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 SelectionRules 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 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 , 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 . 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. In this extended theory it is supposed, with good reason, that the lowest electronic energy state of a molecule requires for Its description several electron pair bond structures (or wave functions), and that in some cases more than one such structure is important. The aromatic hydrocarbons constitute a class of substances in which several such structures are re quired in order to account even qualitatively for the observed facts of structure and reactivity. The notion of resonance, developed particularly by Pauling (9), Introduces into the theory the concept of electron de localization. Pairs of electrons are no longer 9 associated -with particular atom pairs but instead with whole groups of atoms. This occurs to such an extreme degree in certain substances, e.g. metals, that the value of the electron pair method is questionable. This fact, amoung others, has led to the development of an alternative theoretical approach, the method of molecular orbitals, in which the electron pair bond concept has been abandoned entirely. Nevertheless, the electron pair bond idea has been so valuable in organizing structural and other factual Information on simple molecules that it has been retained as an integral part of the chemical theory of valence. Despite its utility the electron pair bond is still an unproven hypothesis and it remains of interest to examine its validity by any available means. In the following two sections two methods are examined, the first being empirical and related to the scattering of electrons, while the second is theoretical and is related to the method of molecular orbitals. 10 (2) Electron Impact Spectra of Saturated and Unsaturated Hydrocarbons. Electron impact experiments of the type previously described are particularly suitable for the study of chemical binding. This is true because, In the energy range studied, only the valence electrons are excited from one energy state to another. It must always be borne in mind, however, that both the Initial and final states are involved in any tran sition while in the development of a theory of valence only one electronic state Is considered, I.e. the lowest state. Nevertheless, certain empirical facts are known which suggest that certain local regions of a given complex molecule affect local regions of the electron impact spectrum. The same might also, obviously, be said of an ultraviolet absorption spectrum, and has been found to be so by other workers. The electron impact work is briefly reviewed below. The electron Impact spectra of methane, ethane, and propane have been studied by Francis (10), and those of cyclopropane, cyclobutane, cyclopentane, and cyclohexane by Begun (11). The spectra of all these compounds were found to have generally similar shapes, with corresponding peaks In approximately the same position. 11 However, one peak which appears in the spectra of propane and the cyclic compounds does not appear in the spectra of methane and ethane. EdmlBten (12) found that the ratio of the scattering cfross sections of ethane and methane is approximately equal to the ratio of the number of carbon-hydrogen bonds in the two molecules. These findings suggest that the characteristics of the spectra of the saturated hydrocarbons might be attributed to the carbon-hydrogen bond. The fact that one peak occurring in the spectra of propane and the cyclic compounds is not found in the spectra of methane and ethane may be due to the fact that methane and ethane do not contain the methylene group which is common to all the other compounds. The environment of a carbon-hydrogen bond of a methylene group is obviously somewhat different from that of a bond of methane or a methyl group, and the effect of the bond on the spectrum might be expected to be somewhat different. These results suggest that local regions of the molecule (C-H bonds) affect local regions of the spectrum. How ever, the bonds in the above compounds are distributed throughout the molecule. In the series of compounds to be discussed next localization is even more clearly establlshed. Begun studied the electron impact spectra of ethylene, propylene, and 1-butene. He found that the spectra of these compounds are somewhat similar to those of the oycloparaffins and propane, with corresponding peaks appearing at about the same energy. There is, however, one additional peak at about 7.2 — 7.6 electron volts which appears in the spectra of all three of the unsaturated compounds. Here, again, it appears that a certain local region of the molecule affects a region of the spectrum. In this particular case, the 7.2 - 7.6 volt peak is thought to be due to a ‘TT electron tran sition from the double bond. 13 (3) Localized and Non—Localized Molecular Orbitals. As mentioned earlier the method of molecular orbitals completely abandons the hypothesis of electron localization. It might be thought, since the theory has had considerable success, that localization of electrons Into pair bonds had been dieproven. Recent work has shown, however, that these two views which seem so divergent are in reality the same, at least for certain molecules in their lowest electronic energy states. Because of its obvious bearing on the present research the argument which reconciles these two views is outlined below. In both the localized and non-localized molecular orbital methods of theoretical treatment, individual molecular orbitals are assumed to be made up of linear combinations of the valence shell orbitals on the constituent atoms. In the non-localized orbital method, an electron is considered as moving in the field of the entire molecular framework, and the molecular orbitals are assumed to be linear combinations of atomic orbitals on all the constituent atoms. In the localized method, an electron Is considered as being restricted to a bond between atoms, and the molecular orbitals are taken as linear combinations of atomic orbitals on only two atoms. In both methods the resulting one-electron 14 molecular orbitals are then combined with spin functions In a determinant to given an atitl symmetric wave function of the molecule. Comparisons of localized and non-locallzed molecular orbital treatments have been made by Francis (10), and Lennard-Jones (13). Francis showed, for the case of the ground state of methane, that it Is possible to derive a set of localized molecular orbitals from a set of non- locallzed orbitals. By setting up a determlnantal wave function of non-localized molecular orbitals and applying the variation method, he obtained a secular determinant which he solved to relate the energies and matrix elements to the coefficients In the linear combinations making up the non-locallzed molecular orbitals. He then transformed the determlnantal wave function by means of a unity determinant to give a new determinant whose elements were linear combinations of the non-locallzed molecular orbitals. Each element contained only one of the hydrogen orbitals. They then had the form of localized molecular orbitals, but they were not orthogonal. Lennard-Jones (13) has derived the general equations which molecular orbitals must satisfy and demonstrated, by the methods of group theory, that these equations may be transformed to others which Involve sets of equivalent functions. The functions are orbitals which have identical distributions in space but differ in direction. These orbitals, however, could have appreciable values in regions other than the neighborhood of an individual bond. Lennard-Jones showed, for the cases of angular XYg and tetrahedral molecules, that the oondltlon for directed orbitals, that is, localized molecular orbitals, is that the energy difference between the non-localized molecular orbitals be small. Lennard-Jones and Pople (14) also discussed the effect of inner shells and of unshared pairs of electrons on the constituent atoms. The theoretical treatments of Francis and Lennard-Jones are somewhat involved. There follows a simple and concise treatment which shows that, in certain cases, the localized and non-locallzed molecular orbital methods are equivalent, in the ground state* Consider a molecule in the ground state, consisting of a central atom with n orbitals available for bonding linked to n atoms, each with one orbital available for bonding. Let the orbitals on the central atom be denoted by y? , y? ,.... , y ^ , and those on the surrounding atoms by 07' » GI ,.... * CZr) . We 16 assume the n non-locallzed molecular orbitals of lowest energy to be where 1 takes the Integral values from 1 to n • Let the spin functions of the electrons be o( and (h , corresponding to spin quantum numbers of + and - We can now set up an antisymmetric wave function, pi (in) % * 6 ) I/, p>U) ^ fid) ^ n fi(xn) 17 In this expression a number in parentheses denotes the coordinates of an electron. Let D be a determinant of magnitude unity, 'it 0 0 n 1 1 i \ ) i 'i i i i i ~ x > = olnn o o 0 oI 1 d,, d, - d m t *z.\ i ( I ! i o 0 'd'in n Then or (|,d u 4 ’4-» 18 Thus has been transformed in such a way that the are replaced by arbitrary linear combinations of the (^/. . Therefore any determlnantal function of this type, in which the i / y are replaced by linear combinations of the ^ ■ can differ from only by a normalizing constant. In matrix notation, let (r-l c z I \ % I a t ./ X. c t in \ h , t.n \ I < ct n t - a t nni nn. Then y - - a y - t b <5~ . Now if b is not singular, that is, if det b ^ 0, then Thus the ^ are linear combinations of the A determlnantal wave function CjJ , similar to with the exception that the (M-' are substituted for the t , can differ from only by a normalizing factor. 