV and an Al film in the region 24-71 eV to separate the absorption cell from the high vacuum of the electron storage ring. Therefore the differ ences between the present results and those reported by Lee et al. [101] in the energy region 16-24 eV are most hkely due to a systematic error in the use of the Sn film in the latter work. Also for the data of Lee et al., in the 23.8-36 eV region second order hght had a significant effect and the experimental error in this region was reported to be as Chapter 5. 81 20 25 30 Photon Energy (eV) • Ph Abs, dipole (e,e) o Ph Abs [101,102] m Ph Abs [103] v Ph Abs from EELS [104] Ph Ion {X+A+B+ C+D) [105] Total Ph Ion (<20 eV) this work 60 £ O h-40 UJ CO CO CO o o 20 40 • Ph Abs, dipole (e,e) — Polynomial fit 120 160 200 PHOTON ENERGY (eV) Figure 5.11: Absolute photoabsorption differential oscillator strengths for the valence shell of CF4. a) 10-100 eV (insert shows ionization efficiency), b) 70-200 eV. c) 10-30 eV (expanded scale). Chapter 5. 82 much as 20%. This may well account for the disagreement between the present work and the data of Lee et al. in the region of 25-33 eV. The photoionization data of Carlson et al. [105], which is the sum of the electronic state partial differential oscillator strengths for the production of the ion states X, A, B, C and D, are also shown in fig. 5.11a. In the region above 34 eV, where the E state starts to be produced [117], the data of Carlson et al. (i.e. the sum of the electronic state partial photoionization differential oscillator strengths X+A-\-B-\-C+D) are therefore understandably lower than the total photoabsorption. Below 22 eV, the data of Carlson et al. are lower than the presently reported total photoionization differential oscillator strengths (i.e. the photoabsorption differential oscillator strengths multiplied by the photoionization efficiency) which are shown by the dashed hne on fig. 5.11a. It is noteworthy that in the 25-34 eV region, the data of Carlson et al. are significantly higher than the present work. The cause of this discrepancy is probably either the presence of higher order radiation (as in ref. [101]) or the method used for determining the absolute cross-section scale in the optical mea surements [105]. In the latter work, the absolute values were obtained by calibrating the apparatus with noble gases and measuring the gas pressure. Such procedures are extremely difficult and can lead to large errors as has been discussed earlier [115,118]. A broad feature (fig. 5.11a) centered at ~ 40 eV is observed in the present pho toabsorption measurements for CF4 and is also seen in the work of Lee et al. [101]. Similar but weaker features are also seen in the spectra of CF3C1 (fig. 5.12a), CF2Ci2 (fig. 5.13a) and CFC13 (fig. 5.14a) at photon energies ~ 40 eV, ~ 40 eV and ~ 37 eV respectively. This feature may be associated with inner valence ionization or possibly scattering (diffraction) of the outgoing (outer valence) photoelectrons by the neighboring atoms in the molecules [121,122,123,124,125], as discussed for CF3C1 in section 5.2.2. Chapter 5. 83 5.2.2 The CF3C1 Photoabsorption Differential Oscillator Strengths The presently reported measurements on CF3C1 are compared with earlier photoab sorption measurements [101,109] obtained using synchrotron radiation hght sources in figs. 5.12a and 5.12b. In fig. 5.12c the present photoabsorption data are also compared in the low energy region (7.5-35 eV) with previously reported results obtained using syn chrotron radiation [101,107] and the helium Hopfield continuum [106] as light sources. The photoabsorption data derived from earher small momentum transfer electron impact measurements [104] which were originally reported in the form of integrated oscillator strengths have been converted to average differential oscillator strengths (i.e. the inte grated oscillator strengths divided by the corresponding energy intervals) and are also shown in fig. 5.12c. The different energy resolution characteristics of the present dipole (e,e) techniques and optical methods (i.e. the large differences in energy resolution and the fact that the energy resolution changes with photon energy in optical experiments—see section 5.2) comphcates comparison of the various data sets at lower energies, particularly in the region of discrete excitation. In particular meaningful comparisons of such data are not possible below 11 eV and such higher resolution data from refs. [106,107] are omitted from fig. 5.12c. The present photoabsorption spectrum is similar in shape to those reported in refs. [101,104,107] in the low energy region below 23 eV. However, the magnitudes of the reported cross-sections [101,104,106,107] vary considerably. Rydberg transitions have been assigned to the various features in the low energy region below 25 eV. In particular, the peak at 9.5 eV has been attributed to the 5e —> 4s Rydberg transition [104,119]. Similarly, Rydberg transitions (5e —> 5s and/or 5e —» 3d), (4e —> 4s and/or la2 —> 4p) and 4ax —» 4s are the assignments for the features at 11.5 eV, 13.5 eV and 16.5 eV Chapter 5. 84 80r > CD N I o O OH E-H (a) CP .1.0 60 40 OH O EH < i—i o CO o <: I—H H 0. 0 ^ 15r OH W &H Q & O i—i E-H PH OH O CO PQ < O E-H O K OH 10 0l o o o c >-o z w o E w 0.5 z o H <c \o z \ 2 0.0 • this work o ref. [108] CF3 20 60 PHOTON ENERGY (eV) Via • Ph Abs, dipole (e,e) o Ph Abs [101] o 20 40 60 80 100 Polynomial fit • Ph Abs, dipole (e,e) o Ph Abs [109] 80h 40 80 120 160 200 0 (c)-• Ph Abs, dipole (e,e) o Ph Abs [101] a Ph Abs [106] • Ph Abs [107] • Ph Abs from EELS [104] 10 20 30 PHOTON ENERGY (eV) Figure 5.12: Absolute photoabsorption differential oscillator strengths for the valence shell of CF3C1. a) 7.5-100 eV (insert shows ionization efficiency), b) 70-200 eV. c) 7.5-35 eV (expanded scale). Chapter 5. 85 [104,119]. The two maxima in the 18-24 eV region have been recently assigned to the Rydberg transitions (4ai —• 5s and/or 2e —> 4p) and 2ai —» 3s [119]. A broad feature (fig. 5.12a) centered at ~40 eV is observed in the present photoab sorption measurement for CF3C1 and is also seen in the work of Lee et al. [101]. A similar but even more prominent broad feature at ~40 eV is also present in the photoabsorption differential oscillator strength spectrum of CF4 (fig. 5.11a). Similar but weaker features are also seen in the photoabsorption differential oscillator strength spectra of CF2CI2 (fig. 5.13a) and CFCI3 (fig. 5.14a) at photon energies ~40 eV and ~37 eV respectively. The amphtudes of these structures decrease as the number of F atoms decreases. In this regard it is noteworthy that these structures occur close to the region of the onsets of ionization of the inner valence (F 2s) orbitals (see chapter 6 and ref. [120]) and it is possible that they are associated with the cross sections for these processes. However it should be noted that MS-Xa calculations and PES partial cross section measurements of CF3CI indicate a maximum in some of the outer valence partial photoionization chan nels in a similar energy range [121]. The authors [121] pointed out that these predicted and observed outer valence structures are not due to shape resonances but are probably associated with scattering (diffraction) of the photoelectrons by the neighboring atoms in the molecule (see also refs. [122,123,124,125]). Above a photon energy of 24 eV the present results agree with those reported by Lee et al. [101] to better than 10%. However in the 16-24 eV region the cross sections reported by Lee et al. [101] are ~20 % higher than the present results (figs. 5.12a and 5.12c). Similar discrepancies in this same energy region (16-24 eV) have also been observed in the comparisons between our results (figs. 5.11 and 5.13) and those of Lee et al. [101] and Wu et al. [110] for the molecules CF4 and CF2CI2. As discussed in section 5.2.1, the differences between the present results and those reported by Lee et al. [101] and Wu et Chapter 5. 86 al. [110] in the energy region 16-24 eV are most likely due to a systematic error in the use of the Sn film in the latter work. The data of Jochims et al. [107] were single point normalized to the photoabsorption measurement reported by Rebbert and Ausloos [108] whereas the data of King and McConkey [104] were put on an absolute scale at a single point to an average of the photoabsorption measurements reported by Jochims et al. [107] and the electron impact measurement reported by Huebner et al. [126]. The previously reported single point normalized results [104,107] are of the same overall shape but are considerably higher than the present results below 23 eV (fig. 5.12c). Above 23 eV the data of King and McConkey [104] approach the present data with increasing photon energy. Our data are also lower than the photoabsorption measurements of Gilbert et al. [106] below 17 eV, whereas at higher energy their data diverge rather drastically from all other measurements (fig. 5.12c). The absolute photoabsorption cross sections of CF3C1 from 124-270 eV have been measured by Cole and Dexter [109] using synchrotron radiation. Agreement with the present work is good below 160 eV but the measurements diverge at the higher energies and exhibit a 20% difference at 190 eV (fig. 5.12b). 5.2.3 The CF2C12 Photoabsorption Differential Oscillator Strengths The presently reported measurements on CF2C12 are compared with earlier photoab sorption measurements [109,110] obtained using synchrotron radiation hght sources in figs. 5.12a and 5.13b. In fig. 5.13c the present photoabsorption data are also compared in the low energy region (8.5-36 eV) with previously reported results obtained using syn chrotron radiation [107,110] and the helium Hopfield continuum [106] as light sources. The previous photoabsorption data derived from small momentum transfer electron im pact measurements [104] have been digitized from the reported diagram and are also shown in fig. 5.13c. Chapter 5. 87 i > N I o 80 K H O K E-H oo o E-1 < hJ r—I u o < r—I OH W En r—t Q 40 0. 0 K 10 O E-H DH PH O CO CQ < o O 0L (a) V > u z w o il! w 0.5K z o < N z 2 0.0 • this work o ref. [108] 20 40 60 PHOTON ENERGY (eV) • Ph Abs, dipole (e,e) ° Ph Abs [110] 20 40 60 80 100 \ ^ "j^ ^ Polynomial fit • Ph Abs, dipole (e,e) o Ph Abs [109] 120 80 40 • Ph Abs, dipole (e,e) 0 Ph Abs [110] 1 Ph Abs [107] 'A * Ph Abs [106] • Ph Abs [111] a Ph Abs from EELS [104] 80 120 160 0^ 200 10 20 30 40 PHOTON ENERGY (eV) Figure 5.13: Absolute photoabsorption differential oscillator strengths for the valence shell of CF2CI2. a) 8.5-100 eV (insert shows ionization efficiency), b) 70-200 eV. c) 8.5-36 eV (expanded scale). Chapter 5. 88 The different energy resolution characteristics of the present dipole (e,e) techniques and optical methods (i.e. the large differences in energy resolution and the fact that the energy resolution changes with photon energy in optical experiments—see section 5.2) comphcates comparison of the various data sets at lower energies, particularly in the region of discrete excitation. A similar difficulty exists in comparing the present results at 1 eV FWHM resolution in the discrete excitation region with the data [104] derived from intermediate impact energy EELS at ~0.05 eV resolution. In particular, meaningful comparisons of such data with the present work are not possible below 12.5 eV and the higher resolution data from references [104,106,107] are omitted from fig. 5.13c in this region. The shape of the presently reported photoabsorption spectrum in the energy region below 25 eV (fig. 5.13c) is similar to the shapes of the spectra reported in refs. [110, 104,107]. However considerable variations exist in the absolute magnitudes of the various data sets. In the structured low energy region below 15 eV Rydberg transitions have been assigned to the various features. In particular, the peak at 13 eV just discernible in the present low resolution work has been attributed to the Rydberg transitions 462 —> 3d and/or 3a2 —> 4s [49,104,119]. The Rydberg transitions 3a2 —> 3d and/or 66x —• 5p and (2a2+5&i) —> 4s are the assignments for the structures in the 15-17 eV region [104,119] (unresolved in the present work). The maximum at 19.5 eV has been assigned to the 7ai —* 4s Rydberg transition [49,104,119], while the broad shoulder at ~24.5 eV has been suggested by Robin [49] to be due to a Rydberg transition originating from the carbon 2s orbitals. A term value of ~3 eV can be derived for this transition from the ionization potential of the C 2s orbitals (2ai + l&2) of CF2C12 presented in chapter 6. The magnitude of this term value is consistent with the assignment (2a1? 162) —> 3s or (2ax, 162) —> 3p, since the typical magnitudes of Rydberg term values are in the range 2.8-5.0 eV for the lowest s orbital and 2.0-2.8 for the lowest p orbital [47]. It should be noted that the Chapter 5. 89 Rydberg transition assigned to a particular structure depends largely on the ionization energies taken from PES measurements (i.e. different ionization energies give rise to different term values (see sections 2.3.1 and 2.3.2) for the same structure and therefore the assignment of the particular structure can be different in utilizing ionization energies from different PES measurements). The rise in photoabsorption differential oscillator strength at 200 eV in fig. 5.13b is caused by excitation of Cl 2p inner shell electrons [119]. Above a photon energy of 24 eV the present results are in excellent quantitative agreement with those reported by Wu et al. [110]. However in the 16-24 eV region the cross-sections reported by Wu et al. [110] are ~10% higher than the present work (figs. 5.12a and 5.13c ). Similar discrepancies in this energy region have been observed in earlier comparisons between our results (figs. 5.11 and 5.12) and those of Lee et al. [101] for the molecules CF4 and CF3C1. As pointed out in section 5.2.1, the discrepancies in the 16-24 eV energy region are most likely due to a systematic error in the use of a Sn film in the work of Wu et al. [110] and Lee et al [101]. The data of King and McConkey [104] and of Jochims et al. [107], which were single point normalized to the photoabsorption measurements reported by Person et al. [Ill] and Rebbert and Ausloos [108] respectively, are of similar shape but proportionally higher than the present results below 24 eV (fig. 5.13c). In the 24-30 eV energy region the data of King and McConkey [104] approach the present data with increasing photon energy, however, above 30 eV their data fall below ours. The agreement between the present results and those of Gilbert et al. [106] is good in the region 12-16 eV, but above 16 eV their data diverge rather drastically from all other measurements (fig. 5.13c). The absolute photoabsorption cross sections of CF2C12 from 124 eV to 270 eV have been measured by Cole and Dexter [109] using synchrotron radiation. Agreement with the present work is good below 130 eV but the measurements diverge at the higher energies and exhibit a 20% difference at 190 eV (fig. 5.13b). Chapter 5. 90 A broad feature of low intensity (fig. 5.12a) centered at ~40 eV is observed. Similar but more prominent broad features were also seen in the photoabsorption differential oscillator strength spectra of CF4 (fig. 5.11a) and CF3CI (fig. 5.12a). They were in terpreted (section 5.2.2) as being associated with inner valence ionization or possibly scattering (diffraction) of the outgoing (outer valence) photoelectrons by the neighboring atoms in the molecules [121,122,123,124,125]. The presently observed feature (fig. 5.12a) probably also has similar origins. Final assignment must await detailed PES experi ments and theoretical calculations. A even weaker feature at ~37 eV is also present in the photoabsorption differential oscillator strength spectra of CFCI3 (fig. 5.14a) 5.2.4 The CFC13 Photoabsorption Differential Oscillator Strengths The presently reported measurements are compared with earlier photoabsorption mea surements [109] obtained using synchrotron radiation as the light source'in fig. 5.14b. In fig. 5.14c the present photoabsorption data are also compared in the low photon en ergy region with previously reported results obtained using synchrotron radiation [107] and the hehum Hopfield continuum [106] as hght sources. The photoabsorption data (~0.05 eV FWHM resolution) derived from small momentum transfer electron impact measurements [104] were reported both in the form of integrated oscillator strengths (in a table) and differential oscillator strengths (in a diagram). In fig. 5.14c in order to make meaningful comparisons with the present results, which were obtained with lower resolution (1 eV FWHM), below 12.5 eV the results from ref. [104] are shown as av erage differential oscillator strengths (i.e. the integrated oscillator strengths divided by the corresponding energy intervals). This has been done in order to smooth away sharp structures in the discrete region. Above 12.5 eV the results are shown as differential oscillator strengths digitized from the reported diagram [104]. Chapter 5. 