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Electron spin resonance spectra of some gaseous free radicals Ferraro, William Charles 1964

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ELECTRON SPIN RESONANCE SPECTRA OF SOME GASEOUS FREE RADICALS by WILLIAM CHARLES FERRARO B.Se., University of British Columbia, 1962 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE MASTER OF SCIENCE in the Department of CHEMISTRY We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September, 1964 In presenting t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the U n i v e r s i t y of • B r i t i s h Columbia, I agree that the Li b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study* I further agree that per-mission for extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by hi s representatives. I t i s understood that copying or p u b l i -c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my wr i t t e n permission* Department of The U n i v e r s i t y of B r i t i s h Colombia, Vancouver 8, Canada Date 3g /9£<+ 7 ! : ~ ABSTRACT The products from a gaseous r . f . electric discharge i n ammonia have been studied using electron spin resonance spectroscopy. A paramagnetic species from the discharge was detected and the results were consistent with i t being the imine (NH) free radical. The E.S.R. Spectrum fi t t e d the theoretical treatment and was similar to that observed for NH i n a frozen matrix. No other radicals could be detected i n the discharge except for the atomic species. The low pressure gas phase E.S.R. spectrum of *%1602 w a s a l s o studied. The results showed that at low pressures the spectrum becomes exceedingly complex. A partial assignment of lines was made from the results of a simplified treatment of the theory. The work served a further purpose i n developing experi-mental techniques for the study of unstable free radical species i n the gas phase. ACKNOWLEDGMENTS I would like to express my deepest thanks to my research director, Dr. J. B. Farmer, for his continuing guidance and enlightening discussions during the course of this work. I would also like to thank Professor C. A. McDowell for suggesting the work on nitrogen dioxide. The assistance of the many technicians i n the depart-ment was also greatly appreciated. In particular, I would like to thank Mr. J. Sallos, of the electronics department, for his untiring efforts i n keeping the spectrometers at peak performance. Thanks are also due for Mr. P. Horn, the members of the glass blowing department, and to Mr. R. Muelchen and technicians of the mechanics shop for their helpful assistance i n preparing and assembling the gas flow system. Finally, I would like to acknowledge the receipt of two assistantships from the Department. TABLE OF CONTENTS PAGE INTRODUCTION A. Preliminary Remarks. . . . . . . . . . . . . . I B. Basic Theory of E.S.R. . . . . . . . . . . . . 3 a) Resonance Conditions 3 b) Hyperfine Structure. . . . . . . . . . . . 4 c) Linewidths 5 d) Relaxation 6 e) Saturation . . . . . . • . . 8 f) Doppler Effect . . . . . . . . . . . . . . 8 EXPERIMENTAL A. Electron Spin Resonance Spectrometer . . . . . 10 a) 100 Kc. X-band E.S.R. Spectrometer • . . . 10 b) Accessory Equipment. 11 B. Gas Flow System 12 C. Gas Purification • . . . . . . . . . • • • • . 16 RESULTS PART I. THE GAS PHASE E.S.R. SPECTRUM OF THE PRODUCTS OF AN R.f. ELECTRIC DISCHARGE IN AMMONIA A. Introduction 18 B. Theory of the Imine Free Radical . . . . . . . 19 C. Experimental Results . . . . . . . 21 D. Discussion of Results. • . • 23 PAGE PART II. THE LOW PRESSURE GAS PHASE E.S.R. SPECTRUM OF 1 4 N 1 6 0 2 A. Introduction • • • . • . • . . . . . . . . . . 33 B. Theory (The 1 4 N 1 6 0 2 Molecule). . . . . . . . . 37 C. Experimental Results • 44 D. Discussion of Results. . . . . . . . . . . . . 47 CONCLUSION. . . . . . . . . . . . . . . . 57 BIBLIOGRAPHY. . . . . . . . . . . . . . . . . . . . . . . 60 TABLE OP ILLUSTRATIONS Figure 1. Block diagram of the 100 Kc. ESR spectrometer. 2. Diagram of the gas flow system. 3. Diagram showing the arrangement of the sampling leak and cavity. IL, ESR spectrum of the gaseous electrical discharge products of ammonia at high pressures. 5 . ESR spectrum of the gaseous electrical discharge products of ammonia showing the doublet structure. 6. ESR spectrum of the gaseous electrical discharge products of ammonia showing the overlapping t r i p l e t structure. 3 _ 7. Variation of the t r i p l e t splitting i n the ^ ground state of NH. 8.. Energy level diagram for the N - 0 and N = 1 rotational states of NH. 9. Populations of the rotational energy levels of the ground state of NH at 300°K. lii. 16 10. ESR spectrum of gaseous N 0 at 0.6 ram. pressure. Ik 16 2 11. ESR spectrum of gaseous N 0^ at 0.3 mm. pressure. 12. ESR spectrum of gaseous 1^N1^0 at 0.1 mm. pressure. 13. Populations of the rotational energy levels of the ground state of "^If^Q at 300 °K. 14. ESR spectrum of gaseous ^"N^Qg at 0.2 ram. pressure and a part i a l theoretical spectrum of the stronger lines. INTRODUCTION A. PRELIMINARY REMARKS The study of unstable transient chemical species, such as free radicals, can yield considerable information about chemical processes and can contribute to a deeper insight into atomic and molecular structure. The important role and the degree i n which free radicals play a part i n chemical reactions are only now being f u l l y realized by chemical re-searchers. Although techniques did exist many years ago for the study of free radicals, the experimental d i f f i c u l t i e s , due to the short lifetimes and extremely reactive nature of these species, greatly hampered workers i n this f i e l d . With the introduction, i n 1945, (1) of the technique of electron spin resonance spectroscopy,*" another powerful tool for the determination and study of paramagnetic species was added. Although investigations using ESR have been applied to a variety of paramagnetic species, such as transition metal ions, triplet-state molecules, odd-electron molecules, radiation-*There exists some confusion i n the literature as to the naming of this technique. It has been called by various workers as electron spin resonance (ESR), electron paramagnetic resonance (EPR and EPMR) and simply paramagnetic resonance (PMR) although, s t r i c t l y , the latter includes nuclear magnetic resonance also. In this work the name electron spin resonance, which i s abbreviated to ESR, w i l l be used. 2. damaged crystals, atomic species, semiconductors and others, the study of free radicals has been particularly important. It has furnished a wealth of information on the identity of species, molecular geometry and structures, interactions of the species with the environment and on energy transfer processes etc. Most ESR work on unstable free radicals has been per-formed by isolating the components i n a frozen inert matrix at low temperatures, thereby prolonging the lifetime and increasing the concentration of these reactive species. The constraining action of the r i g i d medium and the decrease i n thermal activity can effectively prevent the recombination of the entrapped radicals. But by this very action, the trapped radical must necessarily have some interaction with the trapping medium. These perturbations of the environment can severely modify and complicate the spectrum i n some cases by distorting and broadening the spectral lines. Also the possibility of multiple trapping sites (2,3), due to radicals occupying different locations i n the matrix, can confuse the interpretation of the spectra. Hence i t would be very desirable to produce, detect and study free radicals i n the gas phase, free of any matrix interactions. 