19 Since each of the contains only one of the , the are localized molecular orbitals associated with bonds between atoms. It should be noted that no restrictions have been placed on the and dy . They are not assumed to be orthogonal, and the atoms bonded to the central atom need not be Identical. It has, however, been assumed that there are only n orbitals on the central atom and one on each of the surrounding atoms available for bonding. This is true in the case of methane. For the fluorinated methanes however, a refine ment of the foregoing treatment would take account of the unshared pairs In orbitals on the fluorine atoms. The condition that det b Is not obvious. However, It can be shown to be true for the case of methane from the work of Coulson (15). Coulson has derived the following set of non-localized molecular orbitals for methane: yV - <5" ^ . ) ~ /14. (/<■/>* + c r + 61. - crj - Gif) ‘/ i ' ^ (/*~py +■ '■> , - 6^ - o ~ + ( T c f ) ^ ( a a + cr ~ Gi + GZ - crH) 20 where s, px» p^., and p^ are atomic orbitals on carbon, \ and ^ A . are constants, and and Ng are normalizing constants. The determinant of the coefficients of the (JT can readily be shown to be non-vanlshlng. The foregoing treatment indicates that in the cases of certain molecules in their ground states, the localized and non-looalized molecular orbital methods are equivalent. However, as was previously pointed out, it should be borne in mind that excitation processes, such as those studied in this work, involve not only the ground state, but certain excited states as well. This will be discussed in more detail in the following section. 21 (4) Localized and Non—Localized Molecular Orbitals In Excitation Processes Mulllkenls Interpretation of molecular electronic spectra has been developed over a long period of years on the basis of non-locallzed molecular orbitals. During this period the equivalence of localized and non- locallzed molecular orbitals was not recognized, and hence there seemed to be no reason to consider an alternative to the non-locallzed picture. The recent recognition of the equivalence of localized and non-locallzed orbitals In the ground state, however, gave rise to the question of whether electrons are excited from localized or non- locallzed orbitals. It should be pointed out that chemical data shed little light on this question, sinoe most chemical processes are concerned with substances in only their lowest states. The most probable processes for excitation by electron Impact are those In which the state of only one electron Is changed. If this electron Is transferred from a localized molecular orbital to some excited orbital the molecular wave function produced may differ from that obtained if the electron Is excited from a non—localized molecular orbital. It has, in fact, been shown by Hall and Lennard-Jones (28) that, if the excitation leads to 2 2 Ionization, the wave functions do generally differ. It follows, therefore, that the study of processes In which excitation occurs from the ground state to a higher state will provide means for distinguishing between these two alternatives. The success of Mulllken's Interpretation of electronic molecular spectra on the basis of non- locallzed molecular orbitals seems to afford support for this view, and further support Is provided by the work of Lennard—Jones on ionization of polyatomic molecules. On the other hand much experimental work on hydrocarbons by both electron impact and spectroscopic means suggests that regions of the spectrum are characteristic of bond type and thus Indicates excitation from localized orbitals. Further experimental study seems to be in order. 2 3 D . Choice of Compounds. The previous electron impact work which led to the present investigation was confined to a study of hydro carbons. It was thought desirable to investigate a series of compounds which contain, in addition to carbon-hydrogen bonds, a bond of one other type. The spectra of the compounds of this series can then be compared with each other and also with those of the hydrocarbons already studied, In order to determine whether or not certain characteristics of the spectra may be ascribed to the affect of Individual bonds. Furthermore, since it is known that the selection rules for electronic transitions depend upon the symmetry properties of molecules, it was considered desirable that the compounds of the series have a considerable variation in symmetry properties. Methane and its fluorine derivatives constitute a series of the desired type, and were therefore chosen for this investigation. 2 4 II THE ELECTRON SPECTROMETER A. General Description The electron spectrometer In use In this laboratory Is based on the one used by Hughes and McMlllen (6), but has undergone ndunerous modifications by various investi gators. It has been described in detail, along with the various modifications, in the theses of Francis (10), Jones (16), John (17), Dean (18), Edmlsten (12), Berman (19), and Begun (11). However, a brief description will be given here for completeness. The essential parts of the spectrometer are (l) an electron gun, (2) a collision chamber which houses the gun and into which the gas under Investigation is Introduced, (3) a slit system, (4) a velocity analyzer, (5) a collector and measuring device for determining the Intensity of the scattered electrons, (6) electrical control circuits, and (7) a vacuum system with associated vacuum gauges. The system is presented schematically in Figure 1. The electron gun (I) is based on the design of Pierce (20). It consists of four tantalum electrodes and a thermionic emitter. Previous Investigators have used oxide-coated nickel cathodes, but a tungsten ¥ *\ ® of FP-54 FIG. 1 The Electron Spectrometer filament was used in this work, since the compounds used deactivated the oxide coated cathodes. The tungsten filament is a hairpin of 0.010 inch tungsten wire, thinned at the tip to a diameter of about 0.003 inch. The filament is heated by means of a current of about 2 to 4 amperes supplied by two 6 volt storage batteries (N) connected in series. The current is controlled by means of a variable resistance network. The gun is directed along a diameter of the collision chamber, and can be rotated by means of a lever outside the chamber, in order to change the scattering angle . The present investi gation was carried out at a scattering angle of zero. The collision chamber (A) is a cylindrical bronze casting with an inside diameter of 20 cm and 15 cm deep. The front face is removable and contains a glass window covered with a copper screen to prevent a charge buildup on the glass. Electrical connections to the electron gun enter the chamber through tungsten—glass seals (H) at the back of the chamber. The glass is connected to the chamber by means of a copper-glass seal. The collision chamber is connected by three feet of 1 inch copper ‘•Streamline” pipe (F) to a two liter per second KPI oil diffusion pump backed by a Welsh Duoseal mechanical pump. The gas or vapor under investigation enters through a 27 tube (G-) at the back of the chamber. In steady state operation, the gas Is introduced at the rate at which the pump removes it, and the effect of decomposition products of the gas is minimized. The gas may be Introduced through either a Hoke bellows—type needle valve or a capillary leak. The leak consists of a helix of flat tened 1/8 inch copper tubing which may be controlled by varying the diameter of the helix by twisting. The gas inlet portion of the system Is constructed of 3/8 inch copper tubing and Hoke bellows-type valves, and is con nected to a five liter per second DPI oil diffusion pump backed by a Welsh Duoseal mechanical pump. These pumps allow the gas inlet system and the collision chamber to be evacuated without pumping through the slits to the analyzer. The pressure In the collision chamber is measured by means of a Dumond Knudsen gauge connected to the pump line of the collision chamber by 3/8 inch tubing. This gauge was calibrated by John (17), and his calibration Is used. The collision chamber is connected to the analyzer by a 9.2 cm length of 3 cm I. D. pipe (B). This pipe houses a removable assembly which contains the slits S-^ and Sg. Slit 3^ is 1 x 0.069 cm and Sg is 1 x 0.0025 cm. The slits are made of stainless steel. 28 The analyzer chamber (0) la a bronze casting approximately 24 cm long, 12 cm high, and 6.5 cm deep. It is evacuated through a three foot length of 4 inch I. D. copper pipe (J) connected to a Model MF-250 DPI oil dif fusion pump having a capacity of 240 liters per second at 10”4mm Hg. This pump is backed by a Oenco Hypervac mechanical pump. The analyzer pressure Is held below 1 x 10~5 mm Hg, and is measured by means of a cold oathode ionization gauge connected by 1/4 inch copper tubing to the analyzer end of the pipe to the vacuum pump. The theory of the electrostatic analyzer was developed by Hughes and Rojansky (5). It is treated in detail by Francis (10). The analyzer consists of two electrodes, E^ and Eg. The electrodes are 127° segments of concentric cylinders. The Inside and outside diameters, respectively, of the annular space between the electrodes are 10 cm and 14 cm. The electrodes are removable and are insulated from the analyzer chamber by means of sheets of mica. The electrical leads to the analyzer enteto the chamber through copper-glass seals. The slit S3 is 1 x 0.0025 cm. The Faraday cylinder (D) consists of two concentric cylinders. The Inner cylinder receives the analyzed electrons through slit S4 . This slit is 1 x 0.1 cm. 29 The external lead from the Faraday cylinder la a rod encased In Incite. The luolte acts as both an Insulator and a vacuum seal. The current oollected bythe Faraday cylinder is measured by means of an FP-54 electrometer tube circuit. This circuit is a modification of the Barth circuit described by Penlck (21). It is described by John (17). The grid of the tube is connected to the lead from the Faraday cylinder. Four grid resistors are available by switching. The values of these Q -I fi 1 I "|p resistors are approximately 10 , 10 , 10 , and 10"^ ohms. The control circuits for applying voltages to the analyzer and theanodes of the electron gun are described In detail by Begun (11). The analyzer volt age is applied to electrodes E-^ and Eg by means of a one megohm potentiometer in series with a 100,000ohm voltage divider. The potentiometer, variable in steps of 0.1 megohm, selects a fraction of the analyzer batT* tery (L) potential. The voltage divider, variable in steps of ten ohms, selects a fraction of the poten tial of battery M. Most of the analyzer potential is supplied from the potentiometer. The voltage divider is connected in such a way that its voltage subtracts from that of the potentiometer. The potentiometer volt age is measured by reading the voltage across a lOOOohm 3 0 standard resistor by means of a K—1 potentiometer. To measure the voltage divider potential, a fraction from the voltage divider Is applied to the K-l potentiometer. In order to eliminate the effect of secondary emmls— slon from the analyzer walls, a resistance of 9.86 megohm® (0) Is shunted across the analyzer electrodes and an experimentally determined tap on the resistance is grounded. This causes a slight difference between the voltage applied to the electrodes and the open circuit voltage which Is measured. A correction is therefore necessary. Begun (11) has derived the correction formula. In this Investigation, the anodes of the electron gum were connected together. A one megohm potentiometer is available for selecting the accelerating potential from the battery (K). The present work was carried out, however, with the potential supplied directly from the battery. The battery is a bank of 45 volt B batteries, and the accelerating potential was varied by changing the number of B batteries in series. The accelerating potential is measured by reading the voltage across a 1,000 ohm standard resistor In series with the one megohm potentiometer. This voltage Is measured with a K-l potentiometer. 