91 i > I .O E-H O JZi W OH E-H in OH O < r—I o w o < I—I E-H 55 H OH OH OH Q 55 O E-H OH OH O Ul QQ < O E-H O OH (a) 80 40 1 > ;\ £1.0 u 2 W • • • • • • • u z o • • o d IIVZINOI • • V o d IIVZINOI • • • • • this work ° ref. [108] CFC1 20 40 PHOTON ENERGY (eV) Ph Abs, dipole (e,e) •°»»* • 0 20 40 60 80 100 10 \ (b) •—- Polynomial fit • Ph Abs, dipole (e,e) o Ph Abs [109] 0L 160 120 • Ph Abs, dipole (e,e) o Ph Abs [107] & °Ph Abs [106] °r# <*P D ph Abs from EELS [104] 80 120 160 200 PHOTON ENERGY (eV) Figure 5.14: Absolute photoabsorption differential oscillator strengths for the valence shell of CFCI3. a) 6-100 eV (insert shows ionization efficiency), b) 65-200 eV. c) 6-38 eV (expanded scale). Chapter 5. 92 The different energy resolution characteristics of the present dipole (e,e) techniques and optical methods (i.e. the large differences in energy resolution and the fact that the energy resolution changes with photon energy in optical experiments—see section 5.2) complicates comparison of the various data sets at lower energies, particularly in the region of discrete excitation. In particular meaningful comparisons of such data with the present work are not possible below 12.5 eV for CFCI3, and therefore the higher resolu tion data from refs. [106,107] are omitted from fig. 5.14c in this region. The presently reported photoabsorption spectrum is similar in shape to those reported in refs. [104,107] in the energy region below 24 eV (fig. 5.14c). The absolute magnitudes of the photoab sorption cross-sections, however, exhibit considerable variations between the various data sets. Rydberg transitions have been assigned to the features in the low energy region below 24 eV. In particular, the peak at 10 eV just discernible in the present low resolu tion work has been assigned to the Rydberg transition 4e —> 4s [104,119]. Similarly the broad structure at ~15 eV has been attributed to the Rydberg transitions 2e —> 4s and 4ai —> 4s [104,119]. The maximum at ~17.5 eV and the shoulder at ~22 eV have been recently assigned to the Rydberg transitions 3ax —» 4s and le —> 4s [119]. A feature only just discernible at ~37 eV is similar to progressively less intense features observed in CF4 (fig. 5.11a), CF3CI (fig. 5.12a) and CF2C12 (fig. 5.13a). As discussed earlier (section 5.2.2) such features are perhaps due to the onsets of inner valence (i.e. F 2s) ionization processes or possibly scattering (diffraction) of the outgoing (outer valence) photoelectrons by the neighboring atoms in the molecule [121,122,123,124,125]. A more definite assignment of this feature must await more detailed PES partial cross section experiments and theo retical calculations. The rise of differential oscillator strength at ~200 eV (fig. 5.14b) is due to excitation of the Cl 2p inner shell [119]. Chapter 5. 93 The electron impact measurements of King and McConkey [104] and the photoab sorption measurements of Jochims et al. [107] are considerably higher than the present work below 24 eV. Above 24 eV the data of King and McConkey [104] approach the present results with increasing photon energy. The agreement between the present re sults and those of Gilbert et al. [106] is good in the region 13-16 eV, but above 16 eV their data diverge rather drastically from all other measurements. The absolute pho toabsorption cross sections of CFC13 from 124 eV to 270 eV have been measured by Cole and Dexter [109] using synchrotron radiation and at 124 eV these results agree with the present work within 10%. However the measurements diverge at the higher energies and exhibit a 25% difference at 190 eV (fig. 5.14b). 5.2.5 Comparison of the Photoabsorption Differential Oscillator Strengths of CF4, CF3C1, CF2C12 and CFC13 Although the total integrated oscillator strengths for the four freons all have similar val ues (i.e. ~ 33, see section 5.2), the shapes of the photoabsorption differential oscillator strength spectra vary considerably in going through the series CF4, CF3CI, CF2C12 and CFC13, with the oscillator strength becoming progressively more concentrated in the low photon energy region as the number of Cl atoms increases. With increasing number of Cl atoms in the freon molecules, the photoabsorption differential oscillator strength decreases more rapidly in the 20-40 eV region, while above ~40 eV the rate of decrease be comes smaller. For example, at energies ~35 eV above the photoabsorption onsets of the respective spectra the differential oscillator strengths for CF4, CF3C1, CF2C12 and CFCI3 are 0.29, 0.26, 0.20 and 0.14 eV-1 respectively, whereas at ~100 eV above the onsets the values are 0.09, 0.07, 0.06, 0.06 eV-1 respectively. These differences between the differen tial oscillator strengths for CF4, CF3C1, CF2C12 and CFCI3 occur because an increasing Chapter 5. 94 number of molecular orbitals with predominantly Cl 3p atomic character contribute to the differential oscillator strengths. This effect is due to the Cooper minimum [25,127] in the Cl 3p atomic orbital photoionization cross-sections at ~35-40 eV [68]. 5.3 The CF4 Photoabsorption Differential Oscillator Strengths for the C Is and F Is Inner Shells and the Valence Shell Extrapolation In this section the extrapolated CF4 differential oscillator strengths for valence excitations obtained using formula 5.41 and also the differential oscillator strengths for CF4 C Is and F Is excitations obtained from normalization of Bethe-Born converted EELS spectra are compared with the reported results from direct X-ray absorption measurements. The absolute differential oscillator strengths of inner shell excitations for other freon molecules will be reported in chapter 7. As discussed in section 5.2 above, an analytical function was fitted to the valence shell experimental data for CF4 from 70 to 200 eV and was used to estimate the differential os cillator strength for valence shell photoabsorption from 200 eV to infinity. This estimated valence shell contribution is shown by the dashed hnes in figs. 5.15a (valence shell), 5.15b (C Is region) and 5.15c (F Is region) in the photon energy regions 200-250, 270-350 and 670-740 eV respectively. For the comparison to be made below, we have digitized literature results of C Is and F Is inner shell photoabsorption measurements [128,129] and they are also shown in fig. 5.15b and 5.15c by the sohd and dash-dot hnes respec tively. In the region below the C Is IP (i.e. the K edge), there is excellent agreement between our valence shell estimation of the absolute differential oscillator strengths us ing the analytical function and the direct photoabsorption measurements obtained using X-ray characteristic hnes at 248.0 eV (fig. 5.15a) and 277.4 eV (fig. 5.15b). In the present work, we have also converted the earlier reported relative inner shell Chapter 5. 95 i > CM I o o z LJJ CH \— (/) CH O 60 40 20-o IE CL 0 VALENCE Ph Abs, dipole (e,e) this work Polynomial fit Ph Abs [128] 60 40 20 0 d 20 o ui o p 10h z CH 50 C 1s 100 150 200 • Ph Abs from EELS [130] Polynomial fit Ph Abs (valence and C ls)[128] • Ph Abs (valence)[128) X Extrapolation (valence)[128] K-edge 1 = 0 o t— CL. CH O Ul CD < O 0 (b) 280 F 1s .,300 K-edge 320 340 (c) Ph Ab« from EELS [130] Polynomial fit (valence) Ph Abs (valence) and C ls[68] Ph Abs (valence + C Is + F ls)[128] Ph Abs (valence + C ls)[128] Extrapolation (valence)[128] Ph Abs (valence + C Is + F ls)[129] Ph Abs (valence + C ls)[129] 20 10 0 5 '^k^^r^j^^ 0 680 700 720 PHOTON ENERGY (eV) 740 Figure 5.15: Absolute photoabsorption differential oscillator strengths for (a) the Valence-shell, (b) the C Is region and (c) the Fls region of CF4. In each spectrum the dashed line represents the fitted (valence shell, 70-200 eV) and extrapolated valence shell contribution. See text for details. Chapter 5. 96 electron energy loss spectra (ISEELS) of CF4 [130] to absolute photoabsorption differen tial oscillator strengths by using known absolute atomic photoionization differential os cillator strengths, according to the normalization principles discussed in sections 2.3.4.3 and 2.3.8. The procedures used were as follows. Firstly, the estimated background and valence shell continuum contributions were subtracted from the raw ISEELS data [130] by straight hne extrapolation of the pre-ionization edge spectral intensity. (A modified subtraction procedure is used in chapter 7.) The resulting spectrum due to inner shell excitation alone was then converted to an approximate relative optical spectrum by using equations 2.35 and 2.36 where the estimated kinematic (Bethe-Born) factor was taken to be proportional to E2-5. The absolute photoabsorption differential oscillator strengths were then obtained by normalizing the relative optical spectrum at a reasonably high photoelectron energy (i.e. ~25-30 eV above the Is edge) to the sum of corresponding atomic Is cross-sections for the respective constituent atoms [57,70,68]. The carbon Is atomic cross-section at 30 eV above the ionization potential was used to place the C Is spectrum of CF4 on the absolute differential oscillator strength scale (fig. 5.15b). Simi larly, four times the fluorine Is atomic photoionization cross-section at 25 eV above the F Is ionization potential was taken for the normalization of the CF4 F Is spectrum. The so obtained C Is inner shell absolute photoabsorption differential oscillator strength spectrum of CF4 was then added to the valence continuum contribution determined by the present analytical function to give the total photoabsorption differential oscillator strengths in the C Is region as shown in fig. 5.15b. Similar procedures were used for the F Is spectrum shown in fig. 5.15c. Our results are compared to those obtained by direct photoabsorption measurements [128,129]. In the C Is region, the presently converted ISEELS results are higher than the optical measurements [128], especially in the discrete region. This could be due to the uncertainty involved in the background subtraction Chapter 5. 97 procedure. It should be noted that the differential oscillator strengths for CF4 C Is is re-derived in chapter 7 using a modified background subtraction procedure. However, even after the re-derivation, the differential oscillator strength as obtained in chapter 7 is still higher than the optical results in the discrete transition region. This discrepancy may partly be due to a systematic error in the present normahzation method, since for highly fluorinated molecules such as CF4 [44] the presence of potential barriers may depress the photoabsorption cross-section corresponding to the central atom in the region of the con tinuum immediately above the IP. As for the F Is spectra, the converted ISEELS spectra are in good agreement with the optical measurements [128,129] in the continuum region within statistical error. The differences between the photon measurements and the con verted ISEELS spectra in the discrete regions of the C Is and also the F Is spectra might be due to hne saturation (bandwidth) effects which can seriously perturb the intensities of discrete transitions in photoabsorption measurements [26,131]. Since electron impact excitation is non-resonant, such bandwidth effects do not occur in electron energy loss spectra [8,26]. The photoabsorption spectrum of ref. [129] shows an energy shift which is probably due to energy calibration errors. 5.4 Molecular and Dissociative Photoionization of CF4, CF3C1, CF2C12 and CFC13 Time of flight mass spectra have been measured using the dipole (e,e+ion) spectrometer described in section 3.1 in the equivalent photon energy ranges 15.5-80 eV, 12.5-80 eV, 11.5-70 eV and 11.5-49 eV respectively for CF4, CF3C1, CF2C12 and CFC13. Typical TOF mass spectra are shown in figs. 5.16, 5.17, 5.18 and 5.19, obtained respectively at 80 eV for CF4, at 45 eV for CF3C1, at 50 eV for CF2C12, and at 49 eV for CFC13. The positive ions detected in the TOF mass spectra of CF4 were CF3 , CF2 , CF+, C+, F+ Chapter 5. 98 2 3 4 5 TIME OF FLIGHT (/^sec) Figure 5.16: Time of flight mass spectrum of CF4 at 80 eV equivalent photon energy. Chapter 5. 99 2 3 4 TIME OF FLIGHT (/xsec) Figure 5.17: Time of flight mass spectrum of CF3C1 at 45 eV equivalent photon energy. Chapter 5. 100 10-in *E D >. i_ O • — _Q v_ O >-\— CO 0+ CF2CI2 • N+0+F+ hy=50eV n CFCI+ I ] CF2CI+ CCI2 CFClJ n n 1 1 1 r Z 3 4 TIME OF FLIGHT (/usee) Figure 5.18: Time of flight mass spectrum of CF2C12 at 50 eV equivalent photon energy. Chapter 5. 101 % 10-0 CFCI hi/=49eV 5 Cl+ CF c+ F, N+0+F+ N2 CCI+ I 1 n i CFCI+ .nCFCl£ CCl£ m I ft | ccij W T T T I 2 3 4 TIME OF FLIGHT (/xsec) Figure 5.19: Time of flight mass spectrum of CFC13 at 49 eV equivalent photon energy. Chapter 5. 102 and the doubly charged ion CF2+. The CF4 molecular ion was not found, in accord with previous work [132]. For CF3C1, the molecular ion CF3C1+ and the fragment (dissocia tive) ions CF2C1+, CF+, CFC1+, CF+, CC1+, Cl+, CF+, F+, C+ as well as the doubly charged ions CF2C12+ and CFC12+ were detected. The positive fragment (dissociative) ions CFC1+, CF2C1+, CC1+, CFC1+, CF+, CC1+, Cl+, CF+, F+, C+ and the doubly charged ion CF2C12+ were detected for CF2C12. The molecular ion CF2ClJ was not ob served in contrast to the situation for CF3CI. In the TOF spectra of CFCI3, the positive fragment ions CC1+, CFC1+, CC1+, CFC1+, CC1+, Cl+, CF+, F+ and C+ were detected. Unhke the situation for CF3C1, the molecular ion (CFCI3 ) was not detected. Also no doubly charged ions were observed for CFCI3 in contrast to the other freons. Photoion branching ratios determined by integrating the mass peaks in the TOF spectra are re ported diagrammatically in figs. 5.20, 5.21, 5.22 and 5.23 for CF4, CF3C1, CF2C12 and CFCI3 respectively, and also numerically in respective tables 5.17, 5.18, 5.19 and 5.20. It can be seen that the dominant ion produced from CF4 by ionizing radiation in the region 15.5-80 eV is CF3 (see table 5.17 and fig. 5.20) and the molecular ion CF3C1+ is only observed with any appreciable intensity below 30 eV (see table 5.18 and fig. 5.21). In comparing the branching ratios of various photoion fragments produced by pho toionization of CF3CI, CF2C12 and CFC13, it is found that the excited molecular ions favor fragmentation processes involving loss of one or more Cl atoms over loss of an F atom. For example the molecules CF3C1, CF2C12 and CFC13 have a larger yield of the CF3 , CF2C1+ and CFCLj" ions (per C-Cl bond) resulting from loss of a Cl atom than of the CF2C1+, CFChj" and CCht ions (per C-F bond) from lose of an F atom respectively. These phenomena are all consistent with the fact that the bond strength of a C-Cl bond (3.58 eV) is weaker than that of a C-F bond (4.84 eV). It is also observed that the intensities of the ion fragments C+ and F+ are highest for the photoionization of CF4 Chapter 5. 103 100 o < cr o < cr CD O O I— o X Q_ 50 0 10 0 10 0 10 0 10 0 0 w v.. —i CF,+ III It ****** ** ** M XAB CD E F CF,+ CF+ C + F+ tt 10 20 30 40 50 60 70 80 PHOTON ENERGY (eV) Figure 5.20: Branching ratios for dissociative photoionization of CF4. The vertical arrows repre sent expected thermodynamic appearance potentials (see table 5.21) and the hatched hnes indicate the vertical ionization energies [99,98] for production of the electronic states of CF^. Chapter 5. 104 10 0 40 g 20 o 0 E 100 o 2 50 < CD -L 0 0.5 0 10 CF3CI ! ABCOEF Q H ..... I J ~l 1 r T r CF3CI + -1—•—1 1 r CF2CI+ -1 1 1 1— -1 1 1 r . CFCI" i 1 1 1 f 1 1 CF2+ —-*i 1 1 1 1 1 1 0 20 40 60 80 X A 6 EF G H u 1 J CCI+ • • • • • 1 1 1 1 1 ' 'Cl+. 1 -t ; 1 1 1 1 1 III / CF+_ 1 " 1 1 1 1 ' .: F+_ III! 1 1 i"1 II 11 1 1 1 ; . :c+-CF2CI+T 20 ' 1 40 60 80 2 0 20 10 0 PHOTON ENERGY (eV) Figure 5.21: Branching ratios for dissociative photoionization of CF3C1. The vertical arrows represent expected thermodynamic appearance potentials (see table 5.22) and the hatched lines indicate the ver tical ionization energies presented in chapter 6 and reported in ref. [100] for production of the electronic states of CF3C1+. Chapter 5. 105 O I— < Cd O z o z < CD Z O O (— o IE Q_ 20 10 0 100 50 0 0.2 0 5 0 10 0 CF2CI2 CFCI2+ y * . . . "nidi (III II CCI AC EG J K (L.M) NO ... - I I I 1 1 1 -\ CF2CI + 'v. s \ Xfcj D F (H,T) jiijii ij II II AC EG J K (L.U) N 5 1 ' 1 1 1 1 1 ' Cl+ 11 1 "1 1 1 1 1 1 CF+ _ i i/ 1 1 1 1 1 1 • • • * CCI2+ 1 1 11 1 1 f. ' ..." CFCI+ • —i i i i i i 1 . i i......... • • * F+" i i " i i i i ii in ' c+~ -1 1 1 1 1 1 - CF2+ II.' i "i i i i i CF2CI++-4 2 0 20 10 0 10 5 0 2 0 2 0 20 40 ' 60 '80 20 40 PHOTON ENERGY (eV) 60 Figure 5.22: Branching ratios for dissociative photoionization of CF2C12. The vertical arrows represent expected thermodynamic appearance potentials (see table 5.23) and the vertical lines indicate the vertical ionization energies presented in chapter 6 and reported in ref. [100] for production of the electronic states of CF2Clj". Chapter 5. 