3. The study of paramagnetic species i n the gas phase using ESR has been very limited, possibly the result of the experimental d i f f i c u l t i e s involved with these highly reactive species* Beringer and Castle carried out the f i r s t studies on the stable paramagnetic gases oxygen (4), n i t r i c oxide (5), and nitrogen dioxide (6). These were soon followed by similar studies on gaseous atomic species produced in discharge flow system, hydrogen (7), oxygen (8) and nitrogen (9). Since then other studies have been carried out on atomic iodine (10), fluorine (11), chlorine (12), bromine (13), and phosphorus (14). The study gas phase free radicals has been limited to difluoramino (NF 2) (15) and, using electric dipole EFR spectroscopy, OH, OD (16) SH, SD and SO (17). This research was thus undertaken i n an attempt to further knowledge, i n this badly neglected f i e l d of ESR studies, by detecting new paramagnetic species i n the gas phase and by studying the complexities that arise i n interpreting the results, as exemplified by the work on nitrogen dioxide. B. BASIC THEORY OF ESR (a) Resonance Conditions The unpaired electrons of paramagnetic species have a resultant spin angular momentum of v/s(S + 1)' giving rise to a magnetic moment s(s + l)' (o.i) where g is the gyromagnetic ratio (g = 2.0023 for a free electron) and ft is the Bohr magneton ( = ^ T m c ) . In the presence of an external magnetic f i e l d H, the magnetic dipoles w i l l orient themselves with respect to the f i e l d , that i s , the degeneracies associated with the magnetic quantum numbers are removed and the energy levels are s p l i t into a number of Zeeman components. The energy Spin Hamiltonian is given by X s = -g/^/(H • S) (0.2) the eigenvalues giving the energy levels ( E = g/3H2M s) (0.3) Transitions between pairs of these component levels are generally allowed for magnetic-dipole radiation, with the selection rule A Mg = - 1 . The transitions may be induced by applying radiation at the Larmor frequency JJ0 (f>^o= gyS H z ) which i s polarized with i t s magnetic vector perpendicular to the magnetic f i e l d H z . The frequencies of these transitions l i e i n the microwave region for magnetic f i e l d strengths (H z ) of a few thousand gauss. (b) Hyperfine Structure When an unpaired electron interacts with a nucleus having a nuclear spin, there w i l l be a further splitting of the energy levels giving rise to a hyperfine structure. In a magnetic f i e l d the spins are uncoupled and hence the nuclear spin angular momentum i s quantized separately from the electron spin angular momentum. The energy spin Hamiltonian i s now given by where the effect of the second term i s to s p l i t each energy level into (21 + 1) components corresponding to the different values of Mj. The coupling constant for the spin-spin interaction, A, consisting of an isotropic and an anisotropic part, i s electron-configuration dependent and i s a direct measure of the interaction of the unpaired electron with the nucleus. The selection rules governing the magnetic dipole transitions are given by A Ms = - 1 and A M x = 0. phase ESR spectral line shape and linewidth. The interest i n the linewidth arises because by reducing the linewidth there i s the possibility of observing fine or hyperfine structure that might otherwise be lost. Also, the linewidths of resonance lines give considerable information on the various interactions that are present. The line width of gas phase ESR spectral lines are dependant on: (0.4) (c) Lfrnewfrdths There are several factors which affect the gas 6. 1) Natural line width 2) Spin-lattice interaction and relaxation times 3) Spin-spin interactions 4) Unresolved fine or hyperfine structure 5) Saturation effects 6) Doppler effects The natural line width arises from the Heisenberg Uncertainty principle (18). Since the paramagnetic species spends a f i n i t e time, ( A t ) , i n a given energy state, the measurement of the energy must be uncertain by an amount ( AE) where ( At AE 5£ £ ) (0.5) It has been shown (19) that ( = — y 1 ) cps (0.6) i/^imn/2) i s the magnetic dipole matric element and for the microwave region the magnitude of half-line width i s about 10" 4 cps, which i s negligible. (d) Relaxation Since the transition probabilities for induced absorption and emission are equal, i t i s only because of the 7. 2 population differences of the energy levels that there i s a net absorption of energy from the incident radiation. In order for the resonance absorption of radiation to continue, there must be mechanisms, apart from stimulated emission, by which the electron spins in the higher energy state can lose energy and drop back to the lower energy state. Such mechanisms which allow the electron spins to transfer energy by interaction with some system other than the incident radiation, are termed relaxation processes. The usual relaxation processes are the spin-lattice relaxation and the spin-spin relaxation mechanisms, the latter being unimportant for electron magnetic resonance except in a few special cases. Spin-lattice relaxation occurs by the transfer of energy from the spin system to the surroundings (lattice) during a time T„ the spin-lattice relaxation time. In the gas phase, the only mechanisms available for the exchange of energy to the surroundings are those involving the fluctuating magnetic fields produced by molecular motion and those involving changes in the rotational energy state. Since both 2 The population distribution of the energy levels i s given by the Boltzmann distribution (#2 - exp (-j^E) where 97 1 k T N £ i s the number of electron spins in the upper state and the number i n the lower state. Since at room temperature N 2 / N ^ i s slightly less than unity, there w i l l be a greater number of spins i n the lower state. 8. these processes depend on molecular motion, collisions between the paramagnetic species are very important. Thus the gas pressure w i l l strongly affect the spin-lattice relaxation time and hence the linewidth of the spectral lines. Such effects are commonly known as " c o l l i s i o n broadening" or "pressure broadening". (e) Saturation Saturation occurs when the equilibrium population of the energy levels is disturbed, with the result that the population differences between the upper and lower states equalize and there i s no net absorption of energy. This can occur by the use of excessive microwave radiation whereby the rate of transition exceeds the rate of relaxation. It can be seen that the amount of microwave power necessary to cause saturation depends on the spin-lattice relaxation time, being less for long values of T^. (f) Doppler Effect The Doppler effect i s the name given to the change i n frequency that results when a molecule has a component of velocity i n the direction of the propagation of the radiation. The s h i f t i n resonant frequency i s propor-tional to the zero molecular velocity resonant frequency multiplied by the rate of the molecular velocity component i n the direction of radiation propagation to the propagation velocity (approximately the velocity of l i g h t ) . The magnitude of the Doppler effect contribution to the line width i s usually quite small, as for example, i n N©2 where i t was estimated to be about 17 Kcps at room temperature (20). 10. EXPERIMENTAL A. ELECTRON SPIN RESONANCE SPECTROMETER (a) 100 Kc. X-Band ESR Spectrometer The electron spin resonance spectrometer used i n these investigations was designed and b u i l t i n this laboratory. The 100 Kc. X-band spectrometer i s similar to the Varian V-4500 ESR spectrometer but with several improvements giving greater sensitivity and s t a b i l i t y . A block diagram of the spectrometer i s shown i n f i g . 1. The microwave power i s provided by a water-cooled V-153C Klystron Oscillator which delivers approximately 300 milliwatts over i t s tuning range 8.6 to 10 Gc/sec. The klystron frequency i s stabilized by an automatic frequency control (AFC) system which locks the klystron on the resonant frequency of the cavity. The klystron i s coupled to a wave guide which transfers the microwave output via a magic-T bridge and accessory equipment to a rectangular reflection type cavity that resonates i n the T E Q ^ mode. The accessory equipment includes a Polytechnic Research and Development Co. Model X375A Variable Attenuator, Model X870A Slide Screw Turner and Model X910A Terminating Load and Directional Coupler. TERMINAL L O A D REFLECTOR P O W E R S U P P L Y KLYSTRON PHASE SHIFTER ISOLATOR A T T E N -UATOR MAGIC T E E HMR P R O B E C A V I T Y — . . IODULATION C O I L S M A G N E T COILS ••• CRYSTAL DETECTOR IQO Kc RECEIVER MAGNET-OMETER C R 0 100 Kc O S C I L L -ATOR SIGNAL GE^ERATOF FREQUENCY COUNTER 100 Kc MODULATOR; PHASE SHIFTER PHASE DETECTOR RECORDER 4— i N T E -GRATOf? FIGURE I : B L O C K DIAGRAM OF 1 0 0 Kc. E.S.R. S P E C T R O M E T E R 11. The microwave cavity i s situated i n the 2.5 inch gap between the poles of a 6-inch Varian electromagnet that supplies the variable magnetic f i e l d (the microwave frequency being held constant). The cavity was placed such that the length was i n a ver t i c a l position between the magnet poles, thus allowing a horizontal flow system to be used. A 100 Kcps modulating magnetic f i e l d is superimposed on the changing magnetic f i e l d by a pair of auxiliary coils mounted one on each side of the cavity. The resonance absorption signal i s detected by a microwave crystal detector using a s i l i c o n diode which i s situated in one of the arms of the magic-T bridge. The signal is then passed through an amplifying system to a phase sensitive detector and then to a Leeds and Northrup "Speedomax" recorder which graphically records the f i r s t derivative absorption signal. The sensitivity of the -13 spectrometer i s approximately 3 x 10 AH moles of electron spins where AH is the peak width. The spectrometer could also be used with 400 cps f i e l d modulation but the sensitivity i s fifteen times less. (b) Accessory Equipment The magnetic f i e l d was measured by using a proton resonance magnetometer. The magnetometer consists of a probe 12. c o i l containing glycerol which i s inserted i n the magnet gap beside the cavity. The c o i l i s connected to a marginal oscillator which i s frequency modulated at 20 cps. The proton resonance signal i s displayed on an oscilloscope and then a General Radio Co. Model 1001-A Signal Generator i s tuned to zero beat. The frequency of the signal generator i s then measured by a Hewlett-Packard Model 524B electronic Counter. The microwave frequency was measured using a Hewlett-Packard Model 540-A transfer oscillator that was tuned to zero-beat with a microwave frequency harmonic. The frequency of the oscillator was measured with the electronic counter. The microwave power was measured using a Hewlett-Packard Model 430-C Microwave Power Meter. B. GAS FLOW SYSTEM A schematic diagram of the gas flow system i s shown i n f i g . 