3 1 The meter Indicates the total electron emission from the cathode of the electron gun. Ag is a galvano meter and shunt which indicates the beam current. A^ is the filament current meter, and A 4 gives the current collected by the anode. The spectrometer is oriented so that the horizontal component of the direction of electron travel in the analyzer is along the north-south component of the earth’s magnetic field. The other two components of the earth's field, along with other fields due to magnetic objects in the vicinity of the spectrometer, are neutralized by means of a pair of five foot Helmholtz colls. The current to the colls is supplied from two six volt storage batteries connected in series, and is controlled by means of variable resistances. A rotating coil magnetometer, driven by an air motor, is used to measure the magnetic field in the vicinity of the analyzer and collision chamber. This magnetometer is described by Berman (19). The voltage generated in the magnetomer coll is amplified and Indicated on a Dumont Type 208—B oscilloscope. 3 2 B. Modification of the Apparatus It was necessary to know whether or not the usual oxide coated emitters could be used with the fluori— nated methanes. Since only very small samples of these compounds were available, preliminary work was done on "Freon 12" (COlgFg). It was found to deactivate the oxide coated emitter, and it was thought probable that the fluorinated methanes would behave in a similar fashion. For this reason, a tungsten emitter was used in this work. The emitter is a sharp hairpin of 0.010 Inch wire, thinned at the tip to a diameter of about 0.003 inch. The thinning is accomplished by heating the wire and touching it with a block of sodium nitrite. Since the filament requires a higher current than that needed by an oxide coated cathode, it was necessary to make a slight modification in the filament control circuit. Due to the voltage drop along the emitting portion of the tungsten filament, there is an energy distribu tion in the electron beam in addition to the normal thermal distribution. In order to determine whether or not this might cause a serious decrease in resolving power, the energy distribution in the electron beam was investigated. The results are indicated graphically in Figure 2. INTENSITY (ARBITRARY UNITS) NRY SPREAD ENERGY N IET BEAM DIRECT IN A 0 VOLTS (A)503 B29 VOLTS (B)229 AF IT 0.5 WIDTH HALF AF IT 0.4 WIDTH HALF 0. O .5 -0 NRY EETO VOLTS) (ELECTRON ENERGY FIG . . 2 FIG (B) (A) .5 0 + 33 The widths at half height for electron energies of 503 and 229 electron volts are 0.5 and 0.4 volts respectively. The curve for 503 volts is comparable with the one obtained by Dean (18) at about the same energy and using an oxide coated emitter. No data are available for comparison with the curve for the lower voltage. 35 C. Operational Procedure Some time is required to stabilize the battery potentials in the various circuits of the spectrometer. The switches which connect the analyzer and anode potentiometers and the voltage divider across their respective batteries are usually left on overnight preceding a run. The currents in these circuits are of the order of a few hundred mloroamperes, so that the drain on the batteries is not serious, but the slight loading tends to stabilize the batteries. The electro meter tube bridge is turned on at least an hour before the start of the run. The vacuum in the analyzer is checked with the cold cathode ionization gauge. The magnet and the control unit of the gauge are removed before the run is started. The collision chamber vacuum is checked by means of the Knudsen gauge. The electron gun filament and accelerating potential are turned on and the filament current is adjusted to give the desired electron beam current, as measured by means of the beam current galvanometer. When the fila ment is heated, the collision chamber pressure rises, due to outgasslng. The run is not started until the pressure has returned to normal. 36 The magnetic field In the vicinity of the spectro meter is neutralized by adjusting the currents In the Helmholtz coils, using the rotating coil magnetometer as an indicator. The analyzer, voltage divider, and accelerating potentials are measured by means of the K-l potentio meter. Due to interactions of currents in the control circuits, these voltages can not be measured under actual operating conditions. The accelerating potential is measured while the battery Is disconnected from the electron gun. The analyzer and voltage divider potentials are measured with the analyzer electrodes disconnected. The gas under investigation is admitted to the col lision chamber through either the capillary leak or the Hoke needle valve. Some time is required to stabilize the pressure. When the gas is admitted, the beam current usually changes and must be readjusted. The unscattered beam is brought into the Faraday cylinder by adjusting the voltage divider. The lever which rotates the electron gun is adjusted to maximize the Faraday cylinder current, as measured with the bridge Q galvanometer. The 10 ohm resistor and 0.01 galvanometer shunt setting are usually used when measuring the direct 37 beam, and the lO^ohm resistor and 0.1 shunt setting are used for detecting the electrons soattered by the gas. The spectrum is obtained by increasing the voltage divider setting in small steps and reading the bridge galvanometer, while holding the beam current and col lision chamber pressure constant. When peaks are located in the spectrum, the voltage divider setting for the unscattered beam is rechecked, to eliminate the possibility of error due to battery drift. At the conclusion of the run, the analyzer, voltage divider, and accelerating potentials are again measured, and the magnetic field checked by means of the magneto meter. As was stated in the description of the apparatus, the 9.86 meghohm resistance shunted across the analyzer electrodes necessitates correction of the measured analyzer voltage. This is done by means of the formula derived by Begun (11). However, correction of every point of the spectrum would be time-consuming, so that only the tabulated locations of peaks have been corrected. The spectra in Figures 4 to 11 are therefore somewhat distorted. The apparent locations of points on the 38 curves may be in error by as much as 0.5 electron volts. The relationship between analyzer voltage and electron beam energy is given by the relation E = kU, ■where U is the analyzer potential required to bring electrons of energy E into the Faraday cylinder, and k is a constant. Begun (11) has determined this constant by measuring the analyzer voltages required to bring the direct beam and the 21.22 ev peak of heliuminto the collector. Begun*s value is k * 1.257 ± 0.003. Ill EXPERIMENTAL WORK A. Materials The sources and purities of the gases investi gated are given below. (1) Methane Methane was obtained from the Matheson Company. It was described as 99.0 per cent pure. Dlfluoro-, trifluoro-, and tetrafluoro-methane were obtained from Kinetic Chemicals, Inc. They were described as having purities of 99 per cent or greater. Below are listed the code numbers and infra red analyses of these materials. (2) Dlfluoromethane (Code No. FCD - 626) No impurities were detected by infrared. (3) Trifluoromethane (Code No. PCD - 627) Contained 0.03 mol per cent of mono- chloro dlfluoro methane. (4) Tetrafluoromethane (Code No. FCD - 628) Contained 0.05 mol per cent of mono- chloro trifluoromethane. This material also contained about 0.4 per cent of material non-condensable in liquid nitrogen (presumably air). 40 (5) Vinyl fluoride Vinyl fluoride was also obtained from Kinetic Chemicals, Inc. The code number of the material was DV - 347. No analysis was given, but, for the purpose of this research, It was not thought necessary to Investi gate the purity of the sample. (6) Methyl fluoride Methyl fluoride was not commercially available. It was prepared by a modification of the method of Bennett (22). The procedure is described below. A mixture of dimethyl sulfate and anhydrous potassium fluoride was heated to boiling. The methyl fluoride evolved was passed through concentrated sulfuric acid to remove dimethyl ether, 50 per cent potassium hydroxide, drying tubes containing soda lime, and a trap maintained at a temperature of about -55 to -65° C by means of a dry lce-acetone mixture. The gas was collected in a trap Immersed In liquid nitrogen. A simple distillation was then carried out, In which about one third of the methyl fluoride was discarded, a second third collected In evacuated sample bulbs, and the final third discarded. The sample bulbs were then partially Immersed In liquid nitrogen to freeze the methyl fluoride and evacuated to remove any air which may have been present. 41 An Infrared spectrum of the methyl fluoride was obtained, In order to determine Its purity. This spectrum Is shown In Figure 3. No bands are detectable other than those of methyl fluoride reported by Bennett and Mpyer (23). The most common impurity, dimethyl ether, absorbs strongly in the region 10.5 - 11.5 microns (23). It may be seen that the spectrum cf Figure 3 shows no absorption In this region. The methyl fluoride was therefore considered to be of high purity, probably In excess of 99 per cent. I » >■ «w ■ .VI '«?* ' .7!. ** .i\ 4, r % , $ * I’ r ' f'i ■**■." ^.''•'iV^ -. ’ ■- .. VI 'U ^ > , « v ./ ■* V r' «i \ Vvtf ‘V ‘ Vi i / V • , v , : * * i/. £-• \ Ml*. H- ' I." JV V 7 ■„} it* <; v /?*• v .r *]Li«- '.i. ‘ 3't50O * r *:/ 1 , V 'two -•■.^o'.,'. ■!*>■i j1- rv1 -jf ■;'- .i'V!* r^f" ^ "f',' ■;>:*»n Ijs * 7 * v' . 