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An Electron Impact Investigation of the Fluorinated Methanes

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An Electron Impact Investigation of the Fluorinated Methanes AN ELECTRON IMPACT INVESTIGATION OF THE FLUORINATED METHANES DISSERTATION Presented In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of the Ohio State University By EDWIN HENRY LOUGHER, B.S. The Ohio State University 1952 Approved by Advisor ACKNOWLEDGEMENT I wish to express my appreciation to Dr. E. N. Lassettre for his assistance during the course of this investigation. His interest and grasp of the problems involved were a principal factor in the completion of the work. I should like to thank Dr. A. L. Henne for valuable advice and for some of the materials used in this investigation. I wish to thank Dr. A. B. Garrett, the Chemistry Department, and the Ohio State Research Foundation for the assistantships which enabled me to carry this work to completion. Finally, I wish to thank my wife for her continued encouragement and for typing this dissertation. 8 0 0 4 6 1 TABLE OF CONTENTS Page Introduction 1 I. History and Theory 2 A. History of Electron Impact Work 2 B. General Theory of Electron Impact Spectra 3 C. Localization of Valence Electrons 8 (1) The Concept of Localization 8 (2) Electron Impact Spectra of Saturated and Unsaturated Hydrocarbons 10 (3) Localized and Non Localized Molecular Orbitals 13 (4) Localized and Non Localized Molecular Orbitals in Excitation Processes 21 D. Choice of Compounds 23 II. The Electron Spectrometer 24 A. General Description 24 B. Modification of the Apparatus 32 C. Operational Procedure 35 III. Experimental Work 39 A. Materials 39 B. Graphs of Observed Spectra 43 C. Table of Excitation Potentials 53 11 Page. IV. Discussion of Results 54 A. Decomposition by the Emitter 54 B. Discussion of the Spectra 56 C. General Significance 58 D. Theory of Energy States and Selection Rules 62 (1) Bonding Orbitals in the Ground State 63 (2) Excited States ( <5~~ System) 75 (3) Unshared Electron Pairs 85 (4) Interpretation of the Spectra 87 Summary 90 Appendix 91 A. Analyzer Correction Formula 91 B. Electrometer Bridge Calibration Factors 91 C. Tables of Data 92 Bibliography 120 Autobiography 122 H i ILLUSTRATIONS Flcure Pace 1 The Electron Spectrometer 25 2 Energy Spread In Direct Beam 33 3 Infrared Spectrum of Methyl Fluoride 42 4 Methane Spectra 45 5 Monofluoromethane Spectra 46 6 Difluoromethane Spectra 47 7 Trifluoromethane Spectra 48 8 Tetrafluoromethane Spectra 49 9 Comparison of Spectra of Fluorinated Methanes 50 10 Vinyl Fluoride Spectrum 51 11 Vacuum Spectra 52 12 Energy Levels and Selection Rules 79 iv TABLES Xflble Z&ge 1 Excitation Potentials 53 2 Character Table for CH^ 66 3 Irreducible Representations for CH4 (T^) 68 4 Irreducible Representations for CH^F (C^) 68 5 Irreducible Representations for CHgFg (Cgv) 69 6 Irreducible Representations for CHFg CC«3 V ) 69 7 Irreducible Representations for CF4 (T,^) 70 8 Matrices of Coefficients in Variation Equations 73 9 Ground State Energy Levels 74 10 S election Rules 78 v INTRODUCTION This Investigation had two purposes. One was to investigate the electron impact spectra of methane and its fluorine derivatives. The other, and princi­ pal, purpose was to determine whether the valence electrons in a molecule should be considered as localized, that is, associated with specific bonds, or as non-locallzed and as-sociated with the molecule as a whole* Following this Introduction is a history of electron impact work and of the previous work which has indicated the need for this Investigation. Also Included in this section are a review of the general theory of electon impact work and a com­ parison of the methods of localized and non-localized molecular orbitals. The criteria which led to the choice, of methane and its fluorine derivatives for the purpose of this investigation are discussed. Following this section are descriptions of the elec­ tron spectrometer, the experimental procedure, and the materials used. The results are presented as energy spectra, and their significance with respect to localization of electrons is discussed. 