2. The gas flow system consisted of a vacuum system assembly for gas purification and storage, a Welch 1397B mechanical pump having a 375 l i t e r per minute pumping speed and an o i l diffusion pump, backed with a small rotary mechanical pump, having a pumping rate of about 20 l i t e r s per second. The vacuum system assembly consisted of large gas storage bulbs, two vacuum lines with cold traps for gas puri-GAS S T O R A G E BULB THERMOCOUPLE •VARIABLE LEAK METAL VALVE THERMOCOUPLE ^ • T O 360 b/MIN. MECH. PUMP IONIZATION GAUGE ] Oil! L _ T \ •"MFFUS"^' PUMP DIF USION., 2> M E C H -CAPILLARY LEAK F I G U R E 2 . S C H E M A T I C DIAGRAM OF G A S F L O W S Y S T E M . 13. fication and a mercury diffusion pump backed by a small rotary pump for pumping the system down. The gas flow from the vacuum system went via 3/4 inch flexible metal tubing to the 10mm. diameter s i l i c a tubing passing through the micro-wave cavity. In some experiments using a sampling leak, only a small amount of the gas discharge products were passed through the cavity, the main flow of gas being pumped away by the 375 l i t e r per minute mechanical pump. In these cases the gas flow through the cavity was maintained by the o i l diffusion pump. In front of the mechanical pump a liquid nitrogen cold trap was provided to prevent fouling of the pump o i l by condensable vapours. In a l l cases the portion of 10mm. diameter tubing passing through the cavity was made of "Spectrosil" fused synthetic s i l i c a . This was found to be necessary since pyrex glass has a high loss constant i n an 3 electric f i e l d which would lower the Q of cavity by an objectionable amount and ordinary s i l i c a was found to be unsatisfactory (21). Under very high sensitivity i t was found to give a resonance at about g = 2 . This has been observed The Q of a cavity (Quality factor o*| Q-factor) i s defined as Q _ OJ (energy stored) = (*> U V and gives an ^ average energy loss W indication of the sharpness of response of the cavity near resonance. Thus the sensitivity w i l l depend on the Q of the cavity. FIGURE 3. DIAGRAM SHOWING T H E A R R A N G E M E N T OF THE SAMPLING L E A K AND CAVITY. 14. by other workers, for example (22, 23) who have invoked a variety of explanations, the most lik e l y being the presence of impurities. The Spectrosil s i l i c a , having less than 0.3 ppm of known impurities, did not give any background ESR spectrum. Spectrosil, produced by the Thermal Syndicate Ltd. of England, i s a synthetic fused s i l i c a that i s much superior in many respects to ordinary s i l i c a made by fusing natural quartz crystal. Its chief advantage,in this work, was the low content of paramagnetic impurities known to be present. The known impurities i n ppm (parts per million), as given by the manufacturer, as Fe (<0.1), Ca (<0.1), Na (0.04), A l (<0.02), B (<0.01), Ga (< 0.004), K (< 0.004), P «0.001), Mn (< 0.001), Cu (< 0.0002), As (< 0.0002) and Sb (< 0.0001). Even when irradiated with large doses of gamma rays, X-rays, or by pile radiation, very few paramagnetic centers are produced (up to 500 times better than some ordinary s i l i c a ) . ^ Although not too widely known as yet, this s i l i c a has possible uses i n many experiments requiring very high purity s i l i c a . Ground glass joints were used i n the system and metal to glass Kovar seals were used to join the flexible metal This information i s that given by the manufacturers. 15. tubing to the glass system. A^piezon-L stopcock grease was used on the system except when experiments with nitrogen dioxide were done. When using NO2 i n the system, the joints and stopcocks were greased with Kel-F No. 90 grease which was found to be more resistant to attack by NO2 • The gas samples were fed into the storage bulbs from the commercial gas cylinders via flexible "Nalgon" P73-223 tubing. When using the o i l diffusion pump, i t was possible to -6 obtain a vacuum of less than 5 x 10" mm. of Hg i n the flow system. The dissociation of ammonia was accomplished i n an electrodeless radio-frequency e l e c t r i c a l discharge. The t . f • power was obtained from a 6.2 Heps U.S. Army surplus radio transmitter (BC-458-A) which was modified for use i n the laboratory. The transmitter was powered by a Kepco Model 1250 B voltage regulated DC power supply operating at approxi-mately 800 volts and 125 milliamps DC . The transmitter was capable of delivering approximately 100 watts to the 1 cm. wide copper strip electrodes wrapped around the s i l i c a flow tube i n front of the cavity. The two electrodes were separated by about 3 or 4 cm. but the discharge extended over a much larger region depending on the pressure and flow rate of the gas. By careful grounding and shielding of the r . f . discharge i t was 16. possible to get almost no interference with the ESR spec-trometer. To prevent excessive heating of the flow tube near the cavity, a stream of cold a i r was directed against i t i n the region of the discharge. No surface coatings were used on the flow tube to inhibit wall recombinations. Many workers have found that the use of a surface coating to "poison" the glass surface would prolong the lifetimes of atomic species such as N, 0 and H. The most common coating used for this purpose has been metaphosphoric acid although i t s actual role i n preventing recombinations i s not known definitely. In these experiments no surface coatings were used because i n the region of the cavity most coatings would lower the Q-factor of the cavity and also the. presence of any acid coating would cause a re-action with the ammonia gas. C. GAS PURIFICATION The gases used i n these experiments were obtained from commercial high pressure tanks supplied by Matheson Co. No further purification was done to the anhydrous ammonia obtained from the cylinder. However, i n the case of nitrogen dioxide there was a noticeable amount of impurities, mainly other oxides of nitrogen. The purification of NO2 17. consisted of mixing oxygen with the gas overnight and sub-sequently removing the excess oxygen by freezing the NO2 i n a trap of carbon dioxide-acetone. Several trap to trap vacuum d i s t i l l a t i o n s were then performed u n t i l the frozen nitrogen dioxide crystals were white or whitish-yellow, indicating a relatively pure sample. Any traces of other oxides of nitrogen could be readily noticeable due to their bluish or greenish colour i n the solid. The f i r s t and last 10 per cent portions of the prepared NO2 were not used. In spite of the purification, small amounts of n i t r i c oxide and oxygen were probably s t i l l present due to the slowly established equilibrium between nitrogen dioxide and n i t r i c oxide that takes place. 18. RESULTS PART I. THE GAS PHASE E.S.R. SPECTRUM OF THE PRODUCTS OF AN R.f. ELECTRIC DISCHARGE IN AMMONIA A. INTRODUCTION Studies on the photolytic and electric-discharge products of ammonia and similar hydrogen-nitrogen compounds have given evidence for the existence of several unstable intermediate species. The presence of N H 2 free radicals is almost a certainty but there has been some controversy over the supposed isolation of the NH (imine) free radical. Work by Funke (24) on the thermal decomposition of ammonia, by Ramsay (25) on the flash photolysis of hydrazine, y by Thush (26) on the flash photolysis of hydrazoic acid and by Dixon (27) on the flash photolysis of HCNO have given consi-derable evidence for the existence of NH in the gas phase. The results indicated that the NH radical has a ground state and i s , therefore, paramagnetic. Studies have also been carried out, using optical means on the detection of the NH radical trapped i n a matrix at low temperatures. Such work has been carried out on the discharge products of ammonia and hydrazine (28, 29) and the results showed the presence of both NH and N H 2 radicals. 