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Graphs of Observed Spectra The spectra In Figures 4 to 11 were plotted from the data In Part C of the Appendix. The voltage scale Is approximate; accurate voltages can be determined by use of the correction formula in Part A of the Appendix. The legends on the graphs give the accelerating potentials and the locations of peaks ( P^, Pg, etc.) and shoulders (Si, Sg, etc. ). For all compounds except vinyl fluoride, spectra were obtained at two accelerating voltages. The peak locations listed are averages of the values obtained from the two spectra in cases for which the peaks were resolved at both accelerating potentials. Peak locations are considered to be accurate to within ±0.1 electron volt unless otherwise indicated. Shoulders are located only to the nearest volt. The spectra were investigated In the low energy region, and no excitations were found below about seven volts. Because of difficulties encountered in the operation of the spectrometer, the intensity measurements were somewhat unreliable. For this reason, the relative intensities of the peaks on any spectrum may be in error by as much as ten per cent, and relative Intensities between separate spectra may vary by large factors. A certain amount of spectral background was present 4 4 during this investigation. Representative background (vacuum) spectra are shown in Figure 11. The background was not measured before each run on a compound. It should be borne in mind that, due to the unreliability of the intensity measurements, the background spectra Intensities are not necessarily plotted to the same scales as those of any of the compound spectra. In fact, it may be seen from Figures 4 to 11 that the background exerts little influence on the general shapes of the spectra of the compounds investigated. Furthermore, it is evident that no spurious peaks have been Introduced into the spectra by the background. The low voltage spectra of methane and the fluoro- methanes are plotted together on Figure 9 for convenience in comparing the spectra. INTENSITY (ARBITRARY UNITS) O 5 5 O NRY OS EETO VLS UNCORRECTED) VOLTS, (ELECTRON LOSS ENERGY M ETHAN T M ETHAN A VOLTS 2 0 (A)5 8 228 VOLTS 8 2 2 (8) , = P, P3 13.3EV f 00 EV 10.0 01 20 10-15 I. 4 PIG. (B) (A) 5 4 INTENSITY (ARBITRARY UNITS) O E N A H T E M O R O U L F O N O M NRY OS EECT OT, UNCORRECTED) VOLTS, N O TR C (ELE LOSS ENERGY A 496 6 9 4 (A) B 226 VOLTS S T L O V 6 2 2 (B) 4 I51± EV I E 2 . 0 5.1 ± = P4 1. EV V E 13.3 = 3 P - z P i 9.3 EV E 3 . 9 = Pi 5 I EV V E II. 2 . I 0 ± S T L O V I. 5 FIG. IO 15 (A) 20 45 INTENSITY (ARBITRARY UNITS) E N A H T E M O R O U L F I D NRY OS EETO VLS UNCORRECTED) VOLTS, (ELECTRON LOSS ENERGY (A) ) B I S T L O V 4 0 5 S T L O V 9 2 2 Se P* Pz S, R> , S ± 1. V E 10.5 = 1 V E 21 = V E 15.55 = V E 4 . 9 = 4 V E 14 = 24EV V E 12.4 = 7 V E = 17 I 1 20 2 15 IO 5 I. 6 FIG. 47 O INTENSITY (ARBITRARY UNITS) E N A H T E M O R O U L F I R T S T L O V 9 2 2 ) B ( (A) NRY OS EETO VLS UNCORRECTED) VOLTS, (ELECTRON LOSS ENERGY S T L O V 4 0 5 = 42 V E 14.2 = z P =1. EV E 17.4 = 4 V P E 15.8 = 3 P V E 12.5 = P, 1 EV E 0 2 = 51 EV E 2 2 = 2 5 O15 IO 5 G. 7 . IG F (B) (A) 20 48 INTENSITY (ARBITRARY UNITS) O E N A H T E M O R O U L F A R T E T A 504 VOLTS T L O V 4 0 5 (A) NRY OS EETO VLS UNCORRECTED) VOLTS, (ELECTRON LOSS ENERGY S T L O V 9 2 2 (B) | V E 0 | 2 - S *1 ±0.2 EV V E 2 . 0 ± 5 17 * 3 P 58 V E 15.8 - 2 P , 36 V E 13.6 = P, 5 IO G, 8 , IG P (A) ) B ( 15 20 49 INTENSITY (ARBITRARY-UNITS) 0 NRY OS EETO VLS UNCORRECTED) VOLTS, (ELECTRON LOSS ENERGY 5 10 I. 9 FIG. 15 20 50 (2) ( 4 ) INTENSITY (ARBITRARY UNITS) E D I R O U L F L Y N I V ENERGY LOSS (V O LT S , , S LT O (V LOSS ENERGY S T L O V 8 2 2 = 4EV E 14 = ( S = 2 E 12. E V = 3 4 P - 08EV V E 10.8 - 3 P ' z P P, 7. 2 = 5 ± 0.2 V E 2 . 0 ± 8 . 8 V E 10 I. 10 PIG. UNCORRECTED) 15 51 20 i INTENSITY (ARBITRARY UNITS) O 0 2 5 1 IO 5 O M U R T C E P S M U U C A V NRY OS EETO VLS UNCORRECTED) VOLTS, (ELECTRON LOSS ENERGY A 505 VOLTS T L O V 5 0 5 (A) B 229 VOLTS T L O V 9 2 2 (B) , 1.5-0.2 V E 2 . 0 13.05*- = P, ,= V E 9 = S, I. 11 FIG. 52 '8 5 > C. Table of Excitation Potentials For convenience, the locations of peaks and shoulders are tabulated below* The peak locations are considered to be accurate to within ± 0.1 electron volt unless otherwise indicated. Shoulders are located to the nearest electron volt. Table I Excitation Potentials (Electron Volts) Compound Peaks Shoulders Methane 10.0 11.8 13.3 Monofluoro— 9.3 11.1 13.3 15.1 methane + 0.2 ±0.2 Difluoro- 9.4 10.5 12.4 15.55 14 17 methane Trifluoro- 12.5 14.2 15.8 17.4 20 22 methane Tetrafluoro- 13.6 15.8 17.5 20 methane ±0.2 Vinyl 7.2 8.8 10.8 12.3 14 fluoride ±0.2 IV DISCUSSION OF RESULTS A. Decomposition b.v the Emitter In the past, oxide coated emitters have been used In this laboratory as electron sources. In the present investigation, a tungsten filament was used. Since the operating temperature of a tungsten filament is consider ably higher than that of an oxide coated cathode, It was feared that there might be sufficient thermal decompositl of the gases under investigation to give spurious peaks in the spectra, that is, peaks characteristic of decompo sition products. G-lockler (24) reported thermal decompo sition of methane by a tungsten filament, but no decompo sition by an oxide coated cathode. The spectra obtained for methane, using a tungsten filament, (Fig. 4) agree well with those obtained by Francis (10) and Edmisten (12). There is no evidence of a peak In the neighborhood of 7.6 electron volts. A peak might be expected at this voltage as a result of the formation of ethylene following thermal decomposition of methane. It Is therefore evident that, at least In the case of methane, thermal decomposition Is not serious enough to affect the electron Impact spectra. The spectra of methyl fluoride and vinyl fluoride offer further evidence that the effect of thermal 55 decomposition is negligible. Vinyl fluoride is a possible product of the decomposition of methyl fluoride. However, the Intense excitation at 7.2 electron volts in vinyl fluoride (Pig 10) is not evident in the spectrum of methyl fluoride (Pig. 5). Thus it appears that thermal decomposition does not affect the methyl fluoride spectrum. Safary, Romand, and Vodar (25) studied the ultra violet spectrum of hydrogen fluoride gas. They found an absorption maximum at about 7.7 electron volts. Hydrogen fluoride might be expected to be formed as a result of the thermal decomposition of monoflfiiaro-, difluoro-, and trlfluoro-methane, but no excitations are found in the neighborhood of 7.7 electron volts in the electron Impact spectra of any of these compounds (Figures 5 to 7). In view of the above considerations, it seems unlikely that the spectra of the compounds investigated are affected by thermal, decomposition of the gases by the tungsten filament. 56 B. Discussion of the Spectra There appears to be little, if any similarity amoung the spectra of methane and its fluorine derivatives (Figures 4 to 8). Only one systematic trend is apparent, and this is not clear-cut throughout the entire series. This trend is a decrease in the voltage at which scat tering begins, that is, the voltage of the Initial rise of the spectrum, in going from tetrafluoro methane to monofluoromethane. However, methane does not continue the trend; the initial rise of the spectrum of methane is at a slightly higher voltage than that of the mono- fluoromethane spectrum. Inspection of the table of excitation potentials might lead one to believe that certain peaks are characteristic of part of the series of compounds. However, consideration of the intensities makes the apparent correspondence of these excitations seem fortu itous. Consider, for example, the peaks P-j_ and Pg in methane, monofluoromethane, and difluoromethane. There appears to be a rough correspondence in the locations of these peaks, which might suggest that they are caused by similar excitations. However, as can be seen from the spectra, the decrease in intensity of these peaks from 57 mono— to difluoromethane Is so slight that It seems unlikely that the pseaks would completely vanish In trl— fluoromethane. It must then be concluded that they are not truly characteristic of the series. Further considerations similar to that outlined in the previous paragraph, together with the fact that the general shapes of the spectra of the various compounds are entirely different, inevitably leads to the conclusion that there is no true one-to-one correspondence In the excitations of methane and Its fluorine derivatives. In view of the conclusion of the foregoing paragraph, the spectrum of vinyl fluoride (Figure 10) is rather surprising. It will be noted that the most Intense excitation of this spectrum Is the one at 7.2 electron volte. This corresponds quite closely with the intense excitation found In ethylene, propylene, and 1-butene by Begun (11). The significance of the facts noted above will be discussed In the following section. 58 C. q-eneral Slgnlfloanoe It seems appropriate at this point to restate the principal purpose of this investigation. This 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-localized and associated with the molecule as a whole. If the locali zation picture is the correct one, then certain regions of the spectrum will be characteristic of certain local regions of the molecule. If the non-localization picture is correct, then the characteristics of the spectrum must be ascribed to the structure of the molecule as a whole. Three poslbllltles will be considered explicitly for the case of methane and its fluorine derivatives in the following discussion. (1) The valence electrons are localized in electron pair bonds and unshared pairs. In this extreme view, corresponding bonds, for example, carbon-fluorine bonds, and unshared pairs in different compounds are considered Identical in all their characteristics. If this is the true situation, then superposition of the spectra of methane and tetrafluoromethane in various proportions should give exact replicas of the spectra of the other three compounds. It is Immediately evident from the spectra that this is impossible; this localization picture 59 must therefore be rejected. (2) The valence electrons are localized In electron pair bonds and unshared pairs. but the unlike fields of the different molecules cause dlstortlons of the bonds and unshared pairs so that they are not Identical. The spectra should then exhibit a rough correspondence, but ■with excitation potentials and intensities somewhat different amoung Individual members of the series. Con sistent trends in excitation potentials and Intensities might, however, be expected. As was pointed out in the previous section, no such correspondence or consistent trends are noted In the case of methane and the fluoro- methanes. The picture of localization with distortion must, therefore, also be rejected for the case of methane and Its fluorine derivatives. In this connection a question arose, during the course of the investigation, as to the possibility of such extreme distortion from highly electronegative fluorine as to make corresponding excitations unrecognizable. No means for testing this hypothesis