106 0 100 o I— < DC 50 o o X o 2 5 cc DQ CFCI mi % t it XABC D EF 0 HI 0! r 20 -10 0 -| 1 1 r 10 CCh+ T 1 1 1 r— r CFCI2+ -i 1 1 1 1 r CCIo+ ~i i CFCI+ ~r~^ 1 1 1 1 1 r 20 30 40 tlf I f II XABC 0 EF Q fit I CCI+ 1 1' l i CI+_ 1 I / 1 1 1 """* CF+-1 1 1 1 1 1 I *•' F+" t 1 i i i i i i 1 1 : c+-20 PHOTON ENERGY (eV) 30 10 5 0 20 0 10 5 0 0 2 1 0 40 50 Figure 5.23: Branching ratios for dissociative photoionization of CFC13. The vertical arrows represent expected thermodynamic appearance potentials (see table 5.24) and the hatched lines indicate the ver tical ionization energies presented in chapter 6 and reported in ref. [100] for production of the electronic states of CFCI J. Chapter 5. 107 Table 5.17: Photoion branching ratios of CF4 Photon energy (eV) Branching ratio (%) CF+ CF+ 15.5 100.00 16.0 100.00 16.5 100.00 17.0 100.00 17.5 100.00 18.0 100.00 18.5 100.00 19.0 100.00 19.5 100.00 20.0 100.00 20.5 99.86 0.14 21.0 99.74 0.26 21.5 98.52 1.48 22.0 95.86 4.14 22.5 92.08 7.92 23.0 89.98 10.02 23.5 89.19 10.81 24.0 89.17 10.83 24.5 89.91 10.09 25.0 90.90 9.10 25.5 91.39 8.61 26.0 92.63 7.37 26.5 93.54 6.46 27.0 93.99 6.01 27.5 94.83 5.17 28.0 94.44 4.56 28.5 95.58 4.42 29.0 95.83 4.17 CF+ F+ C+ CF2,* continued on next page Chapter 5. 108 Table 5.17: (continued) Photon energy Branching ratio (%) (eV) CF+ CF+ CF+ F+ C+ 29.5 95.62 4.20 0.18 30.0 95.47 4.23 0.30 31.0 95.03 4.31 0.66 32.0 94.06 4.49 1.46 33.0 92.91 4.83 2.27 34.0 91.90 4.99 3.11 > 35.0 89.97 5.42 4.29 0.17 0.15 36.0 88.64 5.40 5.05 0.38 0.53 37.0 86.90 5.56 5.65 0.73 1.16 38.0 85.28 5.64 5.94 1.17 1.97 39.0 83.17 5.78 6.34 1.65 3.06 40.0 81.49 6.07 5.99 2.20 4.25 41.0 80.44 6.12 5.27 2.91 5.26 42.0 81.10 6.04 4.87 3.10 4.90 43.0 81.12 6.37 4.27 3.48 4.77 44.0 81.19 6.36 3.79 3.69 4.82 0.14 45.0 81.62 6.61 3.62 3.96 4.05 0.14 46.0 82.11 6.41 3.63 3.81 3.75 0.29 47.0 81.74 6.58 3.49 4.15 3.64 0.40 48.0 82.02 6.37 3.52 4.14 3.53 0.41 49.0 81.25 6.23 3.73 4.25 3.88 0.64 50.0 81.45 5.85 3.56 4.78 3.87 0.49 55.0 76.90 6.20 4.48 6.70 5.10 0.63 60.0 74.35 6.39 5.05 7.97 5.22 1.03 65.0 72.61 6.77 5.46 9.01 5.15 1.00 70.0 70.96 6.85 5.42 10.46 5.19 1.13 75.0 69.08 6.52 6.09 11.48 5.65 1.17 80.0 67.29 6.42 6.45 12.52 6.18 1.14 Chapter 5. 109 Table 5.18: Photoion branching ratio for CF3C1 Photon Branching ratio (%) energy (eV) CF3Cl+ CF2C1+ CF+ CFC1+ CFt CC1+ C1+ CF+ F+ C+ CF2C12+ 12.5 7.83 92.17 13.0 2.32 97.68 13.5 1.80 98.20 14.0 1.94 97.77 0.29 14.5 1.54 1.06 97.00 0.40 15.0 1.39 3.19 95.17 0.25 15.5 0.97 8.84 90.03 0.16 16.0 0.90 16.10 82.93 0.07 16.5 0.64 24.95 74.27 0.14 17.0 0.55 30.53 68.78 0.14 17.5 0.65 34.54 64.66 0.15 18.0 0.57 35.97 63.28 0.19 18.5 0.44 36.87 62.54 0.16 19.0 0.59 37.19 61.70 0.10 0.42 19.5 0.34 37.58 59.90 0.15 1.31 0.72 20.0 0.34 36.06 58.76 0.10 2.45 2.29 20.5 0.56 33.55 56.87 0.19 4.51 4.32 21.0 0.40 30.11 52.85 0.16 9.46 7.02 21.5 0.45 28.23 50.29 0.32 12.92 7.78 22.0 0.42 28.04 48.30 0.42 14.49 8.33 22.5 0.38 28.37 47.20 0.52 15.29 8.23 23.0 0.44 28.99 46.09 0.55 15.22 8.09 0.62 23.5 0.40 29.51 45.99 0.54 15.17 7.65 0.74 24.0 0.27 30.44 45.13 0.52 14.90 7.88 0.86 24.5 0.27 30.85 44.77 0.49 14.51 7.85 1.26 25.0 0.41 31.64 43.53 0.53 14.23 8.11 1.54 25.5 0.37 32.52 43.02 0.48 13.54 8.14 1.93 26.0 0.43 32.94 42.20 0.44 13.03 8.61 2.35 26.5 0.23 33.67 41.49 0.43 12.69 8.58 2.92 27.0 0.29 34.68 40.46 0.35 12.32 8.56 3.34 27.5 0.26 35.10 40.05 0.33 12.12 8.28 3.87 continued on next page Chapter 5. 110 Table 5.18: (continued) Photon energy (eV) Branching ratio (%) CF3C1+ CF2C1+ CF$ CFC1+ CFj CC1+ C1+ CF+ F+ C+ CF2C12+ 28.0 0.14 35.95 38.58 0.38 11.96 0.08 8.89 4.01 28.5 0.30 36.34 37.84 0.41 11.83 0.17 8.66 4.45 29.0 0.21 37.20 36.60 0.32 11.74 0.22 8.91 4.81 29.5 0.20 37.09 35.64 0.30 11.79 0.33 9.42 5.32 30.0 0.16 37.76 34.75 0.36 11.84 0.39 9.48 5.26 31.0 0.19 38.81 33.32 0.35 12.02 0.70 9.24 5.38 32.0 0.12 39.60 31.40 0.23 12.12 0.87 9.85 ' 5.82 33.0 0.06 40.77 29.49 0.31 12.13 0.97 10.37 5.83 0.08 34.0 0.05 40.62 27.55 0.28 12.97 1.35 10.63 5.90 0.20 0.46 35.0 0.06 40.93 25.77 0.31 13.47 1.43 11.15 5.94 0.22 0.74 36.0 0.07 40.70 24.32 0.40 13.81 1.55 11.83 5.84 0.36 1.13 37.0 0.00 39.36 23.42 0.33 14.43 1.58 12.70 5.91 0.63 1.63 38.0 0.00 38.98 21.98 0.35 14.79 1.76 13.17 5.87 0.81 2.10 0.17 39.0 0.00 38.21 21.38 0.38 15.39 1.60 13.82 5.63 0.96 2.38 0.25 40.0 0.00 37.02 21.10 0.34 15.86 1.45 14.75 5.45 1.10 2.62 0.31 41.0 0.00 36.61 20.65 0.35 15.93 1.33 15.66 5.30 1.22 2.64 0.30 42.0 0.00 36.14 20.78 0.36 16.23 1.22 15.44 5.44 1.41 2.66 0.32 43.0 0.00 36.17 20.66 0.31 16.32 1.17 15.82 5.53 1.40 2.27 0.36 44.0 0.00 35.98 20.88 0.43 16.17 1.03 15.83 5.56 1.48 2.28 0.35 45.0 0.00 35.37 21.06 0.37 16.28 0.91 16.47 5.77 1.40 2.01 0.36 46.0 0.00 35.62 21.45 0.35 16.18 0.88 15.95 5.81 1.45 1.86 0.44 47.0 0.00 35.18 21.15 0.34 15.92 0.96 16.28 6.15 1.54 2.04 0.44 48.0 0.00 34.96 21.44 0.31 15.61 0.95 16.21 6.30 1.68 2.11 0.43 49.0 0.00 34.65 21.25 0.29 15.56 0.99 16.68 6.54 1.67 1.98 0.39 50.0 0.00 34.70 21.10 0.34 15.15 0.97 16.66 6.81 1.84 2.03 0.40 55.0 0.00 31.48 22.11 0.32 15.88 0.87 16.46 7.76 2.22 2.25 0.64 60.0 0.00 30.34 20.63 0.13 15.93 0.93 17.28 8.44 3.01 2.73 0.48 65.0 0.00 29.43 20.15 0.23 15.59 0.97 18.17 8.48 3.41 3.06 0.53 70.0 0.00 29.19 20.02 0.41 15.70 0.94 17.60 8.44 3.79 3.24 0.68 75.0 0.00 28.14 19.27 0.29 15.96 0.97 18.33 8.43 4.58 3.60 0.44 80.0 0.00 27.74 19.07 0.20 14.86 1.04 18.82 8.57 5.37 3.72 0.61 Chapter 5. Ill Table 5.19: Photoion branching ratio for CF2CI2 Photon Branching ratio (%) energy (eV) CFCtf CF2C1+ CCLt CFC1+ CF+ CC1+ C1+ CF+ F+ C+ CF2C12+ 11.5 100.00 12.0 100.00 12.5 100.00 13.0 100.00 13.5 100.00 14.0 0.28 99.72 14.5 1.11 98.89 15.0 1.73 98.27 15.5 3.79 96.21 16.0 6.81 93.19 16.5 9.40 90.60 17.0 11.12 88.88 17.5 12.01 87.56 0.44 18.0 13.18 85.50 1.31 18.5 12.94 83.67 0.42 2.96 19.0 12.57 80.67 1.09 5.67 19.5 12.04 77.66 1.80 8.49 20.0 11.72 73.84 2.90 10.58 0.39 0.56 20.5 11.12 72.44 3.68 11.19 0.56 1.02 21.0 10.85 71.23 4.19 11.52 0.93 1.28 21.5 11.18 69.53 4.60 12.18 0.95 1.56 22.0 11.00 67.56 5.16 12.52 1.33 2.42 22.5 10.69 66.37 5.35 12.71 1.55 3.33 23.0 10.47 65.13 5.63 13.44 1.39 3.93 23.5 10.42 63.31 6.01 13.57 1.64 5.05 24.0 10.43 61.58 6.15 13.60 0.32 2.04 5.87 24.5 10.31 60.80 6.31 13.66 0.32 1.98 6.62 25.0 10.73 59.84 5.71 13.50 0.56 1.87 7.80 25.5 11.03 59.26 5.45 13.24 0.83 2.25 7.93 continued on next page Chapter 5. 112 Table 5.19: (continued) Photon Branching ratio (%) energy (eV) CFC1J CF2C1+ CC1+ CFC1+ CF+ CC1+ C1+ CF+ F+ C+ CF2C12+ 26.0 11.58 58.29 5.17 13.20 1.13 2.54 8.09 26.5 12.23 57.49 5.10 13.06 1.15 2.88 8.09 27.0 12.31 56.57 4.90 13.23 1.50 3.19 8.29 27.5 12.78 55.43 4.93 12.94 1.72 3.65 8.55 28.0 13.30 54.70 4.64 12.90 1.93 4.16 8.37 28.5 14.05 53.23 4.85 12.63 2.05 4.64 8.55 29.0 14.34 52.07 4.72 13.23 2.43 4.81 8.41 29.5 14.76 51.02 4.57 13.24 2.50 5.35 8.56 30.0 15.29 50.03 4.67 13.15 2.54 5.50 8.81 31.0 16.50 46.94 5.01 13.58 2.99 6.16 8.56 0.26 32.0 16.88 44.91 4.89 13.96 3.21 6.82 8.63 0.69 33.0 17.98 42.47 5.00 14.46 3.45 7.59 8.26 0.79 34.0 18.41 39.49 5.66 14.72 3.28 8.65 8.48 1.31 35.0 18.74 37.26 5.78 15.01 3.30 9.83 8.54 1.54 36.0 18.67 35.29 5.75 15.10 3.36 10.93 8.46 0.60 1.83 37.0 18.46 33.15 6.41 15.20 3.21 12.21 8.73 0.57 2.07 38.0 18.66 31.59 6.51 15.16 2.98 13.09 8.73 0.69 2.40 0.19 39.0 18.80 30.77 6.55 15.36 3.06 13.83 8.60 0.61 2.23 0.18 40.0 18.13 29.61 7.26 15.40 2.64 14.65 9.04 0.78 2.11 0.38 42.0 17.83 28.64 7.37 15.25 2.62 15.14 10.08 0.90 1.75 0.42 44.0 17.05 27.67 7.44 15.40 2.78 15.87 10.80 0.89 1.64 0.46 46.0 16.46 27.70 0.09 7.31 15.00 2.81 16.20 11.35 0.94 1.64 0.49 48.0 16.16 27.62 0.00 7.22 15.07 3.02 16.37 11.47 1.05 1.43 0.59 50.0 15.73 27.82 0.10 7.12 15.18 3.29 16.39 11.15 1.17 1.55 0.51 55.0 14.85 26.80 0.08 6.27 14.80 3.58 18.04 11.33 1.39 2.26 0.60 60.0 13.39 26.70 0.11 6.53 14.74 3.62 19.75 11.00 1.65 2.17 0.33 65.0 13.20 25.54 0.15 6.18 14.69 3.56 20.60 10.70 2.13 2.80 0.47 70.0 13.10 25.13 0.17 6.14 14.13 3.75 20.59 10.65 2.67 2.88 0.79 Chapter 5. 113 Table 5.20: Photoion branching ratio for CFC13 Photon Branching ratio (%) energy (eV) CC1+ CFCLJ CC1+ CFC1+ CC1+ C1+ CF+ F+ C+ 11.5 100.00 12.0 100.00 12.5 100.00 13.0 100.00 13.5 100.00 14.0 0.53 99.47 14.5 1.19 98.81 15.0 1.61 98.39 15.5 2.24 97.76 16.0 2.54 97.46 16.5 2.90 96.51 0.59 17.0 3.15 95.63 1.22 17.5 2.32 93.69 0.46 3.54 18.0 1.86 89.98 1.12 6.55 0.49 18.5 2.02 84.87 2.14 10.17 0.23 0.57 19.0 1.72 81.16 2.97 12.57 0.36 1.22 19.5 1.91 79.11 3.43 13.38 0.40 1.75 20.0 1.60 77.30 3.74 13.99 0.58 2.79 20.5 1.63 76.81 3.85 13.68 0.57 3.46 21.0 1.43 75.34 4.23 13.97 0.28 0.53 4.22 21.5 1.66 74.23 4.22 13.72 0.88 0.45 4.85 22.0 1.63 73.38 4.35 13.63 1.36 0.73 4.92 22.5 1.55 72.36 4.70 13.05 1.93 0.80 5.61 23.0 1.56 70.43 4.63 13.11 3.14 0.87 6.26 23.5 1.64 69.77 4.02 12.96 3.83 1.24 6.54 continued on next page Chapter 5. 114 Table 5.20: (continued) Photon Branching ratio (%) energy (eV) CC1+ CFC1J CC1+ CFC1+ CC1+ C1+ CF+ F+ C+ 24.0 1.55 69.50 4.34 11.95 4.65 1.48 6.52 24.5 1.75 68.22 4.10 11.83 5.61 1.89 6.60 25.0 1.67 67.53 3.99 11.59 6.21 2.74 6.29 25.5 1.71 66.25 3.80 11.69 6.71 3.35 6.49 26.0 1.64 66.24 3.61 11.75 7.08 3.78 5.89 26.5 1.73 64.51 4.04 11.16 8.15 4.54 5.88 27.0 1.77 63.68 3.63 11.58 8.32 5.06 5.95 27.5 1.94 62.15 4.26 11.72 8.32 5.38 6.24 28.0 1.91 60.72 4.31 12.10 8.88 5.73 6.36 28.5 2.08 60.27 4.11 12.47 8.89 6.24 5.96 29.0 1.94 59.00 4.35 12.53 8.93 6.40 6.39 0.44 29.5 2.06 57.76 4.75 13.58 8.78 6.53 6.00 0.54 30.0 2.20 56.92 4.73 12.97 8.65 7.56 6.19 0.78 31.0 2.09 49.82 4.91 14.74 9.32 10.98 6.65 1.49 32.0 2.34 47.44 5.28 15.44 9.09 12.37 6.20 1,84 33.0 2.20 44.84 5.42 15.59 9.16 13.67 7.03 2.09 34.0 2.00 43.00 5.72 16.25 9.11 14.66 7.12 2.14 35.0 2.27 41.75 5.67 16.50 9.10 15.86 7.03 1.83 36.0 2.13 38.12 5.73 17.84 8.49 17.92 7.49 2.28 37.0 2.15 35.56 6.93 18.37 8.42 18.67 7.89 2.00 38.0 2.18 34.26 5.98 19.06 8.72 19.85 7.91 0.04 2.00 39.0 2.15 34.07 6.82 18.22 8.89 19.85 7.81 0.21 1.97 40.0 2.05 33.22 6.75 17.29 8.66 20.83 9.16 0.20 1.84 41.0 2.18 31.79 6.90 18.29 9.02 20.89 8.88 0.24 1.82 43.0 2.23 30.21 6.64 18.39 9.71 21.37 9.51 0.27 1.67 45.0 2.01 29.68 6.54 17.55 9.96 22.48 9.72 0.29 1.77 47.0 2.00 29.41 6.63 17.40 10.27 22.72 9.59 0.35 1.63 49.0 1.85 29.87 6.34 16.67 10.32 23.33 9.61 0.30 1.71 Chapter 5. 115 and decrease in the order of CF4 > CF3C1 > CF2C12 > CFC13. In the dipole (e, e+ion) experiments the ratio of the total coincident ion signal to the forward scattered energy loss signal at each energy loss gives the relative photoion ization efficiency as defined in section 2.3.5. Our data show 20 eV , 23.5 eV, 17.5 eV and 14.5 eV to be the lowest photon energies at which the photoionization efficiencies (rji) for CF4, CF3C1, CF2CI2 and CFC13 reach approximately respective constant val ues. Making the reasonable assumption that the photoionization efficiency is unity at high energy [8,20,114], we therefore obtain the result that 77, for CF4, CF3C1, CF2C12 and CFC13 reach 1.0 respectively at ~20 eV, 23.5 eV, 17.5 eV and 14.5 eV. The pho toionization efficiency curves for CF4, CF3C1, CF2C12 and CFC13 are shown as inserts to respective figs. 5.11a, 5.12a, 5.13a and 5.14a, and values of rji are hsted in respective tables 5.12, 5.13, 5.14 and 5.15. Compared to previously reported work [103], our CF4 ion ization efficiency curve is higher and has less structure (insert to fig. 5.11a), probably due to lower energy resolution. The previously reported photoionization efficiencies [108] of CF3C1, CF2C12 and CFC13 determined using neon resonance lamp radiation at ~16.75 eV are in generally good agreement with the present results (inserts to figs. 5.12a, 5.13a and 5.14a). Absolute differential osciUator strengths for production of the fragment (dissociative) ions are obtained by taking the triple product of the photoabsorption, the photoionization efficiency and the photoion branching ratio at each photon energy. The absolute partial differential oscillator strengths for production of the molecular and fragment ions are shown in fig. 5.24 and table 5.12 for CF4, in fig. 5.25 and table 5.13 for CF3C1, in fig. 5.26 and table 5.14 for CF2C12, and in fig. 5.27 and table 5.15 for CFC13. Tables 5.21, 5.22, 5.23 and 5.24 present the appearance potentials (± 1 eV) for the production of ion species respectively from CF4, CF3C1, CF2C12 and CFC13 measured in Chanter 5. 116 i > CM I o *— Y A Q r n I— o z Ul cn \— in cn o o GO o 30 < N Z o o I— o X Q_ cn < Q_ 0 5 0 2 0 2 0 2 0 0.3 0 \ 11 XAB C 0 E F CF4 CF 3 . CF?+ 2 . CF+ c+ J ill_L F+ CF ++ 2 H 60 30 f= 20 40 60 80 PHOTON ENERGY (eV) 0 5 0 2 0 2 0 2 0 0.3 0 o LU CO I CO CO o O < N O o I— o X Q_ < Q_ Figure 5.24: Absolute differential oscillator strengths for dissociative photoionization of CF4. The vertical arrows represent expected thermodynamic appearance potentials (see table 5.21) and the hatched lines indicate the vertical ionization energies [99,98] for production of the electronic states of CFj. Chapter 5. 117 > CD °0.3 CF3C1 0 20 10 o z LiJ C£. I— to O r-< 5 0 to o X A D EF G H ! f Q Z o t— < M Z o o I— o X 30 20 10 0 0.3 0 5 0 \ :\ CF3CI + CF2CI + CFCI + V CF. + 20 40 -1 1— 60 § e XADEFGH TJ CCI + — v ' • • • • • J f *» • • • Cl+ "1 1 1 1 1 Ill y • • . CF+_ • • • 1" 1 1 1 1 III II 1 * • 1 1*" 1 1 1 1 1 C+ . . . 11 11 • • • . ~ 1 1" 1 1 1 CF2CI++ • • • • • < Q_ 80 20 40 PHOTON ENERGY (eV) 60 80 0.5 0 3 0 2 0 0.5 0 0.5 0 0.1 0 Figure 5.25: Absolute differential oscillator strengths for molecular and dissociative photoionization of CF3CI. The vertical arrows represent expected thermodynamic appearance potentials (see table 5.22) and the hatched lines indicate the vertical ionization energies presented in chapter 6 and reported in ref. [100] for production of the electronic states of CFsCl"1". Chapter 5. 118 > X I— o 10 UJ o QT w ^ 60 or o £ 40 % 20 o < 0 zO.04 OC UJ U_ U_ o h-< M Z O o I— o X or < CL 0 2 0 5 0 CFCI2+ • * CF2CI2 — • • • • • • • . - • • • • • • • • i 1 1 CF2CI + \ • • • • • • "iiiiidi i l 1 1 l i CCI2+ AC EG J K (L.M) NO • i . • • • • 1 * CFCI + • * •*•»•••• • • # ^ • • . . 1 i i CF2+ m • • • ' • • . -..«/ , \\ ii in i II A C 1 G J K fi 6 CCI+ • * • . • 1 ~ 1 1 1 1 1 11V A' ci+ -• • • • / ~"1 111 1 1 ,<\ CF + -11; • « . / • « "•(III 1 F+ Mil ..«. 1 1 ••• 1 1 • 1 l C+ JI 111 • * . * • 1 H 1 1 1 1 CF2CI++ • • • • • • • • • • 20 40 60 80 20 40 PHOTON ENERGY (eV) 60 0 4 0 5 0 0.5 0 0.5 0 0.1 0 80 Figure 5.26: Absolute differential oscillator strengths for dissociative photoionization of CF2CI2. The vertical arrows represent expected thermodynamic appearance potentials (see table 5.23) and the ver tical lines indicate the vertical ionization energies presented in chapter 6 and reported in ref. [100] for production of the electronic states of C^ClJ. Chapter 5. 119 > <L> I (— o z LxJ cr t— if) cr' O. 2 0 80 o < 5 o LIJ t 2 £ 0 < o o 5 o X °- 0 cr < CL m & i 11 i cFci3 nit n 1 rr,+ XABC 6 EF G fi T J V^^-l • /•••••••• cci3+ "T 1 1 ill* CFC!2+ 1 1 1 1 1 1 1,'., ••••• .-1 1 / | '" 1 | 1 1 1 1 CF + 1 t ;' •-T'" 1 1 1 1 1 1 1 ••• 1 1 1 1 1 1 F + 1 it 1 ••• 1 1 1 1 1 1 CFCI+ ' r— 1 1 1 1 1 1 1 1 1 ! 11 1 c+ 1 1 1 r-— , ! , , 3 0 4 0 O.i 0 0. 0 PHOTON ENERGY (eV) Figure 5.27: Absolute differential oscillator strengths for dissociative photoionization of CFCI3. The vertical arrows represent expected thermodynamic appearance potentials (see table 5.24) and the hatched lines indicate the vertical ionization energies presented in chapter 6 and reported in ref. [100] for pro duction of the electronic states of CFCI3 . Chapter 5. 120 Table 5.21: Calculated and measured appearance potentials for production of charged species from CF4  Process Appearance potential (eV) calcu- exp eriment al [ref.] lateda this work 6 [135] [136] [137] [138] [139] [103] [140] (1) CF++F 14.74 16 15.9 15.4 16.0 16.2 15.35 15.56 15.52 (2) CF++F2 19.32 21 22.45 22.33 20.3 22.2 (3) CFJ+2F 20.92 (4) CF++F2+F 22.07 (5) CF++3F 23.66 30 22.85 27.32 22.6 (6) C++2F2 28.23 (7) C++F2+2F 29.82 (8) C++4F 31.42 35 29.5 31.5 (9) F++F2+F+C 35.99 35 24.0 36 (10)F++3F+C 37.58 (11) CF1++? 44 44.3 (12) CF2++? 42.7 "Using thermochemical data from ref. [132], assuming zero kinetic energy of fragmentation. 6±1 eV. Chapter 5. 121 Table 5.22: Calculated and measured appearance potentials for the production of charged species from CF3C1  Process Appearance potential (eV) Calculated" Experimental [ref.] This work* [137] [141] [107] [142] [140] [143] [144] [145] [146] [147] (1) CF3C1+ 12.6 12.5 13 12.8 12.45 12.39 12.43 12.91 12.6 (2) CF2C1+ 14.5 15.0 15.5 14.25 16.15 (3) CF++C1 12.7 12.5 12.7 12.95 12.55 12.65 12.57 13.06 (4) CFC1+ 14.5 20.45 (5) CF^+FCl 16.5 (6) CF++F+C1 19.1 19 20 21.0 18.85 18.84 18.85 (7) CC1+ 28 (8) C1++CF3 16.8 (9) C1++CF2+F 20.4 19.5 21 21.0 (10) C1++CF+F2 24.1 (11) C1++CF+2F 25.7 (12) Cl++C+F+F2 29.7 (13) C1++C+3F 31.3 (14) CF++F+FC1 19.3 (15) CF++F2+C1 20.2 20.28 (16) CF++2F+C1 21.8 23.5 22.6 25.0 22.00 (17) F++CF2+C1 24.9 (18) F++CF+FC1 27.6 (19) F++CF+F+C1 30.1 31 (20) F++C+FC1+F 33.2 (21) F++C+Fa+Cl 34.1 34 (22) F++C+2F+C1 35.7 35.0 (23) C++F3C1 24.3 (24) C++F2-I-FC1 25.4 (25) C++F2+F+C1 28.0 (26) C++3F+C1 29.6 33 31 (27) CF2C12++?? 38 (28) CFC12++?? 40 "Using thermochemical data from refs. [133,132,134] assuming zero *± 1 eV. kinetic energy of fragmentation. Chapter 5. 