19. Since both NH and N ^ radicals are paramagnetic they should be suitable for study by ESR. Such studies, thus far, have confirmed the existence of NH£ bug have only indicated inconclusively the presence of NH. When Cole and Harding (30) studied the el e c t r i c a l discharge products of ammonia frozen at 4.2°K they could only detect the presence of atomic hydrogen and atomic nitrogen. However, similar work by Foner et a l (31) using an inert gas matrix showed, i n addition to the atomic hydrogen and nitrogen, a nine line spectrum that could be assigned to NH2 and a broad unresolved underlying resonance near the free-electron value which they could not explain. Gardner (32) recently obtained a similar spectrum from the U. V. irradiated hydrazoic acid at 4.2°K. He tenta-tively assigned this broad underlying resonance to the NH radical undergoing slightly hindered free rotation i n the matrix. B. THEORY OF IMINE RADICAL (NH) The imine radical, like the oxygen molecule, has a t r i p l e t ground state ( X ) which even i n the absence of an external magnetic f i e l d is s p l i t due to the three spin com-ponents. This s p l i t t i n g , termed zero-field s p l i t t i n g , i s the result of spin-spin interaction and spin-orbit interaction, although for orbitally non-degenerate molecules like NH, the latter term vanishes. 20. The spin-spin interaction can be thought of as arising from the classical Interaction of the magnetic dipoles of the electrons. Assuming the t r i p l e t state can be described by a two electron t r i p l e t state function, the Hamiltonian representing this interaction i s given by (33) Further simplification of equation (1.1) can be made by transformation into the principal axes coordinate system and from the fact that and S 2 couple to give a resultant spin S> with $ = 1 • Thus we get )-{ = D(S, 2 - V 3 s 2) + E(S X 2 - Sy 2) (1.2) where D = 3/4 g 2 ^ 2 ) < ^ 1 2 ^ * f U y - 2( ^ l ) (1.3) and - 3/4 « 2 < / » ^ ) ( Y " ^ 2 \ d . 4 ) The terms D and E are termed the zero-field spl i t t i n g or spin-spin interaction parameters. For molecules having axial symmetry, the term i n E vanishes because of the equivalence of the X and Y axes. In the presence of an external magnetic f i e l d we get further splittings due to the interactions of the different 3 magnetic moments present. For a molecule i n a ( £ ) ground 21. state having axial symmetry, which i s the case for NH, the approximate Hamiltonian, i n the presence of an external f i e l d , i s given by y~C= ZBk • §) + D(S Z 2 -1/3 S 2) + A(S • I) + K(S .N) (1.5) where the terms represent, respectively, the electron spin interaction with the external f i e l d , the electron spin-spin interaction, the electron spin-nuclear spin interaction and lastly the spin-rotation coupling interaction. The ESR spectrum of NH could, i n general, be quite complicated depending on the relative magnitudes of the various inter-actions present. These w i l l be discussed later. C. EXPERIMENTAL RESULTS When the products from an yS. electric discharge i n ammonia were passed through the microwave cavity, i n a gas flow system, a broad resonance spectrum near the free-electron value was obtained. This ESR resonance signal was very dependent on the conditions of the experiment, namely, the pressure i n the flow system and the position and power of the r . f . discharge. At high pressures (in the range of several millimeters of Hg pressure) the spectrum consists of a single large resonance line which spans a region of several hundred gauss. 22. The actual line width of this resonance at high pressures i s about 60 gauss. As the pressure i s lowered, the resonance line decreases both i n intensity and i n linewidth as shown i n f i g . 4. In these spectra, the hydrogen atom resonance signals can be noticed on either side of the main absorption line, the separation between the hydrogen lines being about 500 gauss. When the pressure was lowered even more (less than 0.1mm of Hg) the single resonance line could be resolved into a doublet with a possible overlapping signal near the center, as i n f i g . 5. The separation between the components of the + doublet i s about 22.0 gauss (-0.5 gauss) and the linewidths of the components is about 7.8 gauss (-0.5 gauss). When the position of the r . f . discharge was moved closer to the microwave detection cavity, the central portion of the spectrum enhanced and could be resolved into a t r i p l e t structure ( f i g . 6.). The separation of the components of the tr i p l e t being estimated at about 3-4 gauss. It was not possible to further resolve the components of the doublet by lowering the pressure more. Any further decreases i n pressure could not be made since the r . f . elec-t r i c a l discharge could not be sustained at these low pressures. Although the pressures i n the cavity region could not be measured directly, i t was estimated that the lowest pressures 5 0 0 G A U S S 30 GAUSS I J (e) <v I mm. Hg PRESSURE (f) LOWER PRESSURE FIGURE 4 (CONTINUED) S P E C T R U M AT HIGH P R E S S U R E USING A SLOWER SCANNING R A T E . 10 GAUSS I I 9297 .8 Mcps. 3290.0 3310.0 3330 .0 3350.0 H (GAUSS) • 3370 .0 FIGURE 5 E S R S P E C T R U M OF THE GASEOUS E L E C T R I C A L DISCHARGE P R O D U C T S OF AMMONIA AT- LOW P R E S S U R E ( L E S S THAN 0.1 mm. Hg) SHOWING THE DOUBLET S T R U C T U R E . A/ 50 GAUSS I ; ; I (a) L E S S THAN 0.1 mm. Hg PRESSURE. (b) HIGHER PRESSURE ( > I mm. Hg PRESSURE FIGURE 6 . E S R S P E C T R U M OF THE GASEOUS ELECTRICAL DISCHARGE PRODUCTS OF AMMONIA SHOWING THE OVERLAPPING T R I P L E T S T R U C T U R E . (discharge close to cavity) 23. obtained i n these experiments were of the order of 50 microns of mercury or less. In order to obtain even lower pressures, an attempt was made using a sampling leak arrangement whereby the dis-charge could be run at higher pressures, but only a small amount of the discharge products were passed through the cavity. However, this attempt was not successful, probably due to the molecular fragments reacting or reeombining on the o r i f i c e of the leak. D. DISCUSSION OF RESULTS The broad resonance spectrum obtained from the study of the el e c t r i c a l discharge products of ammonia has tentatively been assigned to the imine free radical (NH) i n the gas phase. The results are consistent with those predicted theoretically for the NH free radical and are similar to those obtained i n the solid phase (32). As shown previously the approximate spin Hamiltonian of 3 a ( 21 ) ground state molecule, like NH, i s given by equation (1.5). H = g(ye>>(H/S)+ D(S Z 2 -1/3 S 2) + A(S«I)+ K(S»N) Since the electron spin magnetic moment i s much greater than the rotational magnetic moment, the last term can be neglected for approximate calculations (32). 24. The imine radical, having a ground state, should be approximated by a Hunds case (b) coupling scheme i n which N i s the rotational quantum number (arising from the end over end rotational momentum of the molecule) and S i s the total electronic spin momentum quantum number. Since both S and N are good quantum numbers, S and N can couple further to give J , the total resultant angular momentum. J = (N+S), (N+S-l) (N-S) (1.6) Since S = 1 for NH, this gives rise to three J levels (spin multiplets) for each value of the rotational quantum number N. J = N+l, J = N, J = N-l (1.7) In general, these spinpmultiplets are non-degenerate, being s p l i t by the spin-spin Interaction. The split t i n g of the spin multiplets due to the spin-spin interaction was derived by Kramers (34). He found that for a l l N $ 0 the spin multiplets are s p l i t , the spl i t t i n g being dependent on the value of N. But for the case of N = 0 , there i s an averaging of the rotational wave function over a l l directions leading to a vanishing of a l l the terms i n the spin-spin Hamiltonian. Thus there i s no spin-spin splitting for N = 0 and i t i s non-degenerate except for a three fold spin degeneracy. For N f 0, the energy of the rotational states J = N + 1, H = N 25. and J = N-l are given respectively by Fi<N) = N(N+1) + (2N+3)B^ - ?