on fluorlnated methanes is evident but in the case of compounds with a double bond a region of the spectrum (to 7.2 - 7.6 e.v.) charac teristic of the double bond is well established. It seemed of Interest, therefore, to Investigate the electron 60 Impact spectrum of a fluorine substituted ethylene to see whether or not this region is radically altered. The spectrum of vinyl fluoride (Figure 10) shows that no such radical alteration takes place. This suggests that the field of the fluorine Is not sufficient to radically alter the double bond. This suggests, in turn, that extreme distortion of single bonds in the fluorinated methanes is not the most important factor. The argument Involved is obviously not rigorous, since different compounds are involved, but It does not seem profitable at this time to pursue further the hypothesis of extreme distortion. (3) The valence electrons are non-locallzed. and must be considered as moving in the field of a molecule as a whole. In this case, no similarity of any sort Is to be expected in the spectra of the various compounds under consideration. Since, as was pointed out in the previous section, this complete lack of similarity does exist amor^j the spectra of methane and the fluoromethanes, it must be concluded that the non-localisation picture is the one which must be chosen for these compounds. To summarize, there Is considerable spectroscopic work which Indicates that local regions of an ultraviolet absorption spectrum are sometimes characteristic of bond 61 type. AlsOj electron Impact Investigations of saturated hydrocarbons can be, at least roughly, Interpreted in the same way. Prom the present Investigation, however, the implied general principle does not seem to be verified even approximately in the case of fluorlnated methanes. Although the general principle is not valid, the remark able similarity of the spectra of saturated hydrocarbons, especially methane and ethane, still remains and is unexplained. The present work strongly indicates, how ever, that the explanation is to be sought in the non localized molecular orbital theory. The situation is similar in the case of substituted ethylenes. In the latter case considerable theoretical work has already been done by Mulliken and collaborators. In the case of the fluorlnated methanes of course, the non-localized orbital theory is apparently the only one worth pursuing further. 62 jD. Theory of Energy States and Selection Rules. In the previous section It was concluded that con sideration of non-locallzed molecular orbitals constitu ted the most promising direction for interpretation of the spectra of these compounds. A complete assignment seems to be out of the question since resolution is not sufficiently good. Moreover, in the case of at least one of these compounds (CH4 ), there is apparently no chance of resolving the spectrum, since examination of the ultraviolet absorption spectrum at high resolving power reveals only a continuum. The theoretical consl- cerations advanced by Sooner and Teller (27) make It seem likely that the spectrum of CF^ is also continuous. Some progress can nevertheless be made by consid ering the problem in more detail. The considerations Involve several steps. In the first step group theory Is applied to determine the Irreducible representations to which the ground state molecular orbitals belong. In the second step a group of excited states arising In the LCAO (linear combinations of atomic orbitals) approxima tion is discussed, and selection rules are deduced. The treatment is confined to CP bonding electrons, since the similarities of interest (if any) are to be found In the CT electrons. Finally the contribution of unshared pairs is briefly treated. 63 (l). Bonding Orbitals In the G-round State. As has been discussed In a previous section, the molecular orbitals In the ground state can be replaced by linear combinations without affecting the ground statte wave function for the molecule as a whole. In this way the molecular electrons can be described as occupying bonding orbitals in pairs { (T" bonding electrons) or as occupying orbitals associated mainly with atoms (unshared pairs). These orbitals are localized and, in general, do not belong to irreducible representations of the symmetry group. Non localized molecular orbitals must, however, belong to such Irreducible representations. This point has been discussed in considerable detail by Hall and Lennard-Jones (28). The procedure to be followed, therefore, Involves the assignment of electrons to bonds and unshared pairs in accord with the usual principles of the chemical theory of valence. Then the irreducible representations for the non-localized molecular orbitals can be deduced from group theory. It is to be emphasized that no appeal to any LGAO approximation is Implied at this step. The recent work of Lennard-Jones Indicates that this step is rigorous, at least within the limits in which a molecular 64 orbital (i.e., a one electron wave function to be used In a SLater determinant) constitutes a valid description of the motion of one electron. This method has already been applied by Berman (IS) to the problem of determining selection rules In a variety of cases, and the present treatment closely follow his. Consider first the case of methane. Let ^>7 , and represent C ~ bonding orbitals for CH^. In the ground state each of these is occupied by two electrons with opposed spins. Let represent the i-th non-locallzed molecular orbital. Then (1 ) Let H be a Hamiltonian operator such that can most simply be achieved by adjusting the a^j In such a way as to make the energy integral (2) an extreme. The condition that E be an extreme Is (3) The condition for non vanishing a,. Is (4) 65 and the roots of this equation determine the E1 » Since H is invariant under a symmetry operation for the molecule it follows that the belong to irreducible representa tions of the symmetry group. On the other hand theorbital6 < 5 ^ are equivalent except for orientation in space . Under the operations of the symmetry group, therefore, the ( j y are merely permuted and form therefore a per mutation representation (usually reducible) of the group. This latter fact makes it possible to determine the charac ters of the <5^ (reducible) representation and hence, by reducing this, the irreducible representations whltah it contains. These, of course, are the irreducible represen tations to which the belong. This information is obtained without any need for appeal to (3) or (4), although these will be used later. The example of methane Is treated below in some detail. The symmetry group for CH^ is Td , whose character table is given in Table 2. The first five rows refer to the irreducible representations (see Eyring, Walter, and Kimball) (30) for notation). In the sixth row are given the characters for the reducible ^ representation. In order to reduce the Q representation we make use of orthogonality of group characters. Let )Cf ({*) be the character of an operator of class ^ of the 1-th irreducible representation, let be the number of 66 Table 2 Character Table for CH4(Td ) E 8C 3C 6 ^ 6S 3 2 ^ cl 4 Ax 1111 1 a 2 11 1-1 -1 E 2-120 O T 3 0-1-1 1 Tg(x,y,z) 3 0 - 1 1 -1 0 2 0 6? operators In class and let h be the total number of group operators. Then p hfXi (?) Xj ((-) ~ h £,J f (5) and also , * • ( O i f r *' e) Xi (f'} = {%.ff P = (6 ) Let J6q ~ C p ) be the character of the pD -th class In the <5~ representation. Then ~ X / ( ? ) . (17) Multiply both sides of (7) by ^ ( j ({?) and sum over ^ . Then, using (5), ■ (0 ) r Now a^ gives the number of times the J-th irreducible representation occurs. Using the characters of Table Z we find that the representation occurs once and the Tg representation occurs once. This information is contained in the first row of Table 3. The remaining two rows of Table 3 are explained later. Proceeding in precisely the same way and, for tike time being, ignoring unshared electron pairs, the (5~ representations for CH^F, CH^F^, CHF^, and CF4 have also been reduced with results which appear in Tables 4,5,6, and 7. 68 Table 3 Irreducible Representations for CH4 (T^) E A1 A 2 Ti T2 < r 1 0 0 0 1 s 1 0 0 0 0 p 0 0 0 0 1 LCAO 2 0 0 0 2 Table 4 Irreducible Representations for CH3F A1 A 2 E c r 2 0 1 s 1 0 0 p 1 0 1 0 0 1 GJ 1 0 0 LCAO 4 0 2 69 Table 5 Irreducible Representations for CH^Fg A1 A2 B1 B2 (J" 2 0 1 1 P 10 1 1 T. 1111 1 0 0 1 LCAO 4 0 2 2 Table 6 Irreducible Representations for CHF^ ) A 1 A 2 E g " 2 o : i S I 0 o P I 0 1 1 1 2 O 1 LCAO 4 0 2 70 Table 7 Irreducible Representations for CF^ (Td ) A1 A 2 E T1 T; 1 0 0 0 l S 1 0 0 0 0 P 0 0 0 0 l i r 0 0 1 1 l ° 7 1 0 0 0 l LCAO 2 0 0 0 2 The irreducible representations in the ground state which arise from bonding orbitals have now been obtained and there remains the problem of determining the energies. It i^lll be assumed that matrix elements of H between orbitals which bond tike same pair of atoms is the same in all molecules. This is, of course, an approximation. It is equivalent, however, to the assumption that bond properties are preserved from molecule to molecule and it is of interest to examine the consequences of the hypothesis. Then, ignoring unshared pairs except in so far as these Influence H, the matrices of the coefficients of (3) 71 are as shown In Table 8. There q-^ and refer respectively to diagonal and non-diagonal matrix elements of H between orbitals for C-H bonds, <3g and ^ refer to the corresponding quantities for C-F bonds and is the matrix element between the Inspection of Table 9 reveals several interesting facts. In the first place, E^ is the same (q^- (*>, ) for CH^, and CHpFg, but changes abruptly to q2 “ 2 for C H F 3 and CF4 ' Since, in excitation, electrons are removed, not from localized, but from non localized molecular orbitals this suggests that coincidences in energy might be observed in the first three members of the series, proceeding from either end, but not beyond (except by accident). 