122 Table 5.23: Calculated and measured appearance potentials for the production of charged species from CF2Ci2  Process Appearance Potential (eV) Calculated" Experimental [ref.] "This" [107] [142] [143] [Iii] [146] [U7]-work6 (1) CF2C12+ 11.8 11.75 11.75 12.31 11.87 (2) CFC12+ 14.0 14.15 13.81 13.30 (3) CF2C1+ 11.5 12.10 11.99 12.55 11.96 (4) CC12+ 46 (5) CFC1+ 18.5 17.76 18.60 (6) CF2++C12 14.6 14.90 (7) CF2++2C1 17.1 17.5 17.22 16.98 (8) CC1+ 24 21.60 (9) C1++CF2+C1 18.5 18.76 (10) C1++CF+FC1 21.2 20 (11) C1++CF+F+C1 23.8 (12) C1++C+FC1+F 26.8 (13) Cl++C-r-F2+Cl 27.7 (14) C1++C+2F+C1 29.3 (15) CF++FC1+C1 17.3 (16) CF++F+C12 17.4 17.65 17.35 (17) CF++F+2C1 19.9 20 20.20 19.84 (18) F++CF+C12 25.7 (19) F++CF+2C1 28.2 (20) F++C+FC1+C1 31.2 (21) F++C+F+C12 31.3 (22) F++C+F+2C1 33.8 36 (23) C++2FC1 20.5 (24) C++F2+C12 23.5 (25) C++FC1+F+C1 25.1 (26) C++2F+C12 25.1 (27) C++F2-r2Cl 26.0 (28) C++2F+2C1 27.6 31 (29) CF2C12++?? 38 "Using thermochemical data from refs. [133,132,134] assuming zero kinetic energy of fragmentation. b± 1 eV. Chapter 5. 123 Table 5.24: Calculated and measured appearance potentials for the production of charged species from CFCI3  Process Appearance potential (eV) calculated" Experimental [ref.] "this' [107] jliij [148] [147] [146] [141] work6 (1) CFCLt 1L8 11.46 (2) CCLt 14 13.50 13.25 12.77 13.8 (3) CFC1J 11.5 11.65 11.57 11.97 (4) CCtf 17.5 17.0 17.12 (5) CFC1+ 16.5 16.0 16.02 17.41 16.95 (6) CC1+ 21 20.5 20.00 (7) C1++CF+C12 19.6 18.5 (8) C1++CF+2C1 22.0 (9) C1++C+FC1+C1 25.0 (10) Cl++C-r-F+Cl2 25.1 (11) C1++C+F+2C1 27.6 (12) CF++C1+C12 15.7 15.7 (13) CF++3C1 18.2 18 18.35 18.10 (14) F++CC13 21.6 (15) F++C+C1+C12 29.6 (16) F++C+3C1 32.0 38 (17) C++FC1+C12 20.8 (18) C++FC1+2C1 23.3 (19) C++F+C1+C12 23.4 (20) C++F+3C1 25.9 29 "Using thermochemical data from refs. [133,132,134] assuming zero kinetic energy of fragmentation. b± 1 eV. Chapter 5. 124 the present work and appearance potentials for the various processes calculated from ther modynamic data [132,133,134], assuming zero kinetic energy of fragmentation. Previously reported values are also shown in tables 5.21, 5.22, 5.23 and 5.24 for comparison. The calculated thresholds are denoted by arrows on figs. 5.20, 5.24, 5.21, 5.25, 5.22, 5.26, 5.23 and 5.27, together with the vertical ionization energies for production of the electronic ion states of respective molecules (see section 5.1). 4 5.5 Absolute Electronic State Partial Photoionization Differential Oscillator Strengths for CF4 In this section the electronic state partial differential oscillator strengths for CF4 have been re-derived based on the earlier reported results and the new information available from the present investigations. Those for other freon molecules will be reported in chapter 6. Electronic state partial photoionization cross sections have been reported for CF4 [105] for production of the X, A, B, C and D ion states up to 70 eV photon energy. Yates et al. [149] have reported PES branching ratio measurements for CF4 consistent with the cross-section data of Carlson et al. [105]. However, as discussed in section 5.2.1 above, the reported absolute values of the electronic state partial cross-sections for the X, A, B, C and D states [105] may be incorrect due to the method used for the absolute measurement and/or the effects of higher order radiation (see section 5.2.1). It should be noted that the E ion state has an adiabatic ionization potential of ~34 eV [117], while the appearance potentials of C+ and F+ are ~35 eV in the present work (see table 5.21). Therefore, we can tentatively set the sum of the differential oscillator strengths for production of the E and F ion states to be equal to the sum of those for producing C+ and F+. With these considerations in mind, we have re-analyzed the PES data for CF4 reported by Carlson Chapter 5. 125 et al. [105] as follows: 1. In the energy region below the adiabatic ionization energy of the E state (~34 eV), photoelectron branching ratios were calculated from the previously reported exper imental partial cross-sections [105]. These were then combined with the presently reported photoabsorption and photoionization efficiency results (table 5.12) to ob tain improved estimates of the electronic state partial photoionization differential oscillator strengths of the X, A, B, C and D states of CF4. 2. At higher photon energies up to 70 eV, the originally reported relative intensities for the X, A, B, C and D ion states [105] were used to partition a differential oscillator strength equal to the present total photoabsorption (table 5.12) minus an appropri ate allowance for the combined (E+F) state differential oscillator strengths. Since there are no direct experimental measurements, the combined (E+F) state differ ential oscillator strengths have been equated to the sum of the measured differential oscillator strengths for the production of the C+ and F+ ions (this work) for the reasons described above. These revised electronic state partial differential oscillator strengths are presented nu merically in table 5.25 and are shown together with the MS-Xa calculations [150] and previous PES data [105] in fig. 5.28. The revised values show only small differences from the original PES data [105] for the B, C and D states. Somewhat larger differences exist for the (<20 and 25-35 eV) and (<23 eV) state partial cross-sections. In general, the (resolutionless) MS-Xa calculations give a reasonable semi-quantitative description of the trends in the measured partial cross-sections. The presently estimated differential oscillator strengths for the combined (E+F) states are comparable with the calculation in terms of shape and magnitude. It is noteworthy that for the X state, the presently Chapter 5. 126 Table 5.25: Electronic state partial differential oscillator strengths for the photoionization of CF. Photon Electronic state differential oscillat or strength (10_2eV_1) energy (eV) X A B C b E+F 6 15.5 0.81 16.0 3.64 16.5 7.80 17.0 14.95 17.5 22.47 18.0 9.58 20.26 18.5 12.21 22.00 19.0 14.65 22.82 19.5 10.99 25.72 2.97 20.0 11.58 22.82 7.71 21.0 14.56 24.60 9.45 22.0 18.43 21.47 12.46 23.0 16.34 15.62 8.33 11.10 24.0 16.76 12.57 6.84 11.99 25.0 18.31 11.05 6.36 9.38 26.0 17.97 9.92 6.17 6.78 28.0 18.62 8.70 5.93 5.35 0.42 30.0 19.22 8.72 5.33 4.94 0.72 32.0 17.98 8.76 5.83 5.06 0.92 34.0 16.31 10.42 5.73 6.01 1.31 36.0 14.06 10.62 5.59 6.76 2.05 0.36 38.0 12.52 10.61 5.34 7.36 2.31 1.24 40.0 11.52 10.39 5.11 7.33 2.12 2.52 45.0 9.38 8.60 4.16 5.02 1.70 2.51 50.0 7.78 7.37 3.69 3.40 1.85 2.28 55.0 6.44 6.16 3.21 3.69 1.61 2.82 60.0 5.48 5.81 3.20 3.76 1.25 2.96 65.0 4.58 4.58 3.30 3.28 1.28 2.81 70.0 4.21 4.01 2.81 3.11 1.11 2.83 "Based on branching ratios calculated from previously published PES measurements [105] combined with the present photoabsorption and photoionization efficiency data (table 5.12) and using values of the (E+F) state partial differential oscillator strengths estimated from the partial photoionization differential oscillator strength sum (C++F+). See text for details. 'The electronic state differential oscillator strength sum (E+F) was set equal to the partial pho toionization differential oscillator strengths (C++F+). See text for details. Chapter 5. 127 O i— O UJ CO I CO CO o O < N O O t— o X Q_ 30 20 10 0 30 20 10 0 15 10 5 0 20 15 10 5 0 2 cn < CL 0 0 CF. t S t •C++ F+ X J I I 1—1 l_ c D i i i i 1,1 E + F E 20,? i o 10 o 20^ to ct: O o to O 10 0 10 5 o g 15| 10 t| 5 -0 2 2 O < M 1 § O 0 - 4 15 65 0 o X Q_ CC < 25 35 45 55 PHOTON ENERGY (eV) Figure 5.28: Electronic state partial photoionization differential oscillator strengths of CF4. Open circles—previously reported partial photoionization cross—section ( electronic states) measurements obtained by PES [105] (see text). Solid circles—revised values obtained by combining the present photoabsorption and photoionization data with PES branching ratios derived from reference [105]. See section 5.5 for details. Solid lines—MS-Xa calculations [150]. Squares—summed (C++F+) partial differential oscillator strengths. See text for details. Chapter 5. 128 revised PES cross-sections show a resonance at ~17.5 eV which is predicted by the calculation but not exhibited in the PES data as originally presented [105]. 5.6 The Dipole Induced Breakdown In photoionization once the photon energy exceeds the upper limit of the Franck-Condon region, the internal energy of the molecular ion is independent of the photon energy for a given electronic state and the remainder of the energy is carried by the photoelectron according to Einstein's photoelectric equation. On the assumption that fragmentation ratios for dissociative ionization from each electronic state of the ion are constant when the photon energy is above the Franck-Condon region [77], the partial differential oscilla tor strengths for the production of the singly charged molecular or any stable dissociative (fragment) ion should be a fixed hnear combination of electronic state partial photoion ization differential oscillator strengths at all photon energies. This general approach and possible exceptions such as autoionization, internal conversion to other electronic ion states and multiple ionization have been discussed in ref. [77]. The dipole induced breakdown patterns of many small molecules have been investigated with considerable success by this type of analysis, for example, see refs. [77,114]. The dipole induced break down schemes for CF4, CF3CI and CF2CI2 discussed below have been obtained using the presently reported absolute differential osciUator strengths for molecular and dissocia tive photoionization. The electronic state partial photoionization differential oscillator strengths for CF4 are as reported in section 5.5, while those for CF3CI and CF2CI2 are obtained from the triple product of the presently measured total photoabsorption differ ential oscillator strengths (section 5.2.2), the photoionization efficiencies (section 5.4) and the electronic state branching ratios obtained from synchrotron radiation PES measure ments reported in section 6.2 and ref. [121,151] (see details below). The dipole induced Chapter 5. 129 breakdown of CFC13 is not reported since insufficient PES data is available. 5.6.1 The Dipole Induced Breakdown of CF4 Since stable CF4 is not observed on the time scale of the TOF mass spectrometer and because CFjj" is the only ion produced below the state ionization potential (adiabatic IP = 21.7 eV [99])-see table 5.21, the X, A and B electronic states of singly ionized CF4 must exclusively lead to production of CF3. A consideration of the Franck-Condon width of the C state and the appearance potential of CF^" (~21 eV) indicates that CF£ can be formed from the C state. Similarly the smaller fragments can only be formed from the D and/or higher states. In the region below ~40 eV, CF+ can only be formed from the D state. With these considerations in mind the following relationships between the differential oscillator strengths for formation of CF3 , CFj", CF+, C+ and F+, and those for production of the X, A, B, C, D, E and F ion states are found to provide a reasonably consistent rationalization of the breakdown: ^(CF+) = i|(X-M + B + 0.62C7) (5.42) §(CFJ) = ;§(0.38C) (5.43) £(C+ + F+) = 1L{E + F). (5.45) Fig. 5.29 shows the breakdown relationship as a function of photon energy. In scheme I, the originally presented PES data [105] have been used. The agreement is quite good considering that the PES data and the ion photofragment differential oscillator strengths are from independent measurements using different techniques with independent means of estabhshing the absolute scales. However, as discussed in section 5.2.1, we have some reservations concerning the absolute values reported in the original PES study [105] and, Chapter 5. 130 Figure 5.29: Absolute differential oscillator strengths for the proposed dipole induced breakdown scheme of CF4. Solid circles—present dipole (e, e+ion) experimental data, sohd lines—sums of electronic state partial differential oscillator strengths (scheme I using original PES data [105]; scheme II using revised PES data). See text for details. (a,d) Photofragmentation to CFJ". (b,e) Photofragmentation to CFJ. (c,f) Photofragmentation to CF+. Chapter 5. 131 PES Dipole Ionization Ground State Molecule States (IP eV) 0 00 Fragmentation (%) (e, e+ion) Ion Products E F 40.3 43.3 1 100 7100 CF+3 CF+2 CF+ C++ F + Figure 5.30: Proposed dipole induced breakdown scheme for the ionic photoionization of CF4. See text for details. Chapter 5. 132 therefore, have considered a set of revised PES data as discussed in section 5.5. The revised electronic state cross-sections are used in scheme II of fig. 5.29. Scheme II shows a somewhat better overall fit to the ion data. However it should be remembered that localized variations of the overall breakdown pattern might be expected at lower energies due to the autoionization levels preceding the various ionization hmits. Nevertheless the general consistency of the fits for CF3 , CFJ" and CF+ over the entire energy range up to 70 eV in both schemes lends confidence to the essential correctness of the breakdown scheme as proposed above. Fig. 5.30 shows in diagrammatic form the main features of the proposed dipole induced breakdown scheme for CF4. Further details of the break down pattern of CF4 must await detailed photoelectron-photoion coincidence studies as a function of photon energy. 5.6.2 The Dipole Induced Breakdown of CF3C1 Since the molecular ion CF3C1+ and the ion CF3 are the ions produced from CF3C1 (see table 5.22) below the A state ionization potential [100], the X state must lead to production of CF3C1+ and CF3 . Considering the Franck-Condon region of the A state [100] and the appearance potentials of CF2C1+ and CFC1+, it appears that the ions CF2C1+ and CFC1+ are the fragments produced from the dipole induced breakdown of the A state. By taking account of the present energy resolution (1 eV FWHM), the Franck-Condon width and the ionization energy of the D state [100] and the appearance potential of CFj, it is suggested that the CFj ion is formed from the D electronic state of the molecular ion. Similarly, the ions Cl+, CF+ and CC1+ can be formed from the F, G and H states (ref. [100] and chapter 6) respectively and the ions F+ and C+ from the / state (chapter 6). With these considerations in mind the following relationships between the partial differential osciUator strengths for formation of CF3C1+, CF2C1+,CF3 , Chapter 5. 133 > a, Figure 5.31: Absolute differential oscillator strengths for the proposed dipole induced breakdown scheme of CF3CI. Solid circles—present dipole (e,e+ion) experimental data. Solid hnes—sums of the electronic state partial differential oscillator strengths obtained using the presently determined photoab sorption differential oscillator strengths and PES branching ratio data in the 21-41 eV [121] and 41-80 eV (chapter 6) regions. See text section 5.6.2 for details. Crosses—(d//djT)[0.5(/+/)] obtained the same way as the solid hnes using PES data presented in chapter 6. Chapters. 134 Ground State Molecule PES Dipole Ionization Figure 5.32: Proposed dipole induced breakdown scheme for the ionic photoionization of CF3CI. See text for details. Chapter 5. 135 CFC1+, CF+, CC1+, Cl+, CF+, F+ and C+, and those for production of the X, A, B, C, D, E, F, CT, H and (I+J) electronic states are found to provide a reasonably consistent rationahzation of the dipole induced breakdown of CF3C1 within the energy range of the present data: £(CF3C1+) = ^(OMX) (5.46) ^LCF2C1+) = ^(0.95i + B + 0.6C) (5.47) dE diLi dE{C¥t) = iE(0'99* + °Ad + °At>) (5-48) £(CFC1+) = £(0.05i) (5.49^(CF+) = £(0.67J + E) (5.50) IE <CC1+> = 7E^ (5.51) S(C1+> = 1E{^ (5-52» i<CF+> = IE^ (5.53) £(F+) = £[0.5(7+ i)[ (5.54£(C+) = £[(0.5(7+ j)]. (5.55) Fig. 5.31 shows these breakdown relationships as a function of photon energy. The elec tronic state partial differential osciUator strengths used in fig. 5.31 were obtained from the triple product of the presently measured total photoabsorption differential oscillator strengths (section 5.2.2), the photoionization efficiencies (section 5.4) and the electronic state branching ratios obtained from PES measurements in the 21-41 eV [121] and 41-80 eV (chapter 6) regions. The measurement in chapter 6 includes the inner-valence photoelectron bands. Since only the sum of the branching ratios for the I and J states could be reported (chapter 6), the partial differential oscillator strengths for the produc tion of the I and J states are represented in the form of a sum in the above breakdown Chapter 5. 136 relationships. As can be seen from fig. 5.31 the relationships are reasonably successful in reproducing both the shapes and magnitudes of the photoion partial differential oscilla tor strengths. Fig. 5.32 shows the presently proposed overall dipole induced breakdown scheme for CF3C1. A more detailed investigation of the breakdown patterns of CF3C1 must await photoelectron-photoion coincidence studies as a function of photon energy. 