\l - ^ 210-3)2B^ 2 +^2^2'\hI + V ( N + 1) (I.8-a) F 2(N) = B^N(N + 1) (I.8-b) F 3(N) = B p N(N +1) - (2N-1) B „ - "XL+ y(2N-l) 2B^ 2+ ^ - l ^ -Y l(N) (I.8-c) where ( ^  ) = D/2 and ( V ) are the spin-spin splitting 2 2 constants. More correctly, the term Dp N (N+l) should be subtracted from these equations i f centrifugal distortion effects are to be considered. Herzberg (35) has shown that for large values of B/^J , the formulae can be approximately replaced by F t(N) = B>N(N-f 1) - 2 2 ^ 3 ' f l ) + Y(N+1) (I.9-a) F 2(N) = B^ N(N+1) (I.9-b) F 3(N) = B ^ N + l ) - - Y N (I.9-c) Using; the values of Dixon (27) for NH, Bo = 16.3454 - 0.0015 cm"1 A = 0.928 - 0.007 cm"1 (1.10) Y = -0.053 - 0.002 cm"1 1 26. the spin-spin sp l i t t i n g was calculated for various N values as shown i n f i g . 7. When an external magnetic f i e l d i s applied the (2J+1) degeneracy of the different J levels w i l l be removed giving the Zeeman levels characterized by Mj (Mj = J, .....-J). The energy of this Zeeman spl i t t i n g i s given by *k 3 - -8j</3)HMj (1.11) providing we are not i n the Paschen-Back region, that i s , providing the separation between levels of different J i s large i n comparison with the Zeeman spl i t t i n g of the individual levels. The appropriate value of gj can be obtained from the expression (32) g T . g N + 2 <sij> (1.1.2) SJ SN j ( J + 1 ) + j(j+i) Since g N i s small and <(s • J^ > = J 2 + S 2 - N 2 ,2 . „2 „2 8j ^ i + S - N J(J+l)+St'S+l)-N(N+l) J 2 J(J+1) (1.13) For the case of NH where S = 1, the N = 0 rotational level has gj = 2 and for N = 1 gj = 1 for a l l values of Mj. The energy levels for the N = 0 and N = 1 rotational states have been shown in f i g . 8. 0 2 4 6 8 10 12 14 16 18 20 2 2 24 26 28 30 32 3 4 3 6 38 40 ROTATIONAL QUANTUM NUMBER (N) FIGURE 7. VARIATION OF THE T R I P L E T S P L I T T I N G IN THE 3 GROUND STATE (v = 0 ) OF NH, . ( B 0 N(N+1) subtracted from energy terms } N = I E N E R G Y ( C M _ 1 ) —I 1 i ! 1 i i — 2000 4000 6000 8000 H ( G A U S S ) 10000 - 1 . 5 N = 0 2000 —( j j 4000 6000 H ( G A U S S ) M \ \ \ 8000 10000 FIGURE 8. ENERGY LEVEL DIAGRAM FOR THE N = 0 AND N=l ROTATIONAL STATES OF N H . 27. At the temperature used i n these experiments, namely T 300°K, i t can be shown that only a small number of the rotational states are appreciably populated. The populations of the various rotational levels can be calculated from (36) T^N , O M ... , Bo N(N 1) &c v — - (2N + 1) exp (- ^ > ( 1. 1 4) and i s shown i n f i g . 9 where i t can be seen that only the rotational states with N^5 are populated to any extent at 300°K. However, when using microwave radiation of energy ( ) = 0.3102 cm"1 (9,298 Mcps) most of the allowed transi-tions between Zeeman levels, (AMj = - 1), for the different rotational states, w i l l occur at magnetic fields much greater than those used i n these experiments. At such high fields one would not expect the simple vector model of coupling to hold true and the problem becomes much more complex. Only for the N = 0 rotational state transitions would we expect to be able to observe them i n these experiments. For the N = 0 rotational state, an energy separation between the Zeeman levels (Mj = 1 <s> Mj = 0 and Mj = -l**Mj » 0) 0.3102 cm"1 would be expected to occur i n a magnetic f i e l d of about 3325 gauss. These Zeeman transitions would be observable i n these experiments and presumably one should also observe FIGURE 9 . POPULATIONS OF THE ROTATIONAL ENERGY L E V E OF THE GROUND STATE OF NH AT 3 0 0 °K, 28. hyperfine structure, i f i t i s resolvable, due to the inter-action of the electron spin moment with nuclear spin moments of the hydrogen and nitrogen nuclei. For the N = 1 rotational state, the transitions would be expected to occur at twice the g = 2 magnetic f i e l d and hence would be unobservable i n these experiments due to the limited range of the magnet used. Similarly, transitions between Zeeman levels of other rotational states would probably not be observed in these experiments. Also, transitions between the spin multiplets (A J = - 1 and AN = 0), although observable by paramagnetic resonance (37), would be possible, when using an observing frequency of 0.3 cm~\ only for some of the higher rotational states, which would be sparsely populated. With regard to the experimentally observed ESR spectrum i t can be interpreted i n terms of magnetic dipole transitions between the Zeeman levels of the N = 0 rotational of the 3— -7 ( 2^ ") ground state of the NH free radical. The partially re-solved doublet structure could be due to the hyperfine inter-action of the hydrogen nuclei (I = 1/2 for ^H). Assuming that the interaction with the hydrogen nucleus i s the greater of the two, then each component of the doublet should be composed of 29. three lines due to the interaction with the nitrogen nucleus (1 = 1 for *"4N). However, these could not be resolved i n these experiments, probably because of c o l l i s i o n broadening of the resonance lines. At high pressures, even the doublet structure was unresolvable due to the c o l l i s i o n broadening. The three overlapping lines near the center of the doublet were almost certainly due to free nitrogen atoms. These would be expected to be present i n the discharge and the spectrum of nitrogen atoms i s a t r i p l e t with a spli t t i n g of about 3.8 gauss (9). An interesting feature of the spectrum was the obser-vation that the intensities of the doublet and the overlapping t r i p l e t lines varied differently when the position of the discharge was changed. When the gas discharge was very close to the detection cavity the t r i p l e t spectrum was large i n comparison with the doublet and vice versa when the discharge was slightly farther away. This fact i n conjunction with the observation that no NH or NH,, radicals were detected when using the higher-power 2450 Mcps 125 watt microtherm unit (30,21) suggests that a mechanism similar to that observed by Foner (38) may be present. He found that by using a low power r . f . discharge (frequency of 5 - 10 Mcps range) i n hydrogen peroxide, he could obtain large concentrations of the HO2 radical, the maximum occurring for about 20 per cent 30. hydrogen peroxide decomposition. The concentration of HO2 radicals dropped off rapidly for higher percentage decom-positions. Foner proposed the idea that i n such discharges, a minature "chemical factory" was set up i n which some of the input gas i s decomposed i n the electric discharge to produce an assortment of ions, atoms, radicals and excited molecules. These species reacted further with undecomposed parent molecules giving predominantly one species as the product. Thus, although the i n i t i a l components of the dis-charge are many, within several milliseconds the system becomes considerably simplified. If a similar mechanism were operative for an r . f . discharge i n ammonia, which seems li k e l y since this mechanism has also been proposed for an electric discharge i n hydrazine (38), then this could explain the changes i n the spectrum with position and the failure to observe any radicals when using a microwave discharge. The failure to observe any spectrum which could be assigned to the NH2 radical, which should also be present to some extent, can not, at present be explained. The N H 2 spectrum which i s characterized i n a frozen matrix by nine lines, would be expected to be much more complex i n the gas phase at low pressures due to rotational coupling. The NH^  spectrum may consist of many low intensity lines which might be unobser-31. vable at the low concentrations of NH2 present. At higher pressures the low intensity individual lines may coalesce into a simpler pattern, as i n the case of N0 2 > but would not be resolvable i n the large, broadened spectrum that i s obtained experimentally at high pressures. Thus the ESR spectrum obtained from the study of the e l e c t r i c a l discharge products of ammonia i n the gas phase i s consistent with that predicted theoretically for the imine (NH) radical assuming simple vector-model coupling. Further confirmation may be obtained i f spectra can be obtained at lower pressures. Experiments using ND^  to produce the imine-d radical (ND) may also yield additional information. The hyperfine structure due to the interaction of the electron spin with the nuclear spin of the deuterium atom w i l l now 2 consist of a t r i p l e t ( 1 = 1 for D) rather than a doublet. Again, there w i l l be a further hyperfine sp l i t t i n g due to the interaction of the electron with the nitrogen nucleus. However, the hyperfine spli t t i n g due to the deuterium nucleus w i l l not be as great as in the case of a hydrogen nucleus. The nuclear spin-electron spin coupling constant for a 2 / 1 deuterium nucleus w i l l be gjj ( D>)/gN ( H) times that for a hydrogen nucleus. Since g N (2D) = 0.85738 and g N (1H) = 5.58540, then the hyperfine spli t t i n g in the case of deuterium i s 0.15350 times that for hydrogen. The observed sp l i t t i n g , 32. due to hydrogen, i n NH was about 22.0 gauss and hence in the case of ND, the hyperfine s p l i t t i n g would be about 3 - 4 gauss which would l i k e l y be lost i n the linewidth. The spectrum i n this case would probably consist of a single broad resonance line near g = 2 except at very low pressures when structure might be resolved. The spectrum would be further complicated by overlapping spectra due to nitrogen-atoms and the center line of the deuterium atom resonance, a l l of which are centered near the free electron value. 