72 Eg and E4 , on the contrary, seem to change regularly throughout the series. This suggests that other excitations might be found which show regular trends in energy in passing through the series. These Inferences must, of course, be considered as tentative since, obviously, two states are Involved in any transition. This point is further discussed in the next section. Table 8 Matrices of Coefficients In Variation Equations CH^L (V Pz (X . ^ 9z. k Pz p>2. qc ET (X L(\ Pz v ^ J CH 4 y r pi <^3f3 OH-iP3f V P i ^ (q. +c|i+ if3:) ^ C q . + q ^ ^ , ) if* i, ft *11 K + ^[(CI' ~c|f ’ij Tl^r'uJ i] CHoF 2 V P> V P * . Jz(cfl + qk i’Ql + pj 4 §. + P J k + % - q ^ . V + W i ] ^ P>t] ghf3 qx'pi £( CF 4 VfH ^ ' h ^ ' h Table 9. Ground State Energy Levels 75 (2). Excited States ( (T system). In order to treat excited states some additional approximations must be introduced. For this purpose we consider the LCAO approximation which has beenwidely used by R. S. Mulllfcen and by many others. This will first be set up in subh a way as to include only atomic orbitals Involved In bonding. thus continuing to ignore unshared pairs, whose Influence is discussed later. From this point of view we then consider linear combinations of eight orbitals, four on carbon (2fe, 2px , 2py, 2pj) and one on each attached atom. The approximate molecular orbitals are then linear combinations of these, the \ four lowest being filled in the ground state. This system of eight atomic orbitals again provides a reducible representation for the symmetry group. Since, under the operations of the group, the orbitals on carbon transform only into themselves while the attached orbitals also transform only into themselves the two groups can be treated separately. The reduction of the representation provided by s and p orbitals has been treated by Kimball (29) and his results are given in Tables 3, 4, 5, 6, and 7, in the rows labeled s and p respectively. The attached orbitals are merely permuted under the influence of the group and hence 76 provide the same characters as the representation. The characters for the whole representation are then given by the sums of the corresponding characters for (3"7 s, and p. If the characters obtained In this way are used to reduce the representation the results given in each table In the row labeled LGAO are obtained. The whole procedure here is very similar to that of Kimball (29) and his tables have been used to obtain many of the results. In examining the tables It becomes immediately evident that each Irreducible representation which occurs in the ground state occurs twice In the LGAO representation and hence from the LGAO representation we conclude that each Irreducible representation whlch occurs In the ground state also occurs as an excited state. It now becomes possible to obtain selection rules for all the excitations which are possible between states arising In LCAO approximation of the type considered. These statfces do not, of course, constitute the only molecular states but it seem likely that they constitute Important low lying energy states. It Is to be expected that only transitions between low lying states can be resolved In the present work since higher states, in general, tend to be more closely spaced, 77 although exceptions do occur. In order to obtain selection rules we use the following general principle. If the direct product of the dipole moment representation and the ground state representation be taken and reduced then transitions are allowed to only those states which belong to the irreducible representations occuring in the reduced direct product. In this way the results of Table 10 are obtained. In the table a plus sign indicates that tran sition from the representation at the left to that at the top occurs, while a zero indicates that it is forbidden. The ground states and excited states are indicated diagramatically in Pig. 12. The permitted transitions are shown by arrows. The positions of the energy states are arbitrary. It Is obvious from the diagram that all transitions from ground to excited states, arising in LGAO approximation, are permitted except and B-j—»Bg In CH^Fg and A-j— in CH4 and GF^. As the symmetry is reduced, therefore, more energy states are produced as the result of splitting of the triply degenerate levels, and, in addition, more transitions become permitted. In the intermediate symmetries, therefore, greater complexity is expected in the spectra and this seems to agree with observation. Table 10 Selection Rules 0H3F c¥ g CHF Ai Ai1 3 [ S’ H- "ft ‘' ‘ k B1 E T< AiT Al E* B Sf E- Br Al' Bl E‘ *2 Ai Al- FIG. 12 Energy Levels and Selection Rules 80 In considering the energies of the excited states there Is no firm basis for estimation without very intricate and tedious calculation much too Involved to permit calculations for all states of five molecules. Some qualitative Information can, however, be obtained In the following way. In obtaining the wave functions in LCAO approximation we first suppose that "symmetry" orbitals for the attached atoms are formed from combinations of orbitals on these atoms, the "symmetry" orbitals having the property of belonging to irreducible representations. Then the only orbitals on the central atom which combine with the "symmetry" orbitals are those which belong to the same Irreducible representation. In CHgig, there is a symmetry orbital belonging to B . l?l?om Table 5 we see that one p orbital also belongs to Bg# Hence a linear combination of the p orbital and the symmetry orbital also belongs to Bg. If we make the energy integral an extreme then two linear combinations are found, one corresponding to a high and the other to a low energy state. Let ap + b£ It Is easy to show that the other Is fcp - ajj s ~ ] where £G~J denotes the symmetry orbital. The Inference Is strong that one of these is bonding and the other antibonding. A similar argument can be applied in several other cases, and it seems likely that the 81 excited states are, In general, antibonding. One important point remains. In the ground states it has been shown that states T_, E, and Bc for CEL, CI^F, and CHgFg respectively have equal energies and the implication is Strong that the corresponding excited states also have equal energies in LCAO approximation. This would certainly be true if all electrons were in antibonding states since the same argument as for the ground states would then apply, but since only one electron is excited at a time the generalization does not seem immediately justified. We must therefore consider this matter in more detail. Let 2 ' * ke Lt3A0 molecular orbitals obtained from solution of the problem of rendering the energy integral on extreme. From the above treatment it appears that for each of the substances treated the same Irreducible representations appear in the ground state as in the excited state. Let ^ 2 * 3* and ^ 4 ke ‘fc*ie ground state molecular orbitals and y y and Q the excited state molecular orbitals. Then if the linear combinations V 82 constitute a permutation representation of the symmetry group it follows that ^ 7 ~ T y V * ' also constitute a permutation representation of the group if the are so selected that corresponds t o • This follows because the ( f y y j belong to the same irreducible representations as the C/ 0 + y 0 and hence transform in the same way* Both CjP + and ( y constitute equivalent orbitals. Moreover, since the ( ^ j are molecular orbitals = o and hence it follows that the matrix element of H between a CP orbital and a CP orbital must vanish. Since the UJ oonstitute an equivalent set, being merely permuted under the operations of the group, we can reverse the above argument and obtain expressions for thejg as combinations of the G y . But in so doing the ground state are linear combinations only of theCP * orbitals and the excited state are combina tions only of the Q ~ orbitals. This follows from the fact that the matrix element of H between a CP and a PP orbital must vanish and hence both cannot appear in the same combination. Both the C P + an<3- CT orbitals are equivalent and hence all the arguments applied to the (P for the ground state become applicable to the for the excited states. The same equations for 83 the energies apply. The only difference lies in the fact that q^, q2, and ^ 1 2 mU8'fc be replaced by different values q£% q^etc. which apply to the (T~ orbitals. In particular the disposition of energies in the excited states is subject to exactly the same general remarks as applied to the ground state. The inference that a constant transition energy exists common to the compounds CH4 , CH^F, and OHgFg is there fore precise to the extent provided by the LCAO approximation. Similarly, on proceeding from the opposite direction in the series, a constant transit tlon energy exists common to the compounds CFCHF^, and CHpFg. The above argument, being based entirely on considerations of symmetry, seems to have a validity extending far beyond any LCAO approximation. In fact It appears, at first sight, to have a validity equal to that for the ground state. More careful examina tion shows, however, that an additional hypothesis is Involved. This is, that the molecular orbitals^ are solutions of a wave equation with the same Hamiltonian for each state. Such a statement is rigorously true for the ground state f unctions ( ^ / - •- ■ * the Hamiltonian being that of Hartree-Fock, but no s uch theorem has been established for the entire system^* - 84 Nevertheless, we might reasonably suppose that this is, in fact, a rather good approximation and within those limits the theory is accurate. This leads to the conclusion that the treatment does indeed have validity beyond that implied by an LCAO approximation, and the predictions, except for the assumption of constant matrix elements between similar functions from molecule to molecule and the neglect of unshared pairs, can be regarded as reliable. It is now clear that several features have been predicted which might be expected to be common to the spectra of the various compounds and provide the basis for partial assignments of transitions. There remains, however, the problem of considering the effect of unshared electron pairs, and this will next be considered. In reviewing the above work it seems fair to conclude that the LCAO approximation serves a useful purpose in pointing the way to a general solution, but the results obtained have validity beyond that which might be expected from the LCAO treatment. s 85 (3). Unshared Electron Palra. Next we have to discuss briefly the effect qf unshared electron pairs. These occur only on fluorine atoms and are of two types. First the pairs which, in an extreme assignment, occupy 2 s orbitals on fluorine, and second those which occupy * the 2p orbitals on fluorine. The irreducible representations contained in the representation provided by 2 s orbitals are indicated in Tables 3 to 7 in the row labeled ( f j and those contained in the 2p representation in the row labeled 'Tf * In LCAO approximation it becomes evident that the irreducible representations in the excited states are the same as when the unshared pairs are Ignored. This arises because, although the unshared pair orbitals provide new molecular orbitals, at the same time a pair of electrons is provided to occupy each and hence all of the new orbitals, being occupied, belong to the ground states. This observation is Important since it shows that the transitions previously considered between orbitals of the bonding and anti bonding systems still occur. The presence of unshaced pairs Introduces, however, the possibility of further transitions from the unshared pair orbitals to the anti-bonding G system. The selection rules for such transitions can be easily obtained from our previous tables. 