5.6.3 The Dipole Induced Breakdown of CF2C12 Since the molecular ion CF2ClJ is not observed on the time scale of the TOF mass molecular ion. Similarly the fragment ions CClJ, CFj, CC1+, Cl+, F+ and C+ can be formed from the (N+O), G, K, J, N and (L+M) electronic states (ref. [100] and chapter 6) respectively, and the ions CFC1+ and CF+ from the (H+I) states [100]. With these consideration in mind the following relationships between the partial differential oscillator strengths for the formation of CFClJ, CF2C1+, CCTj", CFC1+, CF+, CC1+, Cl+, CF+, F+ and C+, and those for the production of the (X+A), (B+C), D, (E+F+G), (H+I), J, K, (L+M) and (N+O) electronic states are found to provide a reasonably consistent rationalization of the dipole induced breakdown of CF2C12 within the energy range of the present data: spectrometer and because CF2C1+ is the only ion detected (see table 5.23) below the D state ionization potential of CF2C12 [100], the X, A, B and C electronic states of the molecular ion must exclusively lead to production of the CF2C1+ ion. Considering the Franck-Condon region of the D state [100] and the appearance potential of CFCl^, it appears that CFClJ is the fragment ion produced from the D electronic state of the df_ dE £. dE (5.56) (5.57) Chapter 5. 137 ^(CCl+) = ^[0.015(iV + O)] J^(CFCl+) = -^[0.38(77 + 7~)] %(CF+) = %[0.38(E + F + G)} ^(F+) = ^[0.2(A> + O)] ^(Cl+) = ^[J + 0.647? + 0.485(iV + 6)} 7F(CF+) = TF[0-62(^ + /) + 0.2(iV + 6)] (5.58) (5.59) (5.64) (5.61) (5.63) (5.62) (5.60) i^(C+) = M(L + M) + 0.1(N + d)]. (5.65) Fig. 5.33 shows these breakdown relationships as a function of photon energy. The elec tronic state partial differential oscillator strengths used in fig. 5.33 were obtained from the products of the presently measured total photoabsorption differential osciUator strengths (section 5.2.3) and the electronic state branching ratios obtained from PES measure ments in the 27-41 eV [151] and 41-70 eV ( chapter 6) regions. The measurements in chapter 6 includes the inner-valence photoelectron bands. Due to the unresolvabihty of certain features in the photoelectron spectra reported in chapter 6 and in ref. [151], the branching ratios for the production of the relevant states were reported as sums, i.e. (X+A), (B+C), (E+F+G), (77+7), (L+M) and (N+O), therefore the corresponding partial differential oscillator strengths are presented in similar form in the above break down relationships. In spite of the uncertainties involved in such a simple rationale the correspondence of the proposed scheme with the partial photoionization differential os cillator strengths (fig. 5.33) is reasonably good in terms of both shape and magnitude. Fig. 5.34 shows the presently proposed dipole induced breakdown scheme for CF2CI2. A Chapter 5. 138 more detailed analysis of the dipole induced breakdown scheme of CF2C12 may be ob tained from photoelectron-photoion coincidence studies as a function of photon energy. Chapter 5. 139 V K W (— 0-w g 50r y*0.15(E+F+G cF.cr U 25-W O £0.03r u gjo.oo-I 4 o * 2^ o 5 <* a 10-z o g * o a. oL < < CU 47(E+F+G) o 0.015(N+0) CCL CFC1 0.38(H+T) CF2 + /, 0.38(E+F+G) o 5 0 5 0 10.5 po 1 20 40 60 ccr 0.36K 0.64KVv o J+0.64K+0.485(N+0^ + o 0.62(H-fI)+0.2(N+0) CF 0.62(H+I) o 0.2(N+0) F + ••••• o (L+M)+0.1(N+0) Q * , (L+M) 20 40 60 PHOTON ENERGY (eV) Figure 5.33: Absolute differential oscillator strengths for the proposed dipole induced breakdown scheme of CF2C12. Solid circles—present dipole (e,e-)-ion) experimental data. Sohd lines—sums of electronic state partial differential oscillator strengths using the presently determined photoabsorption differential oscillator strengths and PES branching ratio data in the 27-41 eV [151] and 41-70 eV (chapter 6) regions. See section 5.6.3 for details. Chapter 5. 140 Ground State Molecule CFaClg States (IPeV) PES Dipole Ionization X+A 12.26.12.53 13.11.13.45 D 14.36 E+F+S 15.9,16.30.16.9 H+l 19.3 J 20.4 K 22.4 L+M 27.2 N+5 38.6.41.4 Figure 5.34: Proposed dipole induced breakdown scheme for the ionic photoionization of CF2C12. See text for details. Chapter 6 Photoelectron Spectroscopy and the Electronic State Partial Differential Oscillator Strengths of the Freon Molecules CF3C1, CF2C12 and CFC13 Using Synchrotron Radiation from 41 to 160 eV The presently reported PES spectra for CF3C1, CF2C12 and CFCI3 were measured by Dr. G. Cooper at the Canadian Synchrotron Radiation Facility (CSRF) located at the ALADDIN facility at The University of Wisconsin [152]. The measurement method and apparatus have been described previously [121,153,154,155,156]. Briefly, a 1200 line/mm holographic grating in a Grasshopper Monochromator is used to monochromate syn chrotron radiation from the Aladdin storage ring in Stoughton, Wisconsin. The grating has useful output at photon energies above 40 eV. The sample is photoionized in a free gas jet and the photoelectrons are energy analyzed at the pseudo magic angle using a Leybold Heraeus LHS-11 hemispherical photoelectron spectrometer. The spectrometer is isolated from the optical elements of the beam hne by two stages of differential pumping. The overall resolution of the monochromator/spectrometer apparatus in the present ex periments was in the range 0.2-0.3 eV FWHM, depending upon the photon energy (since AA oc AE/E2 is constant, where E is photon energy) and the pass energy (typically 12.5 or 25 eV) used in the electron analyzer. The transmission efficiency of the photoelectron spectrometer has been found to be effectively constant over the range of photoelectron kinetic energy used in the present work. 141 Chapter 6. 142 6.1 Photoelectron Spectra Photoelectron spectra of CFCI3 and CF2CI2 obtained with synchrotron radiation at 80 eV energy are shown in figs. 6.35a and 6.35b respectively, while the spectrum of CFCI3 at hv = 90 eV is shown in fig. 6.35c. The assignments of the photoelectron bands up to 30 eV ionization energy indicated in the figures follow those given by Cvitas et al. [100], while the assignments of the higher energy bands are the same as those of Potts et al. [157]. Green's function calculations within the two particle-hole Tam-Dankoff approximation (2ph TDA) method performed by Cambi et al. [158] indicate that the one electron description of ionization is not adequate to describe ionization of the inner-valence orbitals of freon molecules (the orbitals with predominantly Cl 3s and F 2s character), and that each inner-valence orbital will give rise to a number of many-body photoelectron states. Therefore the molecular orbital labels for the bands > 25 eV ionization energy in fig. 6.35 are an approximation and give only the major one electron configuration involved in the ion states. Unlike Potts et al. [157] we do not observe clear separations between the F 2s lb^1 and la]"1 states in CF2CI2 or the F 2s le~* and la]"1 states in CF3C1. The reason for this is unclear since the electron energy resolution of the presently reported measurements should be adequate to observe the splittings seen by the authors of ref. [157]. The estimated vertical ionization energies for the inner valence states obtained in the present work are given in table 6.26. The features in the CFCI3 and CF2CI2 spectra (see fig. 6.35) at apparent ionization energies of 46.8 and 48.7 eV (CFC13) and 47.1 and 48.8 eV (CF2C12) are in fact due to Cl 2j»3^2 and 2p\~j2 states respectively produced by third order radiation from the monochromator. The kinetic energies of these peaks match those expected on the basis of the reported ionization energies of the Cl 2p~x states of CFCI3 (207.20 eV (2^3/2), Chapter 6. 143 10 5-CO UJ 0 10 LU 5-> h-< as 5" 0 3e CFCI: (2e,4a,) (46,50,) \ ' (lo2,5e)N>;; i, r h„ = l20eV la, ' ' I L j hv=80 eV 3a. . . : -:: .: • A le2a' v!°i A . Cl 2p-'{3rd Order) 3/2 '/2 rr i 1 r (5a,,la2,3b,) .*' (2b,,4a,) (202,6a,) .5 (4b2,4b,)• .\2b, : » ^ 3a, T h!/ = 80eV CF2Ch Cl 2p-' (3rd Order) (2a,,lb2) lb, la, 3/2 '* rr i r 3e -I 1 hv=90eV 5ai la24e' m • f CR.CI 2e j 5e • t '4a\U le lai 2a, T 10 20 30 40 50 BINDING ENERGY (eV) Figure 6.35: Photoelectron spectra of: a) CFC13 at hu = 80 eV (Insert shows hu = 120 eV); b) CF2C12 at hu = 80 eV; c) CF3CI at hu =90 eV. The assignments shown on the spectra follow those given in refs. [100] and [157] (see section 6.1 for details). The peaks above 45 eV in a) and b) are spin-orbit doublets from Cl 2p ionization by third order radiation (see text). 1 Chapter 6. 144 Table 6.26: Vertical ionization energies for the inner valence regions of CF3C1, CF2CI2 and CFCI3 :  Molecule Ionization ener gy (eV) this work" ref. [157] CF3CI 2a\ le lai 2ai le lax 26.9 40.0 42.5 26.3 40.0b 42.8 6 CF2C12 (2oi,l62) I61 lax (201,163) l&i lai 27.0 38.6 41.4 — 39 41 CFCI3 le 2ai lax le 2ai lai 25.3 27.6 40.0 25.5 27.6 39.5 A± 1.0 ey. 6The ionization energies for the le and lai orbitals of CF3CI given in the text of ref. [157] are 42.8 and 44 eV respectively, however the spectrum shown in fig. 2c of ref. [157] is not consistent with these values. The numbers given in the table therefore have been estimated from fig. 2c of Potts et al. [157]. Chapter 6. 145 208.81 eV (2p-/2) [159]) and CF2C12 (207.47 eV (2p-/2), 209.10 eV {2p~f2) [159]) for hv = 240 eV. The assignment as spin-orbit doublets is supported by the relative intensities and spacing of the two peaks in each case. Further support is gained from the fact that no such spin-orbit doublets appear within the same spectral range of the (first order) spectra at other photon energies (for example see the insert to fig. 6.35a which shows the spectrum of CFCI3 at hv = 120 eV). Fig. 6.35c shows the spectrum of CF3CI at hv = 90 eV. 6.2 Photoelectron Branching Ratios and Partial Photoionization Differential Oscillator Strengths The photoelectron spectra were analyzed by least squares fitting the data to Gaussian peak shapes plus a hnear background function. For some molecular orbitals individual photoelectron branching ratios could not be obtained since the photoelectron bands were too heavily overlapping each other at the resolution used in the present experiments. In these cases branching ratios for groupings of peaks are presented below. Photoelec tron branching ratios of CF3C1, CF2C12 and CFCI3 are presented in tables 6.27-6.29 and in figs. 6.36-6.38 respectively. Where the separate contributions from overlapping peaks could not be adequately determined from the curve fitting procedure, a combined branching ratio is presented. In fig. 6.36 are also plotted the branching ratios reported by Bozek et al. [153] for CF3C1 from 41 to 70 eV. Above 70 eV the branching ratios of the F 2s le and lai orbitals begin to become significant so that comparison of the presently reported results with those of ref. [153] is no longer appropriate since Bozek et al. [153] did not make measurements in the inner valence region. Novak et al. [151] did not directly report their measured photoelectron branching ratios for CF3C1 and CF2C12, instead they quoted partial photoionization cross-sections which they derived from the Chapter 6. 146 Table 6.27: Photoelectron branching ratios of CF3C1 Photon Branching Ratio (%) Energy (eV) 5e 5ax la2 4e 3e 4ax 2e 3ax 2ax (le + 1 41 4.4 10.4 14.1 31.2 21.1 4.0 13.2 1.6 45 4.0 10.7 12.0 27.1 21.0 4.6 15.7 4.7 0.3 50 3.9 10.1 9.7 26.9 19.3 5.6 17.1 7.2 0.4 55 4.2 10.1 8.9 24.1 18.2 5.8 17.2 9.5 1.9 60 5.4 11.3 6.9 25.3 18.0 6.5 17.0 8.5 1.0 65 5.9 9.1 { 52.4 } 8.3 15.8 7.3 1.4 70 6.5 8.8 8.2 24.1 21.8 6.0 16.7 6.4 1.4 75 7.4 8.3 7.6 23.3 21.0 5.4 16.6 5.7 0.8 3.8 80 6.5 7.9 6.3 21.9 19.0 5.5 16.0 5.6 0.8 10.5 85 7.0 7.9 4.6 26.0 16.0 5.6 15.0 5.0 0.4 12.5 90 7.5 5.2 9.4 17.0 22.0 5.1 14.4 4.5 0.4 14.6 95 7.5 6.7 8.3 18.5 18.7 5.1 13.6 4.6 0.5 16.6 100 7.9 6.2 9.7 18.5 19.9 5.0 14.1 4.4 0.6 13.5 105 7.9 6.6 7.5 21.1 15.9 4.0 12.7 4.8 0.4 19.0 110 9.1 8.9 6.9 21.1 15.1 5.6 12.5 5.2 0.5 15.2 115 8.6 7.4 8.9 19.2 16.9 4.4 12.4 5.1 1.0 16.2 120 8.8 8.3 8.8 21.0 17.1 4.5 13.2 4.8 0.9 12.7 130 9.4 8.5 8.6 20.8 16.8 4.8 12.1 4.8 0.4 13.8 140 9.5 8.0 8.5 18.0 15.1 4.5 11.5 4.4 1.0 19.8 150 10.5 8.0 8.1 16.6 15.2 5.3 11.8 5.6 1.1 17.9 160 10.1 7.9 8.1 16.5 17.2 4.6 13.0 6.1 1.4 15.0 Chapter 6. 147 Table 6.28: Photoelectron branching ratios of CF2CI2 Photon Branching Ratio (%) Energy (eV) (4fr2+4fri) (2a1+6ai) Zb2 (5ai+la2+3&i) (26!+4ai) 2b2 3ai (2ai+l&2) (l&i+lai) 41 3.9 5.4 9.4 46.6 13.8 12.9 8.0 45 3.3 6.5 9.1 44.1 14.4 14.2 8.6 50 4.2 7.5 8.5 43.8 14.1 12.9 8.9 55 5.5 8.2 9.1 42.0 15.4 11.1 8.5 60 7.5 7.2 8.9 38.8 14.9 11.6 9.3 2.0 65 7.4 8.0 8.4 39.4 16.0 10.0 8.1 2.7 70 7.0 6.9 6.6 33.0 13.8 8.2 9.9 1.6 13.1 75 8.5 7.0 6.0 34.5 15.2 8.2 6.3 1.5 12.9 80 8.7 6.6 6.5 34.8 14.7 9.2 6.3 2.1 11.2 85 8.7 6.9 6.2 32.7 14.4 7.9 6.2 2.2 14.7 90 10.0 8.1 5.2 32.5 15.2 6.5 6.7 3.8 12.1 95 10.6 9.3 6.2 31.5 14.9 7.2 6.0 3.5 10.8 100 11.1 9.6 7.0 32.6 13.5 8.6 5.8 1.4 10.6 105 11.7 9.5 7.4 32.2 13.0 8.1 5.8 2.5 9.7 110 12.3 10.6 6.7 31.9 13.1 7.5 5.4 2.1 10.2 120 12.2 11.1 7.4 30.6 11.1 7.6 5.1 2.6 12.5 130 11.7 10.2 8.4 30.1 11.1 8.5 5.4 4.5 10.2 140 12.8 11.1 8.3 29.2 11.4 7.2 5.5 3.0 11.6 150 12.2 12.9 7.9 27.5 12.1 6.4 6.2 2.8 12.0 160 13.2 9.1 8.8 26.5 12.2 6.5 6.4 2.8 14.4 Chapter 6. 148 Table 6.29: Photoelectron branching ratios of CFCI3 Photon Branching Ratio (%) Energy (eV) (la2 + 5e + 4e + 5ax) 3e (2e + 4ai) 3ai (le + 2ai) lai 41 20.7 29.0 33.8 10.6 5.8 45 20.8 27.9 35.2 10.2 6.0 50 22.8 27.7 31.5 10.7 7.4 55 28.3 27.3 29.8 10.0 4.6 60 28.4 25.5 30.0 10.1 6.0 65 31.0 26.4 30.1 8.7 3.8 70 28.3 24.0 29.7 6.4 6.5 5.2 75 28.9 21.8 28.3 9.1 7.3 4.6 80 32.4 21.4 27.8 7.5 4.4 6.4 90 32.6 18.1 25.2 7.5 7.7 9.0 100 36.2 18.2 23.2 7.6 6.8 8.1 110 39.2 17.9 22.5 7.4 6.4 6.7 115 41.6 17.8 22.4 7.0 5.7 5.5 120 40.6 18.3 21.2 6.7 6.6 6.7 130 41.4 17.4 20.4 7.0 6.4 7.6 140 42.1 17.2 20.7 7.3 7.4 5.4 150 41.8 17.0 21.8 6.7 4.7 7.9 Chapter 6. 149 6^ O rr CD X o < cc CD o rr r— O LU _J UJ O I— o X CL 4a, • Rf2 8 ° D 8 • . . . . • . CF3CI be i 1 1 1 1 1 5a, . WcP •••• 0 • . • • a • • a r 1 1 1 1 r— 2e 1 1 1 1 1 1 ° °° ° la2 0 0 0 • • » • ' • • .. •.' • • • * • • 1 1 1 1 1 ' 3a, 0 0 t • 0 0 ^ 0 8 • • • • -' 4e *" • . • 3  • • • • • 0 a •  • -I • 1 r i • 2a, -..••••••«.«•««•• - • • • le*la, • • > " i 0 0 ) Wo. . . • oe -... • ) -) 60 ' I0O 140 60 100 140 0 0 20 10 0 10 0 10 0 20 0 PHOTON ENERGY (eV) Figure 6.36: Photoelectron branching ratios for CF3C1. Sohd circles-this work; open circles-ref. [151]; open squares-ref. [153]. Chapter 6. 150 20 ^ 10 o cn CD 0 10 X o 0 -z. < o cn \-o UJ 0 40 LLI 30 O O 20 CL 10 CF2CI2 4b2+4b, -1 r i r-202+ 6ai T r 1 1 1 R 3b2 -i 1 1 1 1 r 5a,+ la2*3b| t o 60 -i 1— 100 —i r 140 2b+4a, -r 1 r— 1 1 r 2b2 ° o • t ; 20 10 0 10 -I 1 1 r-3a i % •. • ••••• • • • 2a,+ lb2 10 10 0 10 -l r lb,+ la, 60 loo" "wo r 0 20 - 10 0 PHOTON ENERGY (eV) Figure 6.37: Photoelectron branching ratios for CF2C12. Solid circles-this work; open circles-ref. [151]. Chapter 6. 151 2 401 Q=30| CD X 20 O CFCh • • • la2+5e+4e*5a cr co 10 Z 0 ° 30 cn 1 h-o LLJ 201 UJ g 101 o X *- 0 -i r 60 3e • • • • • • • • • • • 2e*4a, i 1 1 1—• 3a, i i T r le*2ai la, 30 20 10 0 10 0 10 0 10 100 140 60 100 PHOTON ENERGY (eV) 140 Figure 6.38: Photoelectron branching ratios for CFC13. Chapter 6. 152 product of their branching ratios and previously published photoabsorption cross-sections for CF3CI [101] and CF2C12 [110]. We have therefore recalculated photoelectron branch ing ratios from their published tables of cross-sections [151] in order to facilitate valid comparisons with the present work. The so obtained photoelectron branching ratios of Novak et al. [151] are plotted in figs. 6.36 and 6.37. Note that unlike in the present work and that of ref. [153], Novak et al. [151] did not obtain separate branching ratios for the 5ai, la2 and 4e orbitals of CF3C1 and instead presented combined values for these bands. Thus in these cases their data [151] is not represented in fig. 6.36. Fig. 6.36 shows that in general there is good agreement between the presently reported photoelectron branching ratios and the two previously pubhshed data sets [151,153] for CF3CI from 41 to 70 eV. The agreement seen in fig. 6.37 between the present data for CF2C12 and that of ref. [151] from 41 to 70 eV is equally good. Some significant and systematic differences between the presently reported results and those of Bozek et al. [153] do exist however, for the 5al5 la2, 4e and 3e orbitals of CF3C1. While the combined branching ratio sum (5ai+la2-)-4e-r-3e) of ref. [153] is very similar to that of the present work (not plotted in fig. 6.36), their branching ratios for the 5ax and 4e orbitals are smaller than those presented here, while those for the la2 and 3e are larger. These differences are due largely, if not entirely, to aspects of the respective curve fitting procedures used. It appears that Bozek et al. [153] fitted the overlapping band system comprised of ionization from the 5a1; la2, 4e and 3e orbitals with peaks of equal width, which is not necessarily vahd. Therefore in the present work we have allowed the fitting program to determine individual widths for each peak in the spectrum. The major difference in the two procedures is that the laj1 band is determined to be substantially narrower and the 4e_1 band wider in the present work than in ref. [153]. The He II spectrum of CF3C1 reported by Cvitas et al. [100] clearly shows a narrower Chapter 6. 