33. PART II. LOW PRESSURE GAS PHASE E.S.R. SPECTRUM OF 1 4 N 1 6 0 2 A. INTRODUCTION The i n i t i a l study of the gas phase ESR spectrum of the paramagnetic molecule NO2 was done by Castle and Beringer ( 6 ) soon after the introduction of ESR techniques. They observed the spectrum over a pressure range of 5 to 15mm. of mercury and found i t to consist of an overlapping t r i p l e t which they attributed to the magnetic interaction between the nuclear 14 magnetic moment of nitrogen (1=1 for N) and the electron magnetic moment of the unpaired spin. They also observed that at 1.3mm. of mercury the spectrum consisted of many unresolved lines. They interpreted these lines as arising from the inter-action of the electron magnetic moment with the magnetic moment due to the rotation of the molecule, i n addition to the nuclear spin-electron spin interaction. Beringer (39) noted that one should expect the nuclear magnetic dipole-electronmagnetic dipole coupling to be depen= dent on the rotational level and Lin (40) confirmed this i n his theoretical treatment. The energy Hamiltonian as given by Lin i s ")-{= -g (/^/)H«Ms + A-MsMj + B-MsM* (II. 1) where M N is the projection upon the external magnetic f i e l d direction of the molecular angular momentum jguantum number N 34. and A and B are constants, both of which are rotational-level dependent. Berger (20) studied the pressure dependence of the gas phase ESR spectrum of N02 further. At very high pressures (greater than 40 mm. of mercury) he observed only a single pressure-broadened resonance line. At lower pressures he could resolve the t r i p l e t structure, and at lower pressures s t i l l he observed a great number of lines. At the lowest pressure he studied, 0.65mm. of mercury, the spectrum was quite complex with a great number of unresolved lines. Due to the incompletely resolved spectrum and the lack of available data on the coupling constants he was not able to f u l l y interpret the results. ESR spectra of N02 i n dilute solutions of GCl^ and CS 2 have also been investigated (41) and in both cases a t r i p l e t structure was observed with the outer lines symmetrically displaced from the central absorption peak by about 300 Mcps. This sp l i t t i n g was attributed to an isotropic hyperfine interaction, namely, the Fermi Contact interaction. They found that the interaction corresponded to about 18 per cent S-character on the nitrogen atom using the assumption that the nature of the 2S-orbital i s the same as that for a nitrogen atom. The ESR spectrum of N02 trapped i n a low temperature 35. matrix has been studied by several workers using different media. Jen et a l (42) investigated N02 trapped i n an argon matrix at 4.2°K and found a t r i p l e t structure with a line separation of 162 Mcps. which they attributed to the hyperfine interaction. Although this value does not agree with that obtained i n solution work, i t i s probably the more correct value of the two. Atkins et a l (43) when using ice as the trapping medium, found a value of about 170 Mcps. for the hyperfine interaction. Zeldes and Livingston (44) irradiated crystals of NaNQ2 and found a radical which they identified as N02 with a contact interaction of 153 Mcps for nitrogen. Ard (45) previously had found a paramagnetic species with a spectrum of three equally spaced lines and a spli t t i n g com-parable with that for N02 in NaNO^ when i t was irradiated with X-rays. Adrian (46) observed that N02 was s t i l l rotating slightly i n a matrix of solid Argon and has an isotropic in-teraction Constant of 146 Mcps and a anisotropic constant of 21 Mcps. Farmer, Hutchinson and McDowell (47) have studied N02 trapped in several different inert matrices at 4.2°K. They found a variation of the hyperfine coupling constant with the different matrices used (for a C0£ matrix, the hyperfine constant A=172 Mcps; for N 2, A-154 Mcps; for Ar, A=153 Mcps 36. and for CH^, A=141 Mcps, 165 Mcps.). These variations i n the hyperfine coupling constants were attributed to matrix effects that i s , differences i n matrix interactions for the different host matrices. They also found evidence of multiple trapping sites similar to that observed for atoms (2,3). One can see that i t i s necessary to have an unperturbed system, or nearly so, i n order to obtain reasonably accurate values for the hyperfine coupling constant. Thus, a complete spectral analysis of N02 i n the gas phase, at low pressure, would be advantageous for accurate determinations of the various coupling constants. The rotational microwave spectrum of N02 was only recently obtained and f u l l y interpreted by Bird et a l (48), although they had been working on the problem for many years. An earlier attempt to obtain and interpret the spectrum (41) yielded only information on bond lengths and angles but no values for the coupling constants and harmonic force constants. The present work on N02 was undertaken with the purpose of attempting to completely resolve the low pressure ESR. spectrum of NO,, and thereby interpret and assign the lines with the aid of the recent microwave spectral data. 37. B. THEORY (THE 1 4 N 1 6 0 2 MOLECULE) The general high f i e l d spin Hamiltonian used to inter-pret the results as given by (2) i s Each of the terms of the Hamiltonian w i l l be treated separately and i t s effect w i l l be determined. ^ o i s the unperturbed spin Hamiltonian for the strong magnetic f i e l d case."* Mo= -g(//3/)(W)+ g„ f3N (i.H.) (II.3) With H taken i n the Z-direction of the laboratory coordinate system we have the components of S and I i n this direction as Msand M £ . Since M s and Mj are good quantum numbers (or almost so) and since the selection rules for the strong f i e l d case are A M s = + 1 and AM:= 0, the second term of equation (II.3) drops out and we have X o= -g Ij3l H»MS (II.4) ~y~C^ represents the spin-spin interaction, that i s , the coupling of the electron spin to the nuclear spin. "K s t= g lp>l Sn/3 „ r" 3(S.I -3(§.r)q»r)) ( I U 5 ) r 2 where r i s the radius vector joining the nitrogen nucleus to the odd electron. This describes the interaction everywhere except where the dipole-dipole approximation f a i l s . This ->That i s , the various other interactions are assumed to be small i n comparison with the interaction of the electron spin with the external magnetic f i e l d . 38. situation occurs at a distance from the nucleus (considered as a point) which i s comparable to the "length" of the electron dipole. The terra accounting for the case of the electron spin very close to the nucleus i s given by the> Fermi Contact term, ~)-( f, which w i l l be considered later. Equation (II.5) can be expanded i n a coordinate system (x, y, z) fixed i n the molecule and expressed i n terms of the components of X and S i n this frame (49). When retaining + only the matrix elements of the form AK=0 and AK=-2 i n the expansion, the spin-spin interaction term can be replaced approximately by (4$)). - 3/4/ < rv 2 - i r*> 2\ ( I Y + i I x ) ( S Y + L S J r /Av<5 - 3/4/ R Y 2 - 5 v 2 \ ( l y - i I x ) (S y - i S x ) r^ /AV6 where r x , r Y and r 2 are the three components of the unit r vector -sa- i n the molecular frame. In a strong magnetic f i e l d the angular momenta N, S and I are decoupled and become spatially quantized separately. When the magnitude of }-( 0is large compared to the magnetic fine structure interaction terms, the energy is given approxi-mately by the diagonal matrix elements of the Hamiltonian i n 39. the representation which diagonalizes M X , M S , and M N (components of I, S and N i n the direction of the external field) (40). The interactions of the external f i e l d with the nuclear moment, and with the molecular rotation magnetic moment can be neglected since these terms have no effect on the magnetic resonance transitions of A M $ = -1 and A M N = A M x = 0. With the aid of the relations I , « I X ) X > + I y V ^ + I 2 > 1 y («.7) = S X >Xj. + S Y > Y v + S*^ ?