86 There remains the possibility that when the unshared pair orbitals are considered the previous deductions concerning the positions of energies in the O system might be rendered invalid. It Is believed, however, that this effect Is small for the following reasons. The classifiction into G bonding and unshared pair orbitals constitutes in itself a classification into orbitals belonging to the mole cule as a whole ( G system) and to separate atoms (unshared pairs). This follows because all G bonds in a molecule of the type considered, have an atom in common (carbon) and hence, in toto, Involve the mole cule as a whole. The unshared pairs, however, are on atoms none of tohich are bonded and whose distances apart are correspondingly greater. If the unshared pair orbitals combine significantly with orbitals of the G system electrons must be transferred to carbon because every Q orbital involves carbon. Due to the high electronegativity of fluorine this must be a small factor and as a first approximation it seems reasonable to ignore It, as has been done. In any event it seems necessary to adopt the extreme hypothesis and to refine it as the result of comparison with experiment. 87 (4). Interpretation of the Spectra. In an earlier section It was concluded, on the basis of the observed spectra of methane and its fluorine derivatives, that excitations between electronic energy states must be interpreted on the basis of the non-locallzed rather than the localized orbital picture. The foregoing theoretical treatment provides some Information concerning the nature and disposition of states on the basis of the non-localized picture. Although it is not feasible at this time to make unambiguous assignment of energy levels to the observed excitations there are certain features of the spectra which show some promise of being inter pretable on the basis of the theory. The theory predicts a greater complexity in the spectra of CH3F, CHgFg, and CHF3 than in those of the end members of the series. Inspection of the spectra appears to support this prediction. It should be realized, however, that, due to the low resolving power of the spectrometer, there are undoubtedly many excitations which are not resolved. The theory further predicts that there are certain energy level Intervals which are approximately equal for different members of the series of compounds, that Is, the Interval between the state of energy and the corresponding anti-bonding state in 0H4, CH3F, 88 and CHg^g, and the Interval between the state of energy 9.2 ~ 2 and corresponding anti-bonding state in CF4 , CHFg, and CHgFg. Furthermore, the theory predicts that transitions between these levels are allowed. It is therefore of interest to attempt to find excita tions which are common to the first three members and to the last three members of the series of compounds. It may be seen from Table 1 that there are certain series of excitations which might be Interpreted as transitions between the above mentioned constant levels. These, are the series at 10.0, 9.3, and 9.4 electron volts and at 11.8, 11.1, and 10.5 electron volts in CH^, CH^F, and CH^F^ respectively, and the series at 15.8, 15.8, and 15.&5 electron volts and at 17.5, 17.4, and 17 electron volts in CF^, CHF^, and C H ^ F ^ respectively. The agreement among excitation potentials is not good in the first two series; however, it should be remembered that the derivation of levels common to three compounds was based on the assumption that certain matrix elements have identical values for the three compounds. This is obviously an approximation whose validity is untested. In conclusion it should be pointed out that the theory points the way toward further investigations. 89 The occurrence of certain regularities In the energy states of the compounds investigated suggests that further study of series of compounds might contribute to the understanding of molecular structure. 90 SUMMARY Electron Impact spectra have been obtained for methane and its fluorine derivatives and for vinyl fluoride. Spectra were obtained at a scattering angle of zero degrees and at Incident electron energies of about 230 and 500 electron volts in the case of methane and its fluorine derivatives and at about 230 volts in the case of vinyl fluoride. All substances were in the gas phase at low pressure. An Intense excitation was found at 7.2 electron volts in the spectrum of vinyl fluoride. This corresponds closely with excitations found in certain olefins by Begun. Little similarity was found among the spectra of methane and the fluorinated methanes. It is concluded that interpretation of the spectra must be based on the assumption that the electrons are excited from non-localized rather than from localized molecular orbitals. Using group theory and the method of non-looalized molecular orbitals, a theoretical treatment is presented which provides information concerning the energy levels in the ground and excited .states. Interpretation of the spectra on the basis of the theory is discussed. 91 APPENDIX A. Analyzer Correction Formula Due to the 9.86 megohm resistance shunted across the analyzer electrodes, the measured analyzer voltage must be corrected. The formula derived by Begun (11) is 9.86 x 10^6 _x(l-x) 105+ y(l-y) 106 +- 9.86 x 106_ where X = voltage divider setting y = analyzer fraction = x(voltage divider voltage) - - y(analyzer battery voltage) B. Electrometer Bridge Calibration Factors The sensitivity of the bridge circuit with the galvanometer shunt set at 0.1 was 560 cm per volt. If the 0.1 shunt setting and lO^ohm resistor are taken as a standard, conversion factors for other shunt settings and resistances are: Resistor Shunt 109 1010 1011 0.01 920 129 10.2 0.1 90.1 12.6 1.00 1 8.50 1.19 0.0946 92 C . Tables of Data The tables give "collected current galvanometer" deflections for various settings of the voltage divider. Energy loss peaks are marked with the word "Peak", and the voltage divider setting required to maximize the galvanometer deflection for the direct beam Is recorded afterward and is designated by the letters "D B". The conditions for each run are listed at the top of each table, using the following abbreviations: A - Analyzer voltage (volts) VD - Voltage divider voltage (volts) AF - Analyzer fraction BC - Beam current (microamperes) P - Pressure (mmHg) The lO^ohm resistor was used for the direct beam and the l O ^ o h m resistor was used for all other data. To find the accurate location of a peak, the analyzer correction formula in Part A of the Appendix must be used. All data were taken with a scattering angle of zero degrees. 93 A A P 0.8 VD V. B C 2.70 U 4 P 4.9 4: 10“4mm Hg Shunt Voltaee Divider Deflection (mm) 0.01 0.065 110 (Direct Beam) 0.1 . 0.090 21 0.100 10 00110 ' 5 0.120 1 0.130 0 0.140 0 0.150 0 0.160 0 0.170 0 0.180 0 0.190 1 0.200 2 0.205 7 0.210 14 0.215 30 0.220 59 0.225 98 0.230 135 0.235 161 0.240 165 0.243 167 Peak DB = 0.064 0.245 166 0.250 164 0.255 165 0.260 175 0.265 190 0.270 208 0.275 219 0.280 224 0.285 231 0„290 242 0.295 250 0.300 252 0.302 253 Peak DB » 0.067 0.305 250 0.310 248 0.315 243 0.320 236 0.325 226 94 Methane - 502 Volts (Fig. 4)-»Contld . Shunt Voltage Divider Deflection (mm) 0.1 0.330 221 0.335 212 0.340 203 0.345 192 0.350 185 0.355 17? 0.360 170 0.365 161 0.370 155 0.375 148 0.380 140 0.385 135 0.390 128 0.395 123 0.400 117 0.405 113 0.410 108 0.415 102 0.420 96 0.425 91 0.430 87 0.435 83 0.440 78 0.450 71 0.460 65 0.470 59 0.480 55 0.490 50 0.500 45 0.510 40 0.520 38 0.530 34 0.540 32 0.550 28 0.560 , 26 0.570 25 0.580 23 0.590 22 0.600 20 0.610 18 0.620 1? 0.630 16 0.640 14 0.650 12 95 Methane — 502 Volt.^ (Fig. 4)-Contld. Shunt Voltage Divider Deflection (mm) 0.1 0.660 11 0.670 10 0.680 9 0.690 8 0 . 7 0 0 6 0.710 5 0 . 7 2 0 4 0. 7 3 0 3 0.740 2 0 . 7 5 0 2 0 .760 1 0.770 1 0.780 1 0.790 0 0.800 0 96 Methane - 228 Volta (Fig. 4) A 386.85 v. A F 0.4 VD 43.535 v. B C 5.40 aa. oe P 4.9i lO^mm Hg Shunt Voltage Divider Deflection (mm) 0.01 0.315 106 0.1 0.335 21 0.340 8 0.345 4 0.355 1 0.365 0 0.375 0 0.385 0 0.395 0 0.405 0 0.415 0 0.425 0 0.435 0 0.445 0 0.455 0 0.465 0 0.470 4 0.475 8 0.480 18 0.485 30 0.490 62 0.495 85 0.500 93 0.505 90 0.510 87 0.515 82 0.520 81 0.525 84 0.530 93 0.535 100 0.540 103 0.545 102 0.550 106 0.555 108 0.560 110 0.563 111 0.565 110 0.570 108 0.575 104 0.580 98 97 Methane — 228 Volts (Fig. 4)-Contld. Shunt Voltage Divider Deflect: 0.1 0.585 93 0.590 89 0.595 83 0.600 79 0.605 73 0.610 68 0.620 64 0.625 57 0.635 52 0.645 47 0.655 41 0.675 34 0.685 30 0.695 27 0.705 24 0.715 20 0.725 17 0.735 15 0.745 1 2 0.755 11 0.765 9 0.785 7 0.805 5 In the above run, the location of the third peak was found to be In error. A recheck was made as follows: A 387.25 v. A F 0.4 VD 43.480 v. B 0 5.40 P 4.9/x 10 mm Hg Voltage Divider 0.555 1 0.002 Peak 0.308 Direct Beam 98 Monofluoromethane - 496 Volts (Fig. 5) A 427.17 v. A F 0.8 VD 65.839 v. B C 5.40/^<# P 4.o 4 10~4mmHg Shunt Voltage Divider Deflection (cm) 0.1 0.099 68.068. 0 (Direct Beam) 1 0.110 37 0.115 19 0.120 12 0.125 7 0.130 5 0.135 4 0.140 3 0.145 2 0.150 1 / 0.155 1 / 0.160 1 / 0.165 2 0.170 2 / 0.175 3 / 0.180 4 / 0.185 5 / 0.190 6 / 0.195 9 0.200 16 0.205 30 0.210 42 0.214 47 P 0.220 43 0.225 44 / 0.230 52 0.235 62 / 0.240 65 0.245 67 0.250 79 0.255 93 0.260 108 0 . 26 3 112 P 0. 265 110 0.270 104 0.275 93 0.280 85 0.285 85 0.290 85 0.295 82 0.300 79 Monoflaoromethane - 496 Volts (Fig. 5)-Contld, Shunt Voltage Divider Deflection (cm) 0.305 75 + 0.310 71 / 0.315 67 / 0.320 64 0.325 60 / 0.330 58 0.335 55 / 0.340 54 0.345 52 0.350 49 0.355 46 0.360 43 0.365 41 0.370 38 0.375 36 0.380 34 0.385 0.390 32 0.395 30 0.400 28 0.405 27 0.410 25 / 0.415 24 0.420 23 0.425 21 / 0.430 20 / 0.435 19 / 0.440 18 / 0.445 18 0.450 17 0.460 15 / 0.470 14 0.480 13 0.490 12 0.500 11 0.510 10 0.520 9 / 0.530 9 0.540 8 / 0.550 8 0.560 7 / 100 Monofluoromethane — 226 Volts (Fig. 5) A 426.83 v. A P 0.3 VD 63.746 v. B 0 5 . 40/A- & P 4 . 3 -x lO-^mmlfe Shunt Voltage Divider Deflection (om) 0.1 0.158 15,.0 1 0.170 17 0.175 5 0.180 3 0.185 2 0.190 1 / 0.195 — 0. 200 1 0.205 1 0.210 1 0.215 1 0.220 1 0.225 1 0.230 1 0.235 1 0.240 1 0.245 1 0. 250 2 0. 255 p 0.260 3 / 0.265 7 0.270 14 0.275 19 / 0.2765 20 PPeak DB = 0.160 0.280 18 0.285 15 / 0. 290 16 0.295 21 0.300 ± 0.002 24 / 0.305 24 0.310 24 / 0.315 30 0.320 37 0.326 41 / 0.330 39 4 0. 