153 profile of the la2 band and a wider 4e_1 band, supporting the presently employed curve fitting strategy. We therefore believe the presently reported branching ratios for the 5ai, la2, 4e and 3e orbitals of CF3C1 to be more accurate than those of Bozek et al. [153]. The photoelectron branching ratio sum (5a1+la2+4e+3e) reported by Novak et al. [151] agrees very well with the equivalent summation performed on the presently reported data and that of ref. [153] (not shown in fig. 6.36). Using total photoabsorption differential oscillator strengths for CF3C1, CF2CI2 and CFCI3 presented in sections 5.2.2-5.2.4 along with the presently reported photoelectron branching ratios, we have derived partial photoionization differential oscillator strengths for each of the electronic ion states of the three molecules. These are given numerically in tables 6.30-6.32 and are shown graphicaUy in figs. 6.39-6.41. Bozek et al. [153] and No vak et al. [151] used previously published photoabsorption cross-sections for CF3C1 [101] and CF2CI2 [HO] in order to derive partial photoionization differential oscillator strengths from their electronic state branching ratios. Since their branching ratio data is very sim ilar to the presently reported values except where noted above, any differences in the shapes of the electronic state partial photoionization differential oscillator strengths be tween the values reported in refs. [151,153] and the present values shown in figs. 6.39 and 6.40 from 41 to 70 eV are caused solely by differences in the total photoabsorp tion differential oscillator strengths presented in sections 5.2.2, 5.2.3 and reported in refs. [101,110]. These differences are discussed in sections 5.2.2 and 5.2.3. However, Cauletti et al. [160] used a method of internal cahbration in order to directly measure partial photoionization cross-sections (differential oscillator strengths) at 40.81 eV for the outermost 5e orbitals of CF3C1 and the (4&2+4&i), (2a2+6ai) and 3b2 orbitals of CF2CI2. We therefore compare the present data with that of ref. [160] in figs. 6.39 and 6.40. The partial photoionization differential osciUator strength for the 5e orbitals of CF3C1 at Chapter 6. 154 Table 6.30: Electronic state partial photoionization differential oscillator strengths for CF3C1 Photon Differential oscillator Strength (lO^eV-1) "  Energy (eV) 5e 5ax la2 4e 3e 4a: 2e 3 a! 2ax (le+l< 41 1.24 2.95 3.99 8.83 5.97 1.12 3.73 0.44 45 0.95 2.53 2.85 6.42 4.96 1.08 3.71 1.10 0.07 50 0.78 2.04 1.95 5.41 3.88 1.12 3.44 1.45 0.08 55 0.76 1.83 1.60 4.35 3.27 1.05 3.10 1.72 0.35 60 0.89 1.86 1.14 4.16 2.96 1.07 2.79 1.39 0.17 65 0.87 1.34 { 7.72 } 1.22 2.32 1.07 0.20 70 0.86 1.17 1.10 3.22 2.90 0.80 2.23 0.86 0.19 75 0.89 0.99 0.91 . 2.79 2.53 0.65 2.00 0.68 0.10 0.46 80 0.72 0.88 0.71 2.44 2.11 0.61 1.78 0.63 0.09 1.17 85 0.72 0.81 0.48 2.69 1.65 0.58 1.55 0.52 0.04 1.29 90 0.67 0.47 0.85 1.54 1.99 0.46 1.30 0.41 0.03 1.32 95 0.62 0.56 0.69 1.54 1.56 0.42 1.13 0.38 0.04 1.38 100 0.64 0.50 0.78 1.49 1.60 0.40 1.13 0.36 0.05 1.09 105 0.57 0.48 0.54 1.52 1.15 0.29 0.92 0.34 0.03 1.37 110 0.60 0.59 0.46 1.39 1.00 0.37 0.83 0.34 0.04 1.01 115 0.53 0.46 0.55 1.19 1.04 0.27 0.77 0.31 0.06 1.00 120 0.50 0.47 0.50 1.19 0.97 0.25 0.75 0.27 0.05 0.72 130 0.48 0.43 0.44 1.06 0.86 0.24 0.61 0.25 0.02 0.70 140 0.41 0.34 0.37 0.78 0.65 0.19 0.50 0.19 0.04 0.86 150 0.41 0.31 0.31 0.64 0.59 0.20 0.45 0.22 0.04 0.69 160 0.36 0.28 0.29 0.59 0.62 0.16 0.47 0.22 0.05 0.54 V(Mb) = 1.0975 x 102(d//a\E)(eV-1). Chapter 6. 155 Table 6.31: Electronic state partial photoionization differential oscillator strengths for CF2CI2 ^ Photon Differential oscillator strength (10~2eV *) ° Energy (eV) (4b2+46i) (2ai+6ai) Zb2 (5ai+la2+3&i) (2b1+4a1) 2b2 3ai (2ai+lb2) (l&i+lai) 41 0.84 1.15 2.02 9.99 2.96 2.76 1.70 45 0.63 1.24 1.74 8.48 2.76 2.72 1.64 50 0.71 1.26 1.43 7.33 2.37 2.16 1.49 55 0.81 1.22 1.36 6.27 2.30 1.67 1.27 60 1.03 0.99 1.23 5.36 2.05 1.60 1.29 0.28 65 0.95 1.04 1.09 5.11 2.07 1.30 1.05 0.35 70 0.79 0.77 0.74 3.69 1.54 0.92 1.11 0.18 2.02 75 0.89 0.74 0.63 3.63 1.59 0.86 0.66 0.16 1.36 80 0.86 0.65 0.65 3.46 1.46 0.91 0.63 0.20 1.11 85 0.77 0.61 0.55 2.92 1.29 0.71 0.56 0.20 1.31 90 0.83 0.68 0.44 2.70 1.26 0.54 0.56 0.32 1.00 95 0.82 0.71 0.48 2.43 1.15 0.55 0.46 0.27 0.83 100 0.77 0.66 0.48 2.25 0.93 0.60 0.40 0.10 0.73 105 0.77 0.62 0.49 2.12 0.86 0.53 0.38 0.16 0.64 110 0.76 0.66 0.43 1.98 0.81 0.46 0.34 0.13 0.64 120 0.66 0.60 0.40 1.65 0.60 0.41 0.28 0.14 0.67 130 0.55 0.48 0.39 1.41 0.52 0.40 0.25 0.21 0.48 140 0.52 0.45 0.34 1.19 0.47 0.29 0.22 0.12 0.47 150 0.44 0.46 0.28 0.99 0.43 0.23 0.22 0.10 0.43 160 0.43 0.29 0.29 0.86 0.40 0.21 0.21 0.09 0.47 V(Mb) = 1.0975 x 102(eV-1). Chapter 6. 156 Table 6.32: Electronic state partial photoionization differential oscillator strengths for CFC13 Photon Differential oscillator strength (10 2eV x) a Energy (eV) (la2 + 5e + 4e + 5ax) 3e (2e + 4ai) 3<Xi (le + 2ax) lai 41 2.93 4.14 4.81 1.51 0.83 45 2.69 3.61 4.55 1.31 0.77 50 2.68 3.26 3.70 1.25 0.87 55 3.03 2.93 3.20 1.07 0.49 60 2.88 2.59 3.05 1.03 0.61 65 2.94 2.50 2.86 0.83 0.36 70 2.62 2.22 2.75 0.59 0.60 0.48 75 2.45 1.85 2.40 0.77 0.61 0.39 80 2.51 1.66 2.15 0.58 0.34 0.50 90 2.28 1.26 1.76 0.53 0.54 0.63 100 2.18 1.10 1.40 0.46 0.41 0.49 110 2.01 0.92 1.16 0.38 0.33 0.34 115 2.06 0.89 1.12 0.35 0.29 0.27 120 1.89 0.85 0.99 0.31 0.31 0.31 130 1.68 0.71 0.83 0.28 0.26 0.31 140 1.49 0.61 0.73 0.26 0.26 0.19 150 1.30 0.53 0.68 0.21 0.15 0.25 V(Mb) = 1.0975 x 102(d//d£0(eV_1). Chapter 6. 157 CF3CI 0-2H 0-2-0-• • • 5e 5a, • • • —1— • •••••• » « m m 1 1 1 T~ la? -r 4e • . • 0-5-••••••• • • • • 0-I-0-2-0-I-0-0.3-0-I-0-3e • • • • • • • • • • • • • • • • • 4a, • • • 2e • • • • • • • • 3a, 1 r 1 t 1 2a, J—j-le * la, -2 cr < 60 80 100 120 140 160 PHOTON ENERGY (eV) 0 ;Mb) 2 0 "7 0 f— 2 0 0 UJ m 1 1 in 5 OS cn O 0 5 0 r— 0 < M 1 Z n O u O 2 r— O 0 PH 1 0 < 0.3 r— 0 < 1 0_ 0 Figure 6.39: Electronic state partial photoionization differential oscillator strengths (cross-sections) of CF3CI. Solid circles-this work; open square on the 5e data set-ref. [160]. Chapter 6. 158 i > <D N I o o z y-00 oc o o CO o < z UJ cc < g o I— o X CL Cr: < x 0 i • • • 0-I 0 6-0 2 0 2 0-I 0' I • 0 CF2CI2 • - • • • • • • • 4b2+4b, 2a2+6a, -i I-1 0 3b2 • • • • • r 5ai + la2+3b| -6 •••• . . i 1 2bi+4ai rr 2b; 3a, • • • • • • • • • • • •••••••• -• r 2arlb2 f f t lb|*lai • • • • 2 0 JD I 0 0 2 0 h2 60 80 100 120 140 160 PHOTON ENERGY (eV) 0 •I 0 I 0 •I •0 2 o I— o UJ to I CO CO o o < M Z o o r— o X Q_ < Figure 6.40: Electronic state partial photoionization differential oscillator strengths (cross-sections) of CF2CI2. Solid circles-this work; open squares at 41 eV on the 462+46!, 2ai+6ai and 362 data sets—ref. [160]. Chapter 6. 159 i > CM I r— o z Ul CY. t— 00 cr: O 2-2-oo 0 o UJ p CK Q 0 < M Z o o I o CL 0 0.5 < CL 0.5H 0 CFCI la2+5e+4e+5a. —i— 3e T 1 2e +4a 3at > • • -i 1 . • • • le + 2a, • • • T • • * T r la • • • • 60 80 100 120 140 PHOTON ENERGY (eV) -2 •0 -2 -0 -4 •2 -0 -0 •0.5 0 -0.5 -0 Figure 6.41: Electronic state partial photoionization differential oscillator strengths (cross-sections) of CFC13. Chapter 6. 160 40.81 eV reported by Cauletti et al. [160] is much lower (~ 50%) than that measured in the present work (see fig. 6.39), but the results for CF2C12 (see fig. 6.40) are in good agreement. The fact that Cauletti et al. [160] used an internal standard and in addition did not make their measurements at the magic angle, but attempted to correct for this using approximate theoretical values of the photoelectron asymmetry parameter 0, may account for the large discrepancy for the 5e orbitals of CF3CI. MS-Xa calculations of the outer valence photoelectron branching ratios and par tial photoionization differential oscillator strengths of CF3CI were reported by Bozek et al. [153]. These proved to be in generally good agreement with their experimental values. The presently reported branching ratios and partial photoionization differential oscillator strengths, especially those for the 5a!, la2 and 4e orbitals, further improve the agreement between theory and experiment from 41 to 160 eV. The theoretical results [153] predict weak resonances at high photon energies (>100 eV) in the partial photoionization cross-sections of all the valence orbitals of CF3C1 caused by scattering of the photoelectrons. These resonances should also be visible in the photoelectron branching ratios. While the presently reported branching ratios and differential oscillator strengths for CF3C1 shown in figs. 6.36 and 6.39 suggest the possibility of such weak resonances for various orbitals (e.g. the 3ai and 2e), the data do not unequivocally corroborate their existence. The general features of the photoelectron branching ratios and electronic state par tial photoionization differential oscillator strengths for CF3C1, CF2C12 and CFCI3 shown in figs. 6.36-6.41 may be understood qualitatively in terms of the atomic orbital char acters of the molecular orbitals from which the photoelectron bands are derived. Of course, this discussion implicitly invokes the independent particle and the frozen orbital approximations, and ignores molecular effects such as shape resonances. Such a model was formulated by Gelius [161] in a quantitative way and should increase in validity as Chapter 6. 161 the photoelectron energy increases. It can be used quantitatively in X-ray photoelectron spectroscopy but is only qualitatively useful at the photoelectron energies involved in the present work. Therefore, we may understand shapes of the molecular orbital branching ratios and partial photoionization differential oscillator strengths shown in figs. 6.36-6.41 by reference to the C 2p, C 2s, F 2p, F 2s, Cl 3p and Cl 3s atomic orbital differential oscillator strength curves [68]. For example, the "lone pair" molecular orbitals that have predominantly Cl 3p atomic character (the 5e in CF3C1, the 462, 461; Qa,\ and 3b2 in CF2CI2 and the la2, 5e, 4e and ba\ in CFCI3) increase in branching ratio from 50 to 160 eV. This is because there is a Cooper minimum [25,127] in the Cl 3p atomic or bital photoionization cross-sections at 35-40 eV [68], so that above this energy they first increase in intensity then decrease very slowly with increasing photon energy. Similarly the branching ratio and partial differential oscillator strength characteristics of the molec ular orbitals of essentially fluorine lone pair character (the la2, 4e and 3e in CF3C1 and the 3bl and la2 in CF2C12), are very much hke those of F 2p atomic orbitals [68]. The molecular orbitals having C-F and C-Cl bonding character exhibit differential oscillator strength and branching ratio curves which are generally consistent with mixed C/F and C/Cl character. The inner valence molecular orbitals of CF3C1, CF2C12 and CFCI3 (the 3ax orbitals and all lower lying levels) may be expected to show partial photoionization differential oscillator strengths more consistent with atomic-hke behaviour than the outer valence orbitals since they exist closer to the atomic centres and thus will be less influenced by molecular bonding and symmetry effects. Electron correlation will, however, be more important for ionization of the inner valence orbitals [158], leading to several many-body ion states for ionization of a given molecular orbital. The 3ax orbitals of all three molecules have predominantly C 23 character and exhibit very similar photoionization Chapter 6. 162 differential oscillator strengths from 65 to 160 eV. These differential oscillator strengths are also in semi-quantitative agreement with Hartree-Slater theoretical calculations of the C 2s atomic orbital differential osciUator strengths [68] (within 20%). In addition, however, the 3a! differential oscillator strengths of CF3C1 show different behaviour from those of CF2CI2 and CFCI3 below 60 eV. For the latter two molecules the 3ax differential osciUator strengths continue to rise to lower energy, whereas those for CF3C1 show a maximum at 55 eV photon energy. These types of differences can arise near threshold due to the influence of the molecular field on low energy (slow moving) photoelectrons; in fact this maximum is predicted by the MS-Xo- calculations for CF3C1 [153]. The inner valence orbitals of Cl 3s character (the 2ax for CF3C1, the 2ax and lb2 for CF2C12 and the le and 2ai for CFC13) have very low photoionization differential oscillator strengths from 41 to 160 eV, with magnitudes approximately in proportion to the number of Cl atoms in the molecule. Comparison with the Hartree-Slater calculations [68] for Cl 3s atomic orbitals reveals that the presently reported differential osciUator strengths for these molecular orbitals (per chlorine atom) are substantiaUy lower ( 40-75%) than those expected on the basis of the Gehus model [161]. The inner valence orbitals of predominantly F 2s character (the le and lax for CF3C1, the lbi and lax for CF2C12 and the lai for CFCI3) show similar behaviour, i.e. the differential oscillator strengths are approximately proportional to the number of F atoms in the molecules, but are significantly (10-40%) less than predicted using the Gelius model [161] and the atomic F 2s differential oscillator strengths given in ref. [68]. One possible reason for this is that electron correlation effects cause the inner valence Cl 3s and F 2s orbitals to lead to a large number of many-body final ion states [158], many of which may not be readily visible in the photoelectron spectra above what is assumed to be the (non-spectral) background. Such intensity wiU not be included in the data analysis procedure, and this will result Chapter 6. 163 in branching ratios and partial photoionization differential oscillator strengths for these orbitals which are too low. The present work clearly demonstrates that the partial photoionization differential oscillator strengths (cross-sections) of inner valence orbitals of C 2s and especially F 2s character are quite substantial in the freon molecules and certainly cannot be ignored when attempting to use photoelectron branching ratios and total photoabsorption dif ferential oscillator strengths to calculate partial photoionization differential oscillator strengths for valence level electronic ion states. In the absence of direct experimental measurements of the branching ratios or differential oscillator strengths of the inner va lence orbitals, it may be possible to use estimates based on atomic data. Although the inner valence partial photoionization differential oscillator strengths determined in the present work are substantially lower than would have been estimated from atomic data, it is uncertain whether this is a real effect or a consequence of the many-body nature of the inner valence electronic ion states, leading to underestimates of their true intensities. Photoelectron spectra with much higher signal/noise ratio and possibly higher resolution and/or photoelectron/photoion coincidence measurements will be required to answer this question with greater certainty. Chapter 7 Absolute Dipole Differential Oscillator Strengths for Inner Shell Spectra from High Resolution Electron Energy Loss Studies of the Freon Molecules CF4, CF3CI, CF2C12, CFCI3 and CC14 The CF3CI, CF2C12 and CFCI3 inner shell EELS spectra used to derive absolute differen tial oscillator strengths were measured using the high resolution dipole(e,e) spectrometer described in section 3.2. The CF4 inner shell EELS spectra are from refs. [130,162] and those for CCI4 are from ref. [163]. 7.1 Absolute Differential Oscillator Strengths Absolute photoabsorption differential osciUator strength (cross section) spectra have been obtained from the presently measured inner shell electron energy loss spectra. The proce dures used in the present chapter for obtaining absolute inner sheU differential oscillator strength spectra were as foUows (Similar types of investigation have previously been re ported by Mclaren et al. [44] and also in section 5.3 above). Firstly, the underlying continuum due to valence and less tightly bound inner shells plus any non-spectral back ground was fitted to a function of the form a(E — b)c + d in the energy region just before the inner sheU edge of interest (E is the energy loss and a, 6, c and d are constants). This fitted function was then extrapolated to higher energy and subtracted from the partic ular inner shell electron energy loss spectrum. The resulting spectrum which should be due to the particular inner sheU excitation alone was then converted to an approximate 164 Chapter 7. 