> ( I I- 8 ) I.S = 1^ S X + l y Sy + 1^ S t (II.9) where the are the direction cosines and x, y, |. and X, Y, Z are two sets of axes fixed i n the molecule and the space respectively. Lin (40) has shown the matrix elements to be (Mx M 5 MN ,K/ I'S - 3Lj S8/Mx M s M N N,K) = -2 |ll(N+l)(2N-l)(2N+3r} " 1 j}l(N+l) - 3 M N 2 J [N(N+1) - 3K2 "3 M LM S (11.10) and (M TM SM NN,K=l/(I y+ i T^)(Sy+ i S J/MtMsMNN ,K=1) = -2 jjUN-1) (2N+3)3 " 1 [NCNi 1) ~3M n 23 M XM s (11.11) Thus the Hamiltonian for the spin-spin interaction becomes 2 \ XSI= 2g I pi Su/3„ ( ^ ^ " J " ) CN<N+D "3K22 [N(N+1)(2N-1)(2N-3)] " 1 [N(N+1) -3M* 2]] ^  (11.12) where i s the Kronecker delta, that i s , ^ = 0 for /K| sfc // or = 1 i f |K|= 1 and the t modifying ^ / K I refer to the symmetric and antisymmetric combination of the symmetric top wave functions involved i n the Wang transformation (50). Since the molecule N02 i s a slightly asymmetric prolate top (51 52), K, the projection of N along the molecular axis, i s nearly a good quantum number. For N 0 2 the nuclear spin stati s t i c s (35) require that the rotational energy levels be even with respect to rotation about the C i v. symmetry axis. Thus for a given | K j only one energy state out of the pair of Wang functions (Symmetric and Antisymmetric combination of the symmetric rotor functions) can exist. For N even and |K) =1 ^ i s symmetric with respect to C i v . and for N odd and IK | =1 + i s symmetric where l/2(f(N,K=+l) + T(N,K=-1)) (II.13-a) nj j " = l/2(/ip(N,K=+l) - I]) (N,K=-1)V) (II.13-b) f i s the Fermi contact interaction Hamiltonian governing the case where the dipole approximation cannot be used. The problem was f i r s t treated by Fermi (53) but a semiclassical treatment as given by Ramsay (54) may be used. He considers a distance large with respect to the size of the nucleus and the electron, but small enough that the electron 40. » 41. density i s essentially constant over that distance. The problem i s then one of class i c a l magnetostatics where the energy of interaction depends upon the magnetization at the nucleus. Since the electron distribution can be considered constant, i t i s just equal to the probability of finding the unpaired electron at the nucleus, that i s , j.'U^(0)| 2 . Therefore K F S l 1 8 l / 3 / 8 , ^ ? ( 0 ) | 2 ( l . s ) (11.14) For the strong f i e l d case F = ( T Mx M s (11.15) where CT = ^ 3 g l ^ l gNy3^/1^(0)| 2 (11.16) Since the contribution to ~)-{ p from an S-orbital is very many times larger than that from a ^-orbital, the Fermi contact interaction can be taken as a measure of the S-character of the electron about a given atom. is the spin-rotation Hamiltonian which gives the interaction of the electron magnetic moment with the rotation induced magnetic moment. The spin-rotation interaction i s of two types: (a) the direct interaction of the electron spin with the magnetic f i e l d of the molecular rotation that i s produced by the rotating charges of the nucleus and other electrons. (b) the indirect coupling that occurs via orbital motion and the intermediary of excited orbital states. 42. The two mechanisms give similar forms of Hamiltonians and their contributions to the energy are inseparable. Lin (40) gives the approximate interactions as X Sft= &(N+lfl" 1 (N • S) gtj K. Nd (11.17) where ^  ^ j = £ji a r e t* l e coefficients which represent the sum of the two interactions. Disregarding the effect of matrix elements off-diagonal i n K, except for the states K=-l where matrix elements of the form AK=-2 must be retained and the Wang transformation used to l i f t the degeneracy of the pair, the expression for the spin-rotation interaction becomes ~XsR= X ' ^  ' (11.18) where = l/2( £^ + £ c c ) + \Ti(N+lf\ " 1 ' [5A" (^ s + ^ c c (H.19) t 1 / 4 S.Kl C^»» <"-20) where ^ 1*1 i s t n e Kronecker delta and the + correspond to the symmetric and antisymmetric combination of symmetric top wave functions involved i n the Wang transformation. For the strong f i e l d case ~ > 4 c X- M* MS < X I- 2 I> ~)-( qrepresents the electric quadrupole interaction but in view of the small nuclear quadrupole moment of the nitrogen nucleus i t s effect i s very small and may be neglected. 43. The f i n a l Hamiltonian thus becomes X • -<g//3/Ho • 2g / /3 fi. \ t ^ f y M t \ r J /Aug - 8-TT/3 /fCO / V/S/g^vM!- XM*)-Me (11.22) where f ^  = [n(N+1)'(2N-1)(2N+3)] _ 1 (n(N+1) - 3 M N 2 J • [N(N+1) -3K23 (11.23) f Y = [(2N-l)(2N+3)3 " 1 [N(N+1) -3M*i2J (11.24) 44. C. EXPERIMENTAL RESULTS The gas phase ESR spectrum of N 0^ shows a very marked pressure dependence. At very low pressures «~5mm of Hg) one obtains a spectrum consisting of many lines and as the pressure i s lowered?more and more lines are resolved, spread over a large region of magnetic f i e l d . At the higher pressures, the individual component lines are broadened and they coalesce into a simpler pattern. The central portion of the spectrum increases i n intensity, especially i n three specific spectral regions, and eventually only a t r i p l e t structure i s obtained. Berger (20) noted that further increases i n pressure resulted i n a single broad resonance line being obtained. In these experiments, the gas pressure could be varied at w i l l over the low pressure range ( < 1mm of Hg). Spectra were run at many different pressures and i t was found that the lower the pressure, the more lines that could be resolved. Since the intensity of the resonance lines also decreases with pressure, the lower limit of the pressure range was determined by the signal to noise ratio. Even at the lowest pressures used (approximately 0.1 mm of Hg) the spectrum was not f u l l y resolved. The spectrum in this case consisted of a great number of lines (several hundred) spread over a magnetic f i e l d region of several thousand gauss. The intensity of the lines 45. i n the central portion of the spectrum was the greatest, with the spectrum decreasing to the noise level on either side. Sample portions of the spectrum are shown i n fig.to, n 11 , at several different pressures. Since i t i s necessary to use as low a pressure as possible but with as high a signal to noise ratio as possible, i t i s advisable to have as high a ratio of N0£ to N2O4 as possible (N2O4 i s diamagnetic and thus does not contribute to the ESR signal but s t i l l can cause pressure broadening). The NO2-N2O4 equilibrium has been investigated by many workers i n -cluding Verhoek and Daniels (55). They obtained as the expression for the gas phase equilibrium constant Ke = a + b C?.' = P 2 / p (11.25) 'N204 N0 2/ N2O4 * ™ C S 2 0 4 " S2O4 + 1 / 2 CN0 2 = ( 2 ? t o t a l - W 2RT (11.26) The partial pressure of N02 for a given total pressure can be calculated from 2 PN0 2 = ( 2 " Wk*>-1 £-(a+{3bPt/2Rl}) + £ + * f g § & + 4 jj.-(b/2RT)J x (a + (bPt/RT)) Py"} 1 / 2 (11.27) Values of a and b may be computed for the experimental NOISE LEVEL M> = 9 2 3 4 . 5 Mcps . , H ( G A U S S ) FIGURE 10. E S R S P E C T R U M OF G A S E O U S 4 N , 6 0 2 AT 0 . 6 mm. P R E S S U R E . - 9 2 3 4 . 5 K3cps. FIGURE II. E S R SPECTRUM OF GASEOUS N O g A T 0 . 3 m m , P R E S S U R E 3150.0 3200 .0 3250 .0 3 35 0.0 3 4 0 0 . 0 3 4 5 0.0 H ( G A U S S ) • 14 16 FIGURE 1 2 . E S R SPECTRUM OF GASEOUS N 0 AT < 0 . l m m . P R E S S U R E . 46. temperature by rewriting equation (11.25) i n the form Ke = (a 0 + b 0 C°. ) exp ( '§-) (II.25-a) where a 0 and b 0 are temperature independent. Substituting values for a 6 and b 0 (20) 9 a Q = 8.54 x 10 atm. b e = 1.58 x 10 1 0atm./mole/liter and using the value AH = 14.6 kilocalories/mole (55) one can calculate the values of a and b at T = 300°K. from equations (11.25) and (II.25-a). When this i s done and one calculates the partial pressure of N02 (F N Q^) for the values of total pressures used i n these experiments, one finds there i s v i r -tually complete dissociation of N 2^4 i n t o N 0 2 • This, of course, assumes that the equations above hold true at these low pressures and that the lifetime of an N^ O^  molecule with respect to s p l i t t i n g to form 2N02 i s short. As a check, an attempt was made using a temperature of 350 K but no noticeable increase i n signal intensity could be noticed. Although the spectra obtained in these experiments are many times better resolved than by any previous workers (6, 20), the signal to noise ratio of the spectrometer limited the degree of resolvability (that i s , by limiting the lower limit of pressure that could be used). 