335 34 0.340 29 0.345 28 0.3501; 0.003 28 / Peak DB = 0.159 0.355 28 0.360 27 101 Monofluoromethane - 226 Volte (Fig. 5)-ContlcL. Shunt Voltage Divider Deflection (cm) 0.365 25 0.370 24 0.375 22 / 0.380 21 0.385 20 0.390 19 0.395 18 0.400 17 0.405 16 / 0.410 15 / 0.415 14 / 0.420 13 / 0.425 12 / 0.430 11 / 0.435 10 / 0.440 10 0.450 9 0.460 8 0.470 7 0.480 6 0.490 5 / 0.500 4 / 0.510 4 0.520 3 7^ 0. 530 3 0.540 3 0.550 3 0.560 2. 102 Dlfluoro Methane - 504 Volte (Fig. 6) A 430.84 v. A F 0.8 VD 65.058 v. B C 5.40/Ad . P 3.9 'x 10 mmHg Shunt Voltage Divider Defleotlon (mm) 0.01 0.054 73 0.1 0.105 3 0.115 2 0.125 2 0.135 2 0.145 3 0.155 8 0.160 16 0.165 27 0.170 34 0.173 34 0.175 35 0.178 37 0.180 38 0.183 40 0.185 42 0.190 51 0.195 66 0. 200 87 0. 205 104 0.207 110 = 0.058 0.210 98 0.215 91 0.220 83 0.225 84 0.230 89 0.235 98 0.240 112 0.245 121 0.246 122 0.058 0.250 119 0.255 111 0.260 97 0.265 90 0.270 88 0.275 85 0.280 83 0.285 79 0.290 76 0.295 73 0.300 70 0.305 68 103 Dlfluoro Methane - 504 Volta (Fig. 6)~Qontld> Shunt Voltage Divider Deflection (mm) 0 * 310 67 0.315 64 0.320 61 0.325 57 0.330 54 0.335 51 0.340 48 0.345 45 0.350 42 0.355 39 0.360 37 / 0.365 35 0.370 33 0.375 31 0.380 29 / 0.385 28 0.390 26 / 0.395 25 0.400 24 0.405 23 0.410 22 0.415 21 0.420 20 0.425 18 / 0.430 17 / 0.435 17 0.440 16 0.450 15 0.460 13 0.470 12 0. 480 11 0.490 10 0.500 9 0.510 8 0.520 7 / 0.530 6 / 0.540 5 / 0.550 5 0.560 4 0.570 3 / 104 Dlfluoro Methane - 229 Volts (Fig. 6) A 430.52 v. A F 0.3 VD 64.959 v. BO P 4.2 x 10 nunHg Shunt Voltage Divider Deflection (cm) 0.01 0.148 110 (: 1 O. 200 5 0.210 4 0.220 3 0.230 4 0.240 4 / 0.250 5 / 0. 255 9 / 0. 260 19 / 0. 263 22 / Peak DB = 0.147 0 . 265 20 / 0.270 18 0.273 21 0.275 22 / 0.277 23 p 0. 280 21 / 0. 283 23 0. 285 27 0.290 37 0. 295 49 0.300 64 / Peak DB =: 0.147 0.303 58 / 0.305 49 / 0.310 36 0.313 37 0.315 37/ 0.318 37 / 0.320 37 / 0.323 37 / 0.325 37 / 0.328 41 0. 330 43 / 0.333 48 0.335 52 0.339 56 p 0.147 0.345 50 0.350 40 / 0.355 35 0. 360 34 0.365 33 0.370 31 / hn Vlae iie1 elcin (cm) Deflection Divider1 Voltage H Shunt lloo ehn - 2 Vls Fg 6)-Cont'd. (Fig. Volts 229 - Methane Dlfluoro ooooooooooooooooooooooooooooooooo Oiil>.MCOHOtOCDroCD HHHHHHHHHHNNMWNWWMWCil W^t^CJiOiO>0)Cn- 0 0 1 106 Trlfluoro Methane - 504 Volts (Fig. 7) A 430.05 v. A P 0.8 VD 65.195 v. B C 5.40,JM - Cf P 4.4/x 10 mmHg Shunt Voltage Divider Deflection (mm) 0.01 0.040 138 (Direct 0.1 0.100 9 0.110 7 0.120 8 0.130 9 0.140 11 0.150 15 0.160 25 0.170 68 0.175 98 0.180 143 0.185 189 0.190 205 0.191 206 Peak DB 0.195 196 0.200 172 0.205 165 0.210 165 0.215 165 0.220 161 0. 225 142 0.230 142 0.235 144 0.240 148 0.245 155 0.250 174 0.254 189 Peak DB 0.255 188 0.260 183 0.265 160 0.270 141 0.275 136 0.280 134 0.285 129 0. 290 124 0.295 121 0.300 118 0.305 116 0.310 115 0.315 111 107 Trlfluoro Methane — 504 Volts (Fig. 7)—Cont*d. Shunt Voltage Divider Deflection (mm) 0.1 0.320 106 0.325 100 0.330 93 0.335 86 0.340 80 0.345 75 0.350 69 0.355 65 0.360 61 0.365 59 0.370 56 0.375 51 0.380 50 0.385 48 0.390 46 0.395 44 0.400 41 0.405 40 0.410 38 0.415 36 0.420 35 0.425 33 0.430 31 0.435 30 0.440 29 0.445 28 0.450 27 0.455 26 0.460 25 0.465 24 0.470 23 0.475 22 0. 480 21 0.490 20 0.500 18 0.510 17 0.520 16 0.530 15 0. 540 14 0.550 13 108 Trlfluoro Methane - 229 Volts (Fig. 7) A 429.78 v. A F 0.3 VD 65.115 v B C 5.40 P 4.4/x 10-4mmHg S hunt Voltage Divider Deflection (mm) 0.01 0.150 88 0.1 0.180 11 0.190 8 0.200 7 0.210 6 0.220 5 0.230 5 0. 240 4 0.250 5 0. 260 6 0. 270 7 0. 280 20 0.290 39 0.295 60 0.300 65 0.303 68 0.305 67 0. 310 50 0.315 49 0.320 49 0.325 50 0.330 44 0.335 39 0.340 41 0.343 43 0.345 42 0. 350 43 0.355 47 0.360 53 0.362 54 0.365 53 0.370 46 0.375 37 0.380 35 0.385 34 0.390 33 0.395 31 0.400 29 0.405 28 0.410 28 109 Trlfluoro Methane - 229 Volts (Fig. 7)-Confa. Shunt Voltage Divider Deflection (mm) 0.1 0.415 27 0.420 26 0.425 25 0.430 24 0.435 23 0.440 21 0.445 20 0.450 19 0.455 18 0.460 17 0.465 16 0.470 15 0.475 14 0.480 13 0.485 12 0.490 11 0.495 11 0.500 10 / 0.510 10 0.520 9 0.530 8 0.540 7 0.550 7 110 Tetrafluoro Methane - 504 Volts (Fig. 8) A 430.92 v. A P 0.8 VD 65.128 v. B 0 5.40/ Tetrafluoro Methane - 504 Volts (Fig. 8)-Conttd. 3hunt Voltage Divider Deflection (mm) 0.335 73 0.340 , 70 0.345 65 0.350 61 0.355 55 0.360 52 0.365 49 0.370 45 0.375 42 0.380 39 0.385 37 0.390 34 0.395 33 0.400 32 0.405 30 0.410 29 0.415 27 0.420 26 0.425 25 / 0.430 25 0.435 24 0.445 22 0.455 21 0.465 20 0.475 19 0.485 18 0.495 17 0.505 16 0.515 15 0.525 14 0.535 13 0.545 12 0.555 11 112 Tetrafluoro Methane - 229 Volts (Fig. 8) A 430.61 v. A P 0.3 VD 64.989 v. B C 5.40/^ . P 4.1 x 10 4mmHg Shunt Voltage Divider Deflection (mm) 0.01 0.151 67 (Direct Beam) 0.1 0.200 3 0.210 2 0.220 1 0.230 1 0.240 2 0.250 2 0.260 2 / 0.270 3 0.280 3 0.290 4 0.300 6 0.305 10 0.310 14 0.315 30 0.3190 47 Peak DB = 0.1510 0.320 46 / 0.325 34 0.330 21 0.335 18 0.340 22 0.3455 32 / Peak DB = 0.1500 0.350 28 0.355 27 / 0.360 28 0.365 + 0.005 28 Peak DB =: 0.150 O .370 28 0.375 28 0.380 26 0.385 25 / 0.390 25 O .395 24 0.400 24 0.405 23 / 0.410 22 / 0.415 22 0.420 21 0.425 20 0.430 19 0.435 18 113 Tetrafluoro Methane - 229 Volts (Fig. 8)-Contld. Shunt Voltage Divider Deflection (mm1 0.1 0.440 16 / 0.445 15 / 0.450 14 / 0.455 13 / 0.460 13 0.465 12 0.470 11 / 0.475 10 / 0.480 9 / 0.485 9 0.490 8 / 0.495 8 0.500 7 / 0.510 6 / 0.520 6 0.530 6 0.540 5 / 0.550 5 / 0.560 5 0.570 4 / 0.580 4 0.590 3 / 0.600 3 + 114 Vinyl Fluoride - 228 Volte (Fig.10) A 425.83 v. A F 0.3 VD 64.048 v. B C 5.40/*# . P 4.1 oc 10“ nmmHg 3hunt Voltage Divider Deflection (cm) 0.1 0.136 6..4 1 0.142 77 0.145 10 0.150 3 0.155 2 0.160 1 / 0.165 1 0.170 1 0.175 0 / 0.180 0 / 0.185 0 / 0.190 0 / 0.195 0 / 0.200 0 / 0.205 0 6f 0.210 1 0.215 5 0.220 21 0.225 45 0.227 48 P < 0.136 0.230 42 / 0.235 33 / 0.240 14 0.245 15 0.247+ 0.002 15 Peak DB = 0.137 0.250 14 / 0.255 13 / 0.260 14 / 0.265 18 0.270 25 0.274 27 / Peak DB = 0.138 0.280 24 / 0.285 24 0.290 27 / 0.293 28 / Peak DB = 0.138 0.295 28 0.300 25 / 0.305 24 115 Vinyl Fluoride - 228 Volts (Fig. loi-Qonfd. Shunt Voltaee Divider Deflection (cm) 0.310 22 / 0.315 22 / 0.320 22 / 0.325 22 0 . 330 21 0.335 20 0 . 340 19 0.345 18 / 0.350 17 / 0.355 16 / 0. 360 16 0.365 15 / 0.370 14 / 0.375 14 0.380 13 / 0.385 13 0. 390 12 / 0.395 12 0.400 11 / 0.405 11 0.410 10 0.420 9 0.430 8 / 0.440 7 / 0.450 6 / 0.460 6 0.470 5 0.480 4 / 0.490 4 0.500 3 / 0.510 3 0.520 2 0. 530 2 / 0. 540 2 / 116 Vacuum - 505 Volta (Fig. 11) A 431.15 v. A P 0.8 VD 65.055 v. B C 5 .40 P 4 x^lO^mmHg Shunt Voltage Divider Deflection (cm). 0.01 0.052 12,.1 1 0.067 26 0.072 14 0.082 6 0.092 2 0.102 1 0.112 1 0.122 1 / 0.132 4 0.137 5 0.142 7 / 0.147 10 0.152 15 0.157 19 / 01162 23 0.167 25 0.172 27 0.177 29 0.182 32 0.187 35 0.192 37 0.197 39 / 0.202 43 0.207 45 0.208 i 0.003 45 P i * 0.052 0.212 45 0.217 44 / 0.222 43 / 0.227 41 / 0.232 40 0.237 38 0.242 36 0.247 34 0.252 33 0.257 31 0.262 29 0.267 27 0.272 26 0.277 25 0.282 23 / 0.287 22 117 Vacuum — 505 Volts (Fig. ll)-Cont>d. 3 hunt Voltage Divider Deflection (cm) 1 0.292 20 0.297 19 0.302 17 0.307 16 0.312 15 0.317 14 0.322 13 0.332 12 0.342 10 0.352 8 0.362 7 0.372 6 0.382 5 0.392 4 0.402 3 0.412 3 0.422 2 0.432 2 118 Vacuum - 229 Volts (FIg. 1 1 ^ A 430.85 v. A P 0.3 VD 65.134 v. B C 5.40 P 4 x /10”‘°mmHg Shunt Voltage Divider Deflection (cm) 0.1 0.154 85,.5 1 0.165 39 0.170 13 0.175 7 / 0.180 6 0.185 4 / 0.190 4 0.195 3 / 0.200 3 / 0 . 205 3 0.210 3 0.215 2 / 0.220 2 0.225 2 0.230 2 0.235 3 0.240 3 0. 245 4 0. 250 5 / 0. 255 7 / 0. 260 10 0.265 11 / 0.270 12 0.275 13 0.280 14 0.285 14 / 0. 290 15 0. 295 15 / 0.300 16 0.305 17 0.310 17 / 0.312^ 0.005 17 / = 0.154 0.315 17 / 0.320 17 0.325 16 / 0.330 16 0.335 15 0.340 14 0. 345 13 119 Vacuum - 229 Volte (Fig. iD-Cont'd. Shunt Voltage Divider Deflection (cm) 1 0.350 12 0.355 11 0.365 9 0.375 8 0.385 7 0.395 5 / 0. 405 4 / 0.415 3 / 0.425 2 / 0.435 2 0.445 1 / 0.455 1 0.465 0 / 0.475 0 0.485 0 0.495 0 120 bibliography : 1. F. L. Arnot, "Collision Processes in Gases", Methuen and Co., London (1946) 2 . K. K. Darrow, "Electrical Phenomena In Gases", The Williams and Wilkins Co., Baltimore (1932) 3. G. P. Harnwell, Phys. Rev. 33, 559 (1929) 4- E. C. Dymond and E. E. Watson, Proc. Roy. Soc. A 122. 571 (1929) 5. A. L. Hughes and V. RoJansky, Phys. Rev. 34,284 (1929) 6. A. L. Hughes and J. H. McMillen, Phys. Rev. 34, 291 (1929) 39, 585 (1932) 44, 20 (1933) 7. G. N. Lewis, J. Am. Chem. Soc. 38, 762 (1916) 8. I. Langmuir, J. Am. Chem. Soc. 41, 868 (1919) 9. L. Pauling, "The Nature of the Chemical Bond", Cornell University Press, Ithaca, New York (1948) 10. S. A. Francis, Ph.D. Dissertation, The Ohio State University (1947) 11 . G. M. Begun, Ph. D. Dissertation, The Ohio State University (1950) 3.2. W. C. Edmisten, Ph. D. Dissertation, The Ohio State University (1949) 13. J. Lennard-Jones, Proc. Roy Soc. A 198, 1, 14 (1949) 14. J. Lennard—Jones and J. A. Pojble, Proc. Roy. Soc. A 202. 166 (1950) 121 BIBLIOGRAPHY (CONT1D .) 15. 0. A. Coulson, Trans. Far. Soc. 33, 388 (1937) 16. E. A. Jones, Ph. D. Dissertation, The Ohio State University (1948) 17. G. S. John, Ph. D. Dissertation, The Ohio State University (1949) 18. L. B. Dean, Ph. D. Dissertation, The Ohio State University (1949) 19. A. S. Berman, Ph. D. Dissertation, The Ohio State University (1949) 2 0 . J. R. Pierce, J. Appl. Phys. 11, 548 (1940) 2 1 . D. B. Penick, Rev. Scl. Instr. 6, 115 (1935) 2 2 . W. H. Bennett, J. Am. Chem. Soc. 51, 377 (1929) 23. W. H. Bennett and C. F. Meyer, Phys. Rev. 32, 888 (1928) 24. Glockler, Proc. Nat. Acad. Scl. 10, 155 (1924) 25 E. Safary, J. Romand, and B. Vodar, J. Chem. Phys. 19, 379 (1951) 26. J. Lennard-Jones, Discussions Far. Soc., 10,18 (1951) 27. H. Sponer and E. Teller, Rev. Mod. Phys. 13, 75(1941) 28. G. G. Hall and John Lennard-Jones, Proc. Roy. Soc. A 205. 357 (1951) 29. G. E. Kimball, J. Chem. Phys. 8, 188 (1940) 30. H. Eyrlng, J. Walter, and G. E. Kimball, "Quantum Chemistry", John Wiley and Sons, Inc., New York. (1944) 1 2 S AUTOBIOGRAPHY I, Edwin Henry Lougher, was born in Greenfield, Indiana on May 30, 1920. I received my secondary schooling in Greenfield High School. In 1942 I received the degree of Bachelor of Science in ChemlcaL Engineering from Purdue University in West Lafayette, Indiana. After graduation I worked in the development department of the Sinclair Refining Company In East Chicago, Indiana for one year, and then spent three years as an electronics specialist in the United S t a t e s Navy. In June of 1946 I entered the graduate school of The Ohio State University. I worked as an assistant in the Department of Chemistry during the time of my graduate study. Cft ~ c P, Pi P, P' q.-e f&. P, p- PiX P.-x