2 I HISTORY AND THEORY A. Hlatory of Electron Impact Work In the past, numerous systems have been investi­ gated by means of electron Impact, The early -work was confined to the determination of critical potentials of atoms and molecules. This work is reviewed by Arnot (1) and Darrow (2). More recently, Investigations of energy spectra have been carried out, using some sort of analyzer which separates the electrons of various energies. Harnwell (3) and, Dymond and Watson (4) were some of the first workers In this field. Hughes and RoJansky (5) developed the theory of the 127° electrostatic analyzer which was sub­ sequently used by Hughes and McMIllen (6) for various Investigations. B . General Theory of Electron Impact Spectra Electron Impact spectra are obtained by passing a monoenergetic electron beam through a gas at low pressure. Electrons which undergo Inelastic collisions with molecules or atoms of the gas, thereby exciting the molecules or atoms to higher quantum states, lose some of their energy. The energy losses are, of course, quantized. The electrons of different energies are then separated by means of some sort of velocity analyzer and the relative numbers at the various energies are measured. A plot of the collected current against the electron energy thien gives a spectrum of the gas under Investigation. The spectra are sometimes unresolved over the entire spectral region, due to the thermal energy spead In the electron beam, finite slit widths, and departure from perfect focusing In the velocity analyzer. Spectra obtained for atomic gases exhibit sharper peaks and deeper valleys than those for molecular gases, since molecular spectra have vibrational and rotational fine structure which Is not resolved by the spectrometer. The gas pressures used in the scattering chamberare low - of the order of 10_4: to 10*“^ millimeters of mercury. At such pressures, the mean free path for electrons is great enough so that the effect of multiple collisions, 4 that Is successive excitations of the same atom or mole­ cule, or successive collisions by a single electron, may be neglected. Electron Impact spectra extend to the far ultraviolet region of optical spectra. The selection rules for tran­ sition appear to be the same for electron energies above about 180 electron volts. With beams of lower energy, optically forbidden transitions may occur. A theoretical basis for this follows. Consider an electron in Inelastic collision with a molecule, atom, or Ion. Let the initial energy of the electron be = | **12 an<a- ^ e final energy be Eg - £ Pg2 , where P^ and Pg are the Initial and final momenta in atomic units. If the energy lost by the electron in exciting the scattering particle to a higher energy state be designated as I, then, by the law of conservation of energy, p-^/s - p 22/2 = I * The square of the change in momentum, AP^, is given by A P 2 = Px2 + P 22 - S P ^ g C o s # , where i) Is the scattering angle. At small angles, that is when \9- Osd 0, AP 2 =■ (Pj_ - Pg)2. 5 Now P2 = (P!2 - 21)^ p 2 = px d - V ej.)4 * Expanding and neglecting terms of order higher than (^/g) » P 2 = P 1 U “ -2E> • Then AP = (Px - P2) - XgljT-ir • The Born approximation (7) for the scattering of high energy electron Is CTi = .*+ » where £ = % < / C cJT ' Here (jj~ = the scattering cross section for the 1—th transition, = the wave function for the ground state of the scattering particle, and ^ = the wave function for the 1— th excited state of the scattering particle. The summation Is over all the molecular electrons, and the Integration Is over the coordinates of all the molecular electrons. The symbol ]£)X represents the square of the absolute magnitude of averaged over all molecular orientations. 6 Since P I s email, we may expand the expression for In a Maclaurln series to give <2 ' £n-o ( i Ap)nC n where K l f k-Tf)" d Y AP_ and k ~ |AF( J ^ Now If and are real , <Cn ~ and ic r AP£,’( - apV-' ^ A) +■ ^'p<’ a -tZS'^-)+' Then, since A P = — I— - . 1 , T u J T t ' or, since |< is Independent of the coordinates of the molecular electrons, C = iT-tefi; V* ^ d r ; . But the matrix element of dipole moment /£= 5-/»i rfr , eo that £ = 7c - ^ - r - > But k Is a unit vector, so that If is the angle between k" and , £ . = * Now is the value of C^~ averaged over all possible molecular orientations. But the average value of the square of a direction cosine Is 1/3, so that £ ^ = k5ytA.* Now If o< - - 4 ^ ^ - 2. £ , ) and z. ( e ; - 2 +■ a <f, « v ) , . 2. then -f ^ -+- (3 -fr- { -3 1 1 For high energy electrons, the first term of this expression Is the most important. The second term does not depend upon E^, and all higher terms decrease with increasing E^. Thus, for high energy electrons, the only allowed transitions are those which are optically allowed, that Is, those for which the matrix element of dipole moment does not vanish. 8 0. Localization of Valence Electrons. (1) The Concept of Localization The concept of localization of electrons within a molecule is an Integral part of the chemical theory of valence. The concept of an electron pair bond was Introduced into the theory by G-. N. Lewis (7) and I. Langmuir (8) and strongly implies that in each bond a pair of electrons is localized in the vlclnityof the two bonded atoms. This theory has had many successes in coordinating the properties of large clases of chemical substances and was proposed primarily for this purpose. Nevertheless, in some cases its success was limited, and with the advent of a quantum mechanical theory of valence its limitation was explicitly recognized by introducing the concept of resonance.
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