165 relative optical spectrum using a kinematic Bethe-Born factor estimated to be propor tional to E2'5 (see section 2.2 and equations 2.37 and 2.38). The absolute scale was then obtained by normalizing the relative optical spectrum at a sufficiently high photoelectron energy (typically ~25-35 eV above the IP) to the sum of the corresponding atomic sub-shell optical differential oscillator strengths for the appropriate constituent atoms at that photoelectron energy. The principles underlying this normalization method have been discussed in sections 2.3.4.3 and 2.3.8. For this procedure semi-empirical total atomic cross sections [57] were used to obtain relevant subshell atomic cross sections (differen tial oscillator strengths) by subtracting estimated contributions from shells with lower excitation energies from the total. The accuracy of the background subtraction procedures used to obtained the sub-shell molecular differential oscillator strength spectrum was considerably improved by further constraining the fitting of the background region such that the resulting differen tial oscillator strength spectrum in the higher (photoelectron) energy continuum region matched the shape of the appropriate summed (i.e. C Is, F Is, Cl 2p and Cl (2p+2s)) atomic oscillator strength distributions (see, for example, figure 7 below which illustrates the results of such constrained procedures for Cl 2p,2s spectra). As discussed in sec tion 2.3.4.3, molecular effects, such as EXAFS, are of low amplitude relative to the direct ionization continuum and will thus have httle adverse effect on these procedures as long as the energy range used for matching molecular and atomic spectra is sufficiently large. As discussed in section 2.3.4.3 at sufficiently high photoelectron energy, the molecu lar photoionization differential oscillator strength contributed by each atom in a molecule can be considered, to a first approximation, to be equal to the corresponding atomic pho toionization differential oscillator strength. Therefore the integrated oscillator strengths for the molecule and for the constituent atom above a sufficiently high photoelectron Chapter 7. 166 Table 7.33: Estimations of integrated atomic oscillator strengths (OS) for inner shell excitations in C, F, and Cl atoms  E0 - IPa OS above E0b OS transferred0 OS below E0d C Is 38.7 1.393 0.0913 0.5157 F Is 48.0 1.5 0.275 0.225 Cl 2p 60.2e 4.8 -0.9026 2.1026 aE0 is the photon energy below which the integrated oscillator strength for the given inner shell excitation is to be estimated. Eo — IP is thus the photoelectron energy. 6The integrated oscillator strength from Eo to 1.5 x 106 eV (effectively infinity) as estimated from calculation [69]. See text for details. coscillator strength transferred to other shells due to the Pauli excluded transitions from the present sub-shell to the already occupied orbitals [112]. dUsing the partial TRK sum-rule: the sub-shell oscillator strength below Eo = ( number of electrons in the inner shell) — (OS above EQ) — (OS transferred). ewith reference to the Cl 2pi/2 IP-Table 7.34: Integrated sub-shell oscillator strengths per atom for CF4, CF3C1, CF2C12, CFC13 and CCI4 below E0  Excited shell E0 - IPa Atom6 CF4 CF3CI CF2C12 CFCI3 CC14 C Is 38.7 0.52 0.57 0.57 0.57 0.54 0.53 F Is 48.0 0.23 0.23 0.23 0.23 0.22 Cl 2p 60.2C 2.10 1.99 1.92 1.90 1.84 aEo — IP is the photoelectron energy below which oscillator strength for a given sub-shell is to be integrated. 6frpm table 7.33. cwith reference to the Cl 2p>y2 IP. Chapter 7. 167 energy should be approximately equal. Therefore, assuming that the oscillator strength transfer due to Pauh excluded transitions [38] to already occupied orbitals is similar for both the molecule and summed atomic situation, the integrated molecular oscillator strength per atom is expected (on the basis of the partial TRK sum-rule considerations, see sections 2.3.4.3 and 2.3.8) to be comparable to the corresponding atomic oscillator strength integral up to the same photoelectron energy. The integrated sub-shell oscilla tor strengths for C (Is), F (Is) and Cl (2p) atoms have been estimated using the partial TRK sum-rule considerations and are shown in table 7.33. The integrated oscillator strength above the photon energy E0 was obtained by integrating the calculated pho toionization differential oscillator strength [68,69] from E0 to infinity (actually to the limit of the relativistic Hartree-Slater calculation at 1.5 x 106 eV [69]. The contribution to the oscillator strength above 1.5 x 106 eV is estimated to be less than 2 x 10-6). The oscillator strength transfer due to Pauli excluded transitions is taken from Hartree-Slater calculations [112]. The adequacy of the presently employed background subtraction and normalization procedures is evident from table 7.34 from which it can be seen that the presently obtained integrated molecular oscillator strength per atom is very close to the corresponding integrated atomic oscillator strength. 7.2 Electronic Configurations and Spectral Assignments The CF3C1 and CFC13 molecules are of C3„ symmetry, CF2C12 has C2u symmetry and CF4 and CCI4 have Tj symmetry. The ground state electron configurations may be written as in table 7.35. The valence shell electronic configurations of CF3C1, CF2C12, CFCI3 and CF4 are as reported in the earher PES studies in references [99,100,117,157] and in this thesis work (chapter 6). The inner shell electronic configuration for CF4 is as reported in XPS measurements [86]. Gaussian 76 calculations were carried out for CF4, Chapter 7. 168 Table 7.35: Electronic configurations for the CF4, CF3C1, CF2C12, CFC13 and CC14 molecules" Molecule Cl Is F Is C Is Cl 2s Cl 2p CF4 6 lt62lal 2al CF3C1 ul 2al\e4 3al 4a? ba22eA CF2C12 lbjlal 2allbl 3a\ 2bj4al ba23bl4bl2bllal<6al CFCI3 lalle4 2a\ 3al 2eHal 5al3e4la224e46al5e4 CC14 lt62lal 2al 2t623al 3t624allt\le44tl Molecule Valence orbitals0 Virtual valence orbitals (unoccupied) CF4 CF3CI CF2C12 CFCI3 CC14 3al2t*4al3tlle44tlltl 6al3e47al8al4e49al5e46e4la210al7e4 7al3bl8al5b29al6b210al4b2llal2a25b2 7b212al3a26b28b2 7a28al6e49all0al7e48e4llal9e410e42a 5al546a26tpe4742tl 5a°5t2 (C-F)* 11a? 8e°12a? (C-Cl)* (C-F)* 13a?96° 76?14a? v v 'N v ' (C-Cl)* (C-F)* 12a?lle° 13a? (C-Cl)* (C-F)* 7a°8i2 (c-ci)*  "See section 7.2 for details. fcfrom ref. [86]. cfrom chapter 6 and refs. [99,100,117,157]. Chapter 7. 169 Table 7.36: Dipole-allowed transitions between orbitals for C3v, C2v and Tj symmetries Initial state Final state C3v (CF3C1 and CFCI3) 0l —> ai,e a2 —> e e —• ai,e C2v (CF2C12) ai —> ax,6i,62 a2 —> 61,62 61 —> ai,6i fe2 —> aub2 Td (CF4 and CC14) ax —• t2 t2 —• <2,ii,e,ai e —> i2,ii <x —• t2,ti,e,a2 Chapter 7. 170 CF3CI, CF2CI2, CFCI3 and CCI4 to further aid in the analysis of the energy orderings of the orbitals and to establish the dominant orbital characters (i.e. (C-F)* or (C-Cl)*) of the unoccupied (virtual) valence antibonding orbitals as indicated in table 7.35. The dipole-aUowed transitions for Td (CF4 and CC14), C3t) (CF3C1 and CFC13) and C2« (CF2CI2) symmetries are shown in table 7.36. The reported Cl 2p, C Is and F Is inner shell electron ionization energies [164,165] for CF4, CF3C1, CF2C12, CFC13 and CC14 are shown in tables 7.37-7.40 (see below). The transitions in the various inner shell spectra have been tentatively assigned using the information in table 7.35 and 7.36. Term values for transitions given Rydberg final orbitals are expected to be transferable between different inner shell spectra of the same molecule. In contrast term values for core to particular virtual valence orbital transitions are not in general transferable. 7.3 C Is Spectra Figs. 7.42 and 7.43 show the presently obtained high resolution (short energy range) and low resolution (long energy range) C Is dipole differential oscillator strength spec tra respectively for CF3C1, CF2C12 and CFC13, together with spectra determined from earlier reported EELS measurements for CF4 [130] and CC14 [163]. We have Bethe-Born converted and normalized the high and low resolution EELS spectra of CC14, reported earlier by Hitchcock and Brion [163], to yield dipole differential oscillator strength spec tra. In section 5.3 we have also presented a C Is long range absolute differential oscillator strength spectrum for CF4, derived from earher obtained small angle EELS data [130], by approximate Bethe-Born conversion followed by single point normalization to the atomic differential oscillator strength. In the case of the C Is of CF4 the background was ear lier estimated (section 5.3) using very approximate procedures. However the integrated osciUator strength and peak intensity of the CF4 data are apparently too high and we Chapter 7. 171 have therefore re-derived the CF4 C Is differential oscillator strength spectrum with the presently used more stringent and consistent procedures for accessing the background. The CF4 C Is short range EELS spectra reported in reference [162] have been also placed on an absolute differential oscillator strength scale in the present work. These newly nor malized C Is spectra for CF4 and CC14 are also presented in figs. 7.42 and 7.43. The higher resolution C Is spectrum of CF4 [162] is shown on an expanded energy scale as an insert at the top right of fig. 7.42. The C atomic differential oscillator strength spectrum [57] was used to obtain the absolute scale for the C Is molecular spectra by matching the overall shapes at high photoelectron energy over a wide energy range as discussed in section 7.1 above. The energy positions, term values and possible assign ments of the observed features in the recently reported C Is spectra of CF3C1, CF2C12 and CFCI3 and are hsted in tables 7.37-7.39 and those for CF4 and CC14 are summarized in table 7.40. Also shown in the tables are the integrated oscillator strengths for selected transitions for CF3C1, CF2C12, CFCI3 and CC14 obtained by fitting Gaussian peaks (not shown in the figures) to the spectral features. The integrated oscillator strength up to the C Is IP for CF4 is shown in table 7.40. Strong chemical shift effects with increasing fluorination can be seen in fig. 7.42. It can also be seen that the "center of mass" of the pre-ionization edge osciUator strength distribution moves towards the respective IP as the number (degeneracy) of (C-F)* an-tibonding orbitals increases and that of (C-Cl)* decreases, in going from CC14 to CF4. From the transition energies and IPs it is apparent that the term values for the more prominent peaks are in two energy ranges. Furthermore the changes in intensity distri bution with successive fluorination suggest that the larger and smaUer term value groups are associated with the (C-Cl)* and (C-F)* normally unoccupied orbitals respectively. With these considerations in mind the prominent pre-ionization edge spectral features Chapter 7. 172 I > C\| I o cn c CD L_ CO o _o 'o C/J o D 4 c CD o CD Q 0 c s —i 1 1 1 r-299 * 300 301 /^L\ III II A5-67 8 9 CF4 AE=70meV CF3CI AE=67meV \ A2 / V s - A II II III II I B 3 5 8 10 C1s edge 1 I I II I 2 3 4 5 7 Cis edge 4 -0 -8 -CF2CI2 AE=65meV N II II I Ml I K • 1 2 3 4 56 7 9 C1s edge # » : \ CFCI3 AE=67meV III II i i £ /\ 2 3 4 5 . 6 7 Cis edge \ ecu V AE=250meV 1 2 C1s edge  ~l I [ I I I I j I I I I [ I I T" 290 295 300 Photon Energy (eV) 4 0 4 0 4 0 Figure 7.42: Differential osciUator strength spectra for C Is excitation of CF4, CF3C1, CF2C12, CFC13 and CCI4 in the discrete region. The CF4 and CCI4 spectra were derived from EELS measurements in refs. [162,163] respectively. See section 7.3 and tables 7.37-7.40 for details. Chapter 7. 173 12 10 8 T> ^ CD 4 CM I O 2 ^-^ 0 _C CD -i 1 1 1 1 1 r r——i 1 1 r 00 o 4-= 2 cn o O O 4 CD 0 -2-0 C1 s CF4 AE=500meV 9 CF3CI 1 AE=300meV 11 CF2CI2  1 AE=300meV CFCI AE=290meV 10 i 3 ecu i AE=350meV -1 1 1 r 0 10 20 -1 1 1 r 30 40 Photoelectron Energy (eV) Figure 7.43: Differential oscillator strength spectra for C Is excitation of CF4, CF3C1, CF2C12, CFC13 and CCI4 in the discrete and continuum regions. The CF4 and CC14 spectra were derived from EELS measurements in refs. [130,163] respectively. See section 7.3 and tables 7.37-7.40 for details. Chapter 7. 174 Table 7.37: Experimental data for C Is, F Is and Cl 2s, 2p excitations of CF3C1 Feature" Photon Oscillator Term value Possible energy (eV) strength6 (xlO"2) (eV) assignment (final orbital) C Is 1 294.16 4.8 6.15 llOi 2 296.66 16.4 3.65 8e 3 297.3 3.0 12ai 4 298.07 2.24 4p 5 298.82 1.49 5s 6 298.93 1.37 bp 7 299.46 0.85 6s IP 8 .(300.31)c 303.12 0 -2.81 shape resonance 9 ~318.0 —17.7 XANES F Is 1 690.51 N 4.53 llax 2 692.60 I 15.5 2.44 8e+12ai 3 694.5 0.5 ? IP (695.04)«v 0 4 720 -25 XANES Cl Is D 2823.5 6.7 llai E 2827.4 2.8 12ai+8e F 2827.3 2.4 4p IP 2830.2 0 Cl 2s 9 IP 271.5 (278.84)c 7.3 0 virtual valence Cl 2p3/ 2 Cl 2pi/2 C12p3/2 C12p1/3 Cl 2p 1 201.13 1.6 6.70 llO! 1' 202.71 1.1 6.73 lid! 2 204.31 0.6 3.52 5.13 8e+12oi 3,2' 205.74 2.09 3.7 4p 8e+12ai 4 206.26 1.57 5s 5 206.56 1.27 5p 3' 207.32 2.12 4p 2^3/2 IP 4' (207.83)d 0 208.0 1.44 5s 5' 208.26 1.18 bp 2P1/2 IP (209.44)d 0 6 214.8 -7 -5.4 N 7 8 219.6 228.0 -11.8 -20.2 -10.2 I -18.6 J XANES "For features, see figs. 1 and 2 for C Is, figs. 3 and 4 for F Is, figs. 5 and 6 for Cl 2s and 2p and ref. [166] for Cl Is. ^Integrated oscillator strengths. See sections 7.3-7.5 for details. cfrom XPS measurement [165]. dfrom XPS measurement [164]. Chapter 7. 175 Table 7.38: Experimental data for C Is, F Is and Cl 2s, 2p excitations of CF2CI2 Feature0 Photon Oscillator Term value Possible energy strength'' (eV) assignment (eV) (XlO"2) (final orbital) C Is 1 292.73 3.7 6.22 13oi 2 293.62 6.2 5.31 9i)2 3 295.05 3.88 7&i 4 295.60 3.33 14ai 5 296.48 2.46 4p 6 296.87 2.06 4p' 7 297.46 1.47 5s 8 297.6 1.33 5p 9 298.10 0.83 6s IP (298.93)c 0 10 301.93 -3 shape resonance 11 315.6 -16.7 XANES F Is 1 689.40 -\ 5.26 13ai+962 2 691.90 £ 9.6 2.78 761+14a1 3 693.37 1 1.31 5p IP (694.68)c J 0 4 697.54 -2.86 shape resonance 5 717.92 -23.24 XANES Cl Is D 2823.0 6.6 13ax+9b2 d E 2826.4 3.2 14a1 + 7fcl d F 2827.2 2.4 4p IP (2829.6) 0 Cl 2s 11 IP 271.3 (278.63)c 7.3 0 virtual valence Cl 2p3/2 Cl 2px/2 Cl 2p3/2 Cl 2p1/2 Cl 2p 1 200.73 2.1 6.74 13ai 2 201.39 0.7 6.08 962 1' 202.32 1.2 6.78 13a! 2' 203.01 0.4 6.09 9(>2 3 204.04 1.7 3.43 76i 4 204.40 3.07 14ai 5 205.17 2.3 4p 6 205.38 2.09 V 7,3' 205.80 1.67 3.3 5s 7&i 4' 206.02 3.08 14a! 5' 206.76 2.34 4p 6' 207.02 2.08 4p' 2p3/2 IP (207.47)<= 0 7' 207.78 1.32 5s 2pi/2 IP (209.10)e 0 8 216.3 -8.8 -7.2 ~\ 9 222.8 -15.3 -13.7 S XANES 10 230.6 -23.1 -21.5 J °For features, see figs. 1 and 2 for C Is, figs. 3 and 4 for F Is, figs. 5 and 6 for Cl 2s and 2p and ref. [166] for Cl Is. integrated oscillator strengths. See sections 7.3-7.5 for details. cfrom XPS measurement [165]. d9&2 and 7&i have been mistakenly denoted as 10&2 and 661 in ref. [166]. efrom XPS measurement [164]. Chapter 7. 176 Table 7.39: Experimental data for C Is, F Is and Cl 2s, 2p excitations of CFCI3 Feature" Photon Oscillator Term value Possible energy strength* (eV) assignment (eV) (xl0~2) (final orbital) C Is 1 291.42 3.3 6.12 12ai 2 292.24 9.7 5.30 lle(l) 3 292.83 4.71 lle(2) 4 294.22 3.32 13ai 5 294.87 2.67 Ap 6 296.10 1.44 5s 7 296.71 0.83 6s IP 8 (297.54)c 300.7 0 -3.16 shape resonance 9 305.51 -7.97 10 318.60 -21.1 XANES F Is 1 688.7 \ 5.63 12ax-|-lle 2 690.42 V 3.8 3.91 13ai IP (694.33)c 1 0 2 697.80 -3.47 shape resonance 3 720.0 -25.67 XANES Cl Is D 2822.8 6.5 12ai E 2825.7 3.6 lle+13ai F 2827.1 2.2 4p IP (2829.3) 0 Cl 2s 8 IP 270.9 (278.24)c 7.3 0 virtual valence Cl 2p3/2 Cl 2p1/2 Cl 2p3/2 Cl 2p1/2 Cl 2p 1 200.65 3.6 6.55 12ax 2 201.79 0.5 5.41 lle(l) 1' 202.33 1.4 6.48 12ai 3,2' 203.15 0.9 4.05 5.66 lle(2) lle(l) 4 203.96 2.9 3.24 13ai 3' 205.11 3.70 lle(2) 4' 205.62 3.19 13ai 2P3/2 IP (207.20)d 0 2P1/2 IP (208.81)d 0 5 216.6 9.4 -7.8 -s 6 222.7 15.5 -13.9 V XANES 7 233.7 26.5 -24.9 J "For features, see figs, 1 and 2 for C Is, figs. 3 and 4 for F Is, figs. 5 and 6 for Cl 2s and 2p and ref. [166] for Cl Is. ''Integrated oscillator strengths. See text sections 7.3-7.5 for details. cfrom XPS measurement [165]. dfrom XPS measurement [164]. Chapter 7. 177 Table 7.40: Experimental data for C Is, F Is and Cl 2s, 2p excitations of CF4 and CCI4 Feature" Photon Oscillator Term value Possible energy6 strength0 (eV) assignment (eV) (XlO"2) (final orbital) CF4 C Is 1 297.45 ^ 4.35 \ 2 297.77 4.03 ) 5t2 plus 3 298.54 3.26 ( outer well states 4 298.81 2.99 J 5 299.45 2.35 3p 6 299.66 > 29 2.14 ? 7 299.87 1.93 1 8 300.31 1.49 4s 9 300.60 \ 1.20 4p 10 301.03 ) 0.77 5s IP (301.8)d -/ 0 F Is 1 ~690.5 ~ 5 5ai 2 692.9 1 s 25.4 2.6 5t2(l) 2 ~ 694 1.2 5t2(2) IP (695.52)d> ) 0 CCLi C Is 1 290.9 9.9 5.5 8t2 2 294.5 1.8 5s IP (296.38)d 0 3 ~303 ~7 shape resonance Cl 2s 4 271.8 6.2 virtual valence IP (278.04)d 0 C12p3/2 C12p1/2 C12p3/2 C12pi/2 Cl 2p 2p3/2IP (207.04) e 0 2p1/2IP (208.73)6 0 1 -217.7 -10.7 -9 >| 2 -224.7 -17.7 -16 i XANES 3 -235.2 -28.2 -26.5 J "See figs. 1 and 2 for C Is features, figs. 3 and 4 for F Is features, and figs. 5 and 6 for Cl 2s and 2p features. experimental results for CF4 are from [162] and those for CC14 are from [163] Integrated oscillator strengths. See text sections 7.3-7.5 for details. dfrom XPS measurement efrom XPS measurement 165]. 164]. Chapter 7. 178 have been assigned assuming that the term values for a particular type (i.e. (C-Cl)* and (C-F)*) of antibonding orbital have similar values in the different molecules. The oscil lator strength concentrated within a broad band (feature 1) in the CCI4 spectrum which corresponds to the dipole allowed transition to the 8t2 C-Cl antibonding orbital [163] is redistributed (see fig. 7.42 and tables 7.37-7.40) upon successive fluorination among the transitions to 12ai ((C-Cl)*, feature 1) lie ((C-Cl)*, feature 2 and 3, see discussion be low) and 13ax ((C-F)*, feature 4) for CFC13 (see table 7.39); to 13a! ((C-Cl)*, feature 1), 9b2 ((C-Cl)*, feature 2), 7h ((C-F)*, feature 3) and 14ax ((C-F)*, feature 4) for CF2C12 (see table 7.38); to llax ((C-Cl)*, feature 1), 8e ((C-F)*, feature 2) and 12ax ((C-F)*, feature 3) for CF3CI (see table 7.37); and finally concentrates in a single broad band again in CF4 (see table 7.40), corresponding to the transition to the 5t2 (C-F)* antibond ing orbital [150]. Under the present assignment, the term values for transitions from the C Is orbitals to (C-Cl)* antibonding orbitals are found to be between 5.4-6.2 eV while those to (C-F)* antibonding orbitals are between 3.3-3.9 eV. In the CFC13 spectrum the feature 2 and the shoulder shown as feature 3 are ~0.6 eV apart and they are probably the two Jahn-Teller components of the transition to the lie virtual orbital. A Jahn-Teller splitting of ~0.8 eV has been observed in PES studies [167]. It is interesting to note from fig. 7.43 that a minimum followed by an above IP maximum is observed near the ionization edge in the C Is spectra of CF3C1, CF2C12, CFCI3 and CCI4. In proceeding from CC14 to CF3C1, the minimum shifts towards the IP and finally moves above the IP in CF3CI. In the case of CF4, there is no localized near-edge maximum above IP. A potential barrier due to the presence of the halogen ligands in the freon molecules is expected to affect the absorption spectra as discussed in section 2.3.6. CCI4 and CF4 belong to the same symmetry point group Tj with the same central atom (C) and they each have similar ax and t2 manifolds of unoccupied valence Chapter 7. 179 orbitals (see table 7.35). Theoretical calculations on the LiFg system [168] with varying Li-F distance have shown that the longer the Li-F distance, the stronger the inner well strength, i.e. the lower the energy of state supported by the potential, with respect to the ionization limit (i.e. a larger term value). Consistent observations on spectra for the molecular series SiBr4, SiCl4 and SiF4 [169], BBr3, BC13 and BF3 [170], and PBr3, PC13 and PF3 [171] have also shown that the corresponding virtual valence feature and/or shape resonance feature shifts to higher energy with respect to the IP of the central atom as the hgand changes from Br to Cl to F. In the present situation, the fact that the term value of the prominent C Is —> t2 transition in CC14 (5.4 eV) [163] is larger than that in CF4 (~3.4 eV) [130,162] illustrates that the inner well potential of CC14 is stronger and this is consistent with the C-Cl bond length (1.77 A) for CC14 being greater than the C-F bond length (1.32 A) for CF4 [172]. Moreover, the presence and the absence of the above IP near edge spectral maximum in the CC14 and CF4 spectra respectively is consistent with the CF4 inner well strength being so small that an above IP shape resonance is not seen. We assign the maxima features above the IP to transitions to shape resonance states (see fig. 7.43 and tables 7.37-7.40). These shape resonances may be associated with virtual orbitals involving Cl 3d components. Such an interpretation is consistent with the absence of such resonances in the case of CF4. The weak structures superimposed on the broad band at ~298 eV in CF4 are probably due to transitions to outer well states which are not Rydberg in character. The remainder of the pre-ionization edge features in all molecules are interpreted as transitions to Rydberg states. The Rydberg transition features are usually sharp in shape as discussed in section 2.3.2. The narrow shapes and similar term values of features 8 for CF4, 5 for CF3C1, 7 for CF2C12, 6 for CFC13 and 2 for CC14 (fig. 7.42) suggest that they are associated with Rydberg orbitals of the same type (s). Other Rydberg transitions are Chapter 7. 180 similarly identified. The fact that feature 9 is well resolved from feature 8 for CF4 suggests that the corresponding Rydberg transitions (p) are associated with the shoulders 6 for CF3C1 and 8 for CF2C12. Similarly features 10 for CF4, 7 for CF3C1, 9 for CF2C12 and 7 for CFC13 are all of the same type (s), and also features 5, 6 and 7 for CF4, 4 for CF3C1, 5 and 6 for CF2C12, and 5 for CFCI3 are of the same type (p). It is interesting to note that the very weak 6s Rydberg transition (feature 2) in the CC14 spectrum increases in intensity with successive fluorination so that it is much more intense for CF3C1 than for CCI4. When the series proceeds to CF4, the Rydberg feature merges with the single band. 7.4 F Is Spectra Figs. 7.44 and 7.45 show the presently obtained high resolution (short range) and low resolution (long range) F Is differential oscillator strength spectra for CF3C1, CF2C12 and CFCI3 along with that for CF4 presented in section 5.3. The spectra in fig. 7.45 are presented with photoelectron energy as the x axis. Energies, term values, integrated oscillator strengths up to IPs and possible assignments for transitions in the F Is spectra are presented in tables 7.37-7.40. It has recently been demonstrated from X-ray absorption experiments for CF3CI, CF2C12 and CFC13 that transitions from Cl Is to C-F antibonding orbitals have appre ciable intensities [166] in addition to those to (C-Cl)* antibonding orbitals, even though the Cl Is orbital is localized in a very small spatial region at the Cl atomic sites in the molecule. In keeping with this observation [166] transitions to both C-F and C-Cl an tibonding orbitals are used to interpret the F Is spectra obtained in the present work. The strong band (feature 2) below the F Is IP in the CFC13 spectrum (fig. 7.44) can therefore be attributed to the transition to the 13ai (C-F)* antibonding orbital. Since Chapter 7. 181 I > 5 CD CM 1 4 CP c 2 CD Z O = 0 "u O 1 -i 1 1 1 1 1 i 1 1 i r A s • * * * * I \; F1s edge CF4 :* AE=500meV S i • II 1 /** 2 3 » A, CF3CI \,AE=260meV 3F 1s edge CF2CI2 AE=140meV 3 F 1s edge CFCI3 AE=265meV 1 £ 2 F 1s edge 1—r-690 1 1 1 1 1 r 686 690 694 698 Photon Energy (eV) Figure 7.44: Differential oscillator strength spectra for F Is excitation of CF4, CF3CI, CF2CI2 and CFCI3 in the in discrete region. The CF4 spectrum was obtained from section 5.3. See section 7.4 and tables 7.37-7.40 for details. Chapter 7. 182 6- A > cd CM I o 4-ii i « cn c CD •+-> 00 o 'u CO O o 1 -1 -c CD CD 0-1 • OH i t t tiimTr s CF* AE=500meV CF3CI AE=310meV CF2CI2 AE=300meV ' CFCI3 4 5 AE=300meV T 0 10 20 30 ~40~ 50 Photoelectron Energy (eV) 0.5 0 Figure 7.45: Differential oscillator strength spectra for F Is excitation of CF4, CF3CI, CF2CI2 and CFCI3 in the discrete and continuum regions. The CF4 spectrum was obtained from section 5.3. See section 7.4 and tables 7.37-7.40 for details. Chapter 7. 183 the overall band is asymmetric, the expected weaker transitions to the (C-Cl)* anti-bonding orbitals (12ai,lle) here therefore been assigned to the lower energy shower (feature 1). Similarly transitions to the (13ai+962,(C-Cl)*) and (7&i+14ai,(C-F)*) are assigned to features 1 and 2 in the F Is spectrum of CF2C12. Likewise, the llai ((C-Cl)*) and (8e+12ai) ((C-F)*) final orbitals have been assigned to the two features 1 and 2 in the CF3C1 spectrum. The broad CF4 pre-ionization edge band has been attributed to the transitions to the r2 and ar states [150]. The shoulder 1 in the CF4 spectrum may correspond to the transition to the 5ax orbital. The partially resolved features 2 and 3 may be due to transitions to the 5r2 orbital where the degeneracy is removed by the Jahn-Teller effect. In the long range F Is spectra (fig. 7.45) a minimum followed by a maximum is observed near the edge in the spectra of CFC13, CF2C12 and possibly CF3C1 as in the C Is spectra. The minimum shifts from below the IP for CFC13 to above the IP for CF2C12 and CF3C1. The above IP spectral maxima, hke those in the C Is spectra are probably due to transitions to virtual orbitals involving Cl 3d participation (shape resonances), since the structure is not present in the CF4 spectrum. The fact that these above edge resonances are relatively more intense in the C Is spectra than in the F Is spectra (compare figs. 7.43 and 7.45) is consistent with spatial overlap considerations for the respective initial and final states if the later have Cl 3d character. 7.5 Cl 2s and 2p Spectra The presently obtained high resolution Cl 2p differential oscillator strength spectra for CF3CI, CF2C12 and CFC13 are shown in fig. 7.46. Gaussian peaks were fitted to the pre-ionization edge spectra in the low energy region. Three peaks for CF3C1 and five peaks Chapter 7. 184 for CF2C12 and CFCI3 were fitted as shown in fig. 7.46. Long energy range, low resolution Cl 2p, Cl 2s and C Is spectra of CF3C1, CF2C12, CFC13 and CC14 are shown in fig. 7.47 on a common photoelectron energy scale (respective to Cl 2pi/2). The CCI4 differential oscillator strength spectrum was obtained by converting the previously reported EELS spectrum [163] using the method outhned in section 7.1. It should be noted that the CCI4 EELS spectrum had to be digitized from the figure in ref. [163] and therefore the resulting "noise level" on the spectrum in fig. 7.47 is greater than for the other spectra shown. In fig. 7.48 the molecular spectra are shown as differential osciUator strength per Cl atom in the molecule in order to facihtate comparison. The Cl atomic spectrum (also shown in fig. 7.48) for Cl 2p and Cl 2s excitations [57] was used to normahze the Cl 2p molecular spectra (see section 7.1 for details). Energies, term values, integrated osciUator strengths and possible assignments for various transitions in the Cl 2s, 2p spectra of CF3C1, CF2C12, CFC13 and CC14 are presented in tables 7.37-7.40. Also shown in tables 7.37-7.39 are results from Cl Is X-ray absorption spectra for CF3C1, CF2C12 and CFCI3 recently reported by Perera et al. [166]. Two series of structures related to the Cl 2p3/2 and Cl 2p1/2 ionization potentials respectively are observed in the Cl 2p spectra of CF3C1, CF2C12 and CFC13 (fig. 7.46). The intensities of the series related to the Cl 2p3/2 IP are greater than those for Cl 2p\/2 as expected. The present assignment of the lower energy structures is based on the transitions to the normaUy unoccupied virtual valence molecular orbitals. Only two peaks (1 and 1') are observed at low energy in the CF3C1 spectrum (fig. 7.46) and they assigned to transitions to the llai C-Cl antibonding orbital. The less intense peaks 2 and 2' can then be attributed to transitions to the C-F antibonding orbitals, 8e and 12a!. In the CF2C12 spectrum two pairs of peaks (1 and 1', 2 and 2') have been fitted to the Chapter 7. 185 -i 1 r -i 1 1 1 1 r Cl 2p edges 3 4 5 3/2 i—n 12c, i2a^; AE=60meV 200 -1 1 1 1— 205 1 r 210 Photon Energy (eV) Figure 7.46: Differential oscillator strength spectra for Cl 2p excitation of CF3CI, CF2C12 and CFC13 in the discrete region. See section 7.5 for details. Chapter 7. 186 10 8 I > CD CM I o CP c CD CF3CI AE=300meV 9 Cl 2s i C 1s CF2CI2 AE=300meV C 1s CFCI3 AE=290meV IB I 5 6 7 8 Cl 2s CCk AE=350meV 1 1 1 1 2 3 4 Cl 2s C 1s T 1 1 1 r -1 1 1 r 12 10 8 6 4 2 0 18 16 14 12 10 8 6 4 2 0 0 20 40 60 80 100 Photoelectron Energy (eV) Figure 7.47: Differential oscillator strength spectra for Cl 2p, Cl 2s and C Is excitations of CF3CI, CF2CI2, CFCI3 and CCU in the discrete and continuum regions. The CCI4 spectrum was derived from EELS measurements in refs [163]. See section 7.5 and tables 7.37-7.40 for details. Chapter 7. 187 Figure 7.48: Differential oscillator strength spectra per Cl atom for Cl 2p, Cl 2s and C Is excitations of CF3C1, CF2C12, CFCI3 and CCLj (measured, this work and ref. [163]) and for Cl 2p and Cl 2s excitations of the Cl atom (ref. [57]). See section 7.5 for details. Chapter 7. 188 spectrum at low energy and we interpret these as being due to transitions to the 13a! and 9&2 C-Cl antibonding orbitals. Notice that the fitted peak 2, related to the Cl 2p3/2 hole state, is more intense than peak 2' associated with the Cl 2px/2 hole. Peaks (3 and 3', 4 and 4') are assigned as transitions to the C-F antibonding orbitals 7bi and 14aj. In the CFCI3 spectrum peaks 1 and 1' can be attributed to transitions to the 12ax C-Cl antibonding orbital. Considering the term values and of peaks 4 and 4', it is likely that they are due to transitions to the 13a! C-F antibonding orbital. The two pairs of peaks (2 and 2', 3 and 3') can then assigned to transitions to the two components of the lie antibonding orbital whose degeneracy is removed due to the broken symmetry of CFCI3 when an electron in the Cl inner shell is promoted. Since 2' and 3 share the same fitted Gaussian peak in the spectrum, the fact that peak 2 has lower intensity is not inconsistent with the above observation that the series related to Cl 2p3/2 exhibits larger intensities. In the present assignments 7.37-7.39 the term values for transitions to C-F antibond ing orbitals are in the region 4-7 eV, while those for C-Cl antibonding orbitals are in the region 3-3.5 eV, similar to the observation on the C Is spectra (section 7.3). Rydberg structures are heavily overlapped and are superimposed on the rising ionization edge. Tables 7.37-7.40 list the tentative assignments. The long energy range spectra in figs. 7.47 and 7.48 show delayed onsets (see sec tion 2.3.4.1) which resemble the Cl atomic situation [25]. In the spectra per Cl atom shown in fig. 7.48, all four molecular spectra are very similar in overall shape at pho toelectron energies above ~25 eV. It should be noted that in this higher energy region all molecular spectra exhibit rather similar low amplitude EXAFS modulations on the photoionization continuum (see sections 2.3.4.2 and 2.3.4.3) with respect to the situa tion in the smooth atomic Cl spectrum [57] indicated by the solid hne in fig. 7.48. The Chapter 7. 189 similar modulations in this region are due to the fact that EXAFS is the result of sin gle scattering processes in which the high energy photoelectron is scattered by only one neighboring atom as discussed in section 2.3.4.2. In the present situation the neighboring electron scatterers are C, F and Cl atoms, each of which is at a similar distance (i.e. Cl-C (~1.75 A), Cl-F (~2.53 A) and Cl-Cl (~2.88 A)) from the ionized Cl atom in each of the different molecules [172]. Similar types of EXAFS modulation pattern have been seen in the Cl 2p spectra of CH2C12, CHC13 and CC14 [163]. From fig. 7.47 it can be seen that there are also additional structures in the spectra for CF3C1 (features 6 and 8), CF2C12 (features 8, 9 and 10) and CFC13 (features 5,6 and 7) and CC14 (features 1, 2 and 3) in the near edge region below ~25 eV photoelectron energy. The term values and magnitudes of these XANES structures are different in the various molecules (see fig. 7.48), since XANES is the the effect of multiple scattering of the outgoing photoelectron by the neighboring atoms as discussed in section 2.3.4.2. The Cl 2s spectra are broadened due to the short lifetime of the excited states with respect to autoionizing decay to the underlying Cl 2p continuum. The energies and possible assignments of these features are shown in tables 7.37-7.40. Chapter 8 Conclusions This work has presented dipole (e,e) and dipole (e,e+ion) experimental results including the total and partial (photoion) absolute optical differential osciUator strength spectra of CF4, CF3CI, CF2C12 and CFCI3 in the valence sheU excitation region; the high res olution absolute optical differential oscillator strength spectra for Cl 2p, Cl 2s, C Is and F Is inner sheU excitation of CF3C1, CF2C12, and CFC13 and for N Is and 0 Is inner shell excitation of N02. This work has also reported the absolute photoionization partial (electronic state) differential osciUator strength spectra for CF3C1, CF2C12 and CFCI3 and proposed dipole induced breakdown pathways for CF4, CF3C1 and CF2C12 by combining the results from the dipole (e,e) and dipole (e,e+ion) measurements and previously pubhshed synchrotron radiation measurements. The good agreement between the differential osciUator strength spectra obtained in the present work using the dipole (e,e) technique and previously measured spectra using synchrotron radiation where available, plus the good agreement between the dipole (e,e) experimental and the MCQD theoretical results has demonstrated that the EELS tech nique is a useful alternative to experiments utilizing synchrotron radiation for studying photoabsorption and photoionization processes. 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