47. D. DISCUSSION OF RESULTS In order to simplify the interpretation of the observed ESR spectrum of N02 at low pressures, i t i s necessary to have some idea of the magnitudes of the various inter-actions present. This allows one to theoretically predict the effect of the terms on the spectrum. The term ( ~}~(Sj) was found previously to be rotational state dependent. It would be helpful, therefore, to determine the degree of rotational level dependence. The rotational dependent part of the electron-spin-nuclear spin coupling constant i s expressed by <?C = < f y ^ t Sin T V * * ) (11.28) A 2 ' \ ' ' ~ • »here "\ = WpU.fi. ( (^f^X* > 2 P O <«.29> ' A 2 A 2* r Y -r* and X = 3/4 g//3/ g „y&, < \ Y 3 ^ > 2p a <".30) and the factors -f^ and "f^ as defined i n equation (11.23 and 11.24) are rotational-state dependent. Berger (20) has calculated values of and f for N02 by correcting for the amount of 2P & character of the unpaired electron. He obtains values of "A =21.8 Mcps. ""f = -8.7 Mcps. To determine the rotational state dependence of the coupling constant, the factors -p^  and - f ^ have to be con-48. sidered (equations (11.23), (11.24)) -fT = CN(N+l)-3Md 2 3 CN(N+1)-3K 2J * (N(N+1) (2N-1) (2N+3)3 "Ft = rN(N»l) - 3M«M 2 -3 [(2N-1) (2N£3)] Although -p^  depends on N, K and M N , i t i s most useful to treat i t i n terms of the M N sublevels. Values of ( "f^ • ^ and . "fc) have been calculated for different values of N, K and M N along with the relative population of the levels i n Tables I, II and III. In order to obtain the relative rotational energy level populations, i t i s necessary to consider symmetry restrictions. Although N02 i s an asymmetric-top molecule, i t i s nearly a prolate symmetric-top molecule and can be treated as such, since I B « I c • For a slightly asymmetric top molecule, K (projection of N along the molecular axis) i s s t i l l almost a "good" quantum number and a f a i r representation of the energy levels i s given by (36)". E (N, K) = N(N+1)(B+C) .+ rA-(B+C)~~| K 2 (11.31) 2 2 With K—N and A, B and C are the reciprocal moments of inertia, C A = " etc. The rotational level populations cah 8 T T 2 C 1 a then be calculated by: TABLE l a VARIATION OF ( f A ) WITH M N AND N Rota-tional Level (N) MH = 0 K = 0 (only for even N) C-^ TO Relative (Mcps)Populat'n M„ = 1 [fA.-X) Relative (Mcps) Populat/n MM = 2 (Mcps) Relative Populate 0 2 4 6 8 10 12 14 16 18 20 100 0 6.24 5.66 5.55 5.50 5.49 5.48 5.47 5.47 5.46 5.46 1.000 0.988 0.960 0.919 0.864 0.800 0.729 0.654 0.577 0.501 0.427 5.45 ~0 3.12 4.81 5.14 5.28 5.36 5.37 5.39 5.40 5.41 5.42 0.885 0.860 0.824 0.774 0.717 0.654 0.586 0.517 0.449 0.383 5.45 ^0 •6.24 2.26 3.97 4.58 4.90 5.06 5.32 5.34 5.36 5.38 5.44 885 860 824 774 717 654 586 517 0.449 0.383 o Rota-tional Level N MN = 3 > Mw =4 MM =5 l.Pv)0 Relative (Mcps) Populat'r {-pv } V Relative i (Mcps) Populat'n (•fa. A) Relative (Mcps) Populat'n 0 2 4 6 8 10 12 14 16 18 20 100 •1.98 1.98 3.44 4.14 4.52 4.76 4.93 5.04 5.11 0.762 0.729 0.686 0.635 0.579 0.519 0.458 0.398 0.339 5.43 -0 •7.93 •0.79 1.89 3.09 3.80 4.23 4.50 4.70 4.84 5.42 0.762 0.729 0.686 0.635 0.579 0.519 0.458 0.398 0.339 -4.36 -0.23 1.75 2.84 3.52 3.96 4.26 4.49 5.41 0.638 0.600 0.556 0.506 0.462 0.401 0.348 0.296 TABLE Ib Rota-tional Level (N) K = 0 (Only for even N) M* = 6 M« = 7 M M =8 (f^.JO Relative (Mcps) Populat'n ( f ^ Relative (Mcps) Populat'n ( f v ) 0 Relative (Mcps) Populat'n 0 2 4 6 8 10 12 14 16 18 20 100 mm mm -8.72 0.638 -2.76 0.600 Oao 0.556 1.69 0.506 2.56 0.462 3.30 0.401 3.74 0.348 4.06 0.296 5.39 -0 tm mm mm mm mm ' mm -5.73 0.518 -1.85 0.480 0.32 0.437 1.27 0.392 2.00 0.346 3.12 0.300 3.56 0.256 5.37 ~0 mm mm -9.18 0.518 -4.09 0.480 -1.29 0;437 0.47 0;392 1.61 0.346 2.40 0;300 .2.97 0.256 5.35 -0 TABLE H a VARIATION OF (T>/V) WITH K AND N Rota- MiM =0 Sublevel -tional K = 0* K = 1 K = 2 Level Relative Relative Relative N (Mcps) Populat'n (Mcps) Populat'n (Mcps) Population 0 0 1.000 mm _ 1 mm -4.36 0.967 • • - ma 2 6.24 0.988 3.12 0;953 -6.28 0.855 3 ** 4.36 0.932 0 0.844 4 5.66 0.960 4.81 0;926 2.26 0;830 5 mm 5.03 0.909 3.36 0.814 6 5.55 0.919 5.15 0.886 3.97 0.795 7 5.25 0.867 4.34 0;774 8 5.50 0.864 5.28 0.835 4.60 0;747 9 mm mm ' 5.31 0.806 4.76 0.721 10 5.49 0.800 5.34 0;771 4.88 0;692 11 5.36 0.743 4.97 0;661 12 5.48 0.729 5.37 0;704 5.06 0;631 13 - - 5.38 0.669 5.10 0;600 14 5.47 0.654 5.39 0.631 5.16 0;565 15 mm - 5.40 0.594 5.19 0;532 16 5.47 0.577 5.40 0.556 5.23 0;497 17 - 5.41 0.518 5.25 0;463 18 5.46 0.501 5.42 0.482 5.27 0.432 19 - mm 5.42 0.444 5.29 0;400 20 5.46 0.427 5.43 0.412 5.31 0.370 100 5.45 - 0 5.45 - 0 5.44 -0 TABLE l i b Rota- M N = 0 Sublevel tional K = 3 K = 5 K = 10 Level Relative Relative Relative (N) (Mcps) Populat'n (Mcps) Population (Mcps) Population 0 i 2 3 mm -7.26 0.700 -mm mm mm mm 4 -1*98 0.692 • - - -5 0.56 0.682 -8.39 0.405 - mm 6 1.98 0.662 -4.36 0.370 mm mm 7 2.86 0.643 -1.87 0.360 - -8 3*44 0.624 -0*22 0.348 -9 3.84 0.600 0.92 0.337 - • 10 4,14 0.577 1.75 0.323 -9.48 0.021 11 4.26 0.553 2.36 0.307 -6.97 0;021 12 4.52 0.526 2.84 0.294 -5.06 0.020 13 4.66 0.496 3.22 0.278 -3.54 0;019 14 4,77 0.472 3.52 0.263 -2.34 0.017 15 4.85 0.442 3.76 0.248 -1.37 0.016 16 4.93 0.415 3.96 0.232 -0.56 0.015 17 4.98 0.386 4.12 0.214 0.12 0.014 18 5.04 0.361 4.26 0.202 0.67 0;013 19 5.07 0.334 4.38 0.187 1.15 0.012 20 5.11 0.308 4.48 0.172 1.56 0.011 100 5.43 -0 5.41 ^6 5.29 r6 TABLE III VARIATION OF ( 4 v T ) WITH M N AND N Rota- /K/ = 1 tional MM = 0 Mn = 1 MM = 5 Level C-fV^ Relative C-P-j,-v} Relative (,-f>t) Relative (N) (Mcps) Populat'r i (Mcps) Populat'n (Mcps) Populat'n 0 1 mm' -3.48 mm 0.967 1.74 0.856 ... 2 -2.49 0.953 -1.24 0.849 -3 -2.32 0.932 -1.74 0.830 • - -4 -2.26 0.926 -1.92 0.825 - • - • 5 -2.24 0.909 -2.01 0.809 3.34 0.634 6 -2.22 0.886 -2;06 0.789 1.74 0;619 7 -2.21 0.867 -2.09 0.772 0.75 0;605 8 -2.20 0.835 -2.10 0.744 0;09 . 0.584 9 -2.19 0.806 -2.12 0.717 -0.361 -0.562 10 -2.19 0.771 -2.13 0.686 -0.70 0.538 11 -2.19 0.743 -2.14 0.662 -0.95 0.519 12 -2U8 0.704 -2.14 0.626 -1.14 0.491 13 * 0.669 -2.15 0.596 -1.28 0.467 14 * 0.631 • 0.562 -1.40 0.441 15 0.594 • 0.528 -1.51 0.415 16 0.556 -2.16 0.495 -1.58 0.388 17 0.518 • 0.462 -1.64 0.362 18 • 0.482 0.428 -1.70 0.336 19 • 0.444 0.396 -1.75 0.310 20 * 0.412 -2.17 0.366 -1.79 0.287 100 -2.18 ~0 -2.18 -0 -2.16 ~ 0 4 9 « l £ l « - (2N+1) exp ( - S g j ^ ) (H.32) However, not a l l of the rotational levels are occupied due to symmetry restrictions. Assuming the case of a symmetric top molecule with the symmetry axis as the principal axis: of the intermediate moment of inertia, the rotational wave function (^/^ ) i s symmetric or antisymmetric according to whether K i s even or odd with respect to an 180° rotation about the symmetry axis. The behavior of the total wave function with regards to any symmetry operation depends on the individual behavior of the electronic ftPe. ) ,vibrational ( / l p v ) » rotational (^/^ a n d s P i n O^s) w a v e functions ( ^ a ^ • l | j v • • ^ \ ) s ) . Since for the case of 1 4N 1^0 2 2 (1) i t i s i n the ground electronic energy state A^, which i s totally symmetric; (2) i t i s in the lowest vibrational state which i s also totally symmetric (the ground vibrational state wave function i s always symmetric); (3) i t i s planar with two identical nuclei with zero nuclear spin symmetrically disposed about the symmetry axis; then a l l those rotational levels which are antisymmetric with respect to are missing. Thus, the K=G levels w i l l be missing when N i s odd and the K levels when they are allowed, are non-degenerate. The relative rotational level 50. populations have been calculated, as shown in f i g . 13, using the symmetric top case equations, for various values of N and K at 300°K. One can see that a great number of rotational levels are appreciably populated at this temperature which leads to a very complicated ESR spectrum for N02« With regards to the rotation-dependent part of the spin-spin coupling constant ( ° 0 , one can see from Tables I, II and III that the variations of the coupling constant with!: respect to changes i n N w i l l be, i n general, quite small. This situation results i n a great number of energy levels that are nearly degenerate and hence an overlapping of the spectral lines w i l l occur. One then obtains inhomogeneously broadened resonance lines which represent groups of transitions rather than individual transitions. This i s quite evident in the ex-perimentally obtained spectrum i n which most of the resonance lines are incompletely resolved, even at the lowest pressures used. The line widths of most of the lines observed, are of the order of 2 Mcps or so and since the variation i n the coupling constant i s usually much less than this, for the more populated levels, one would not expect to be able to resolve the individual transitions. For the case of /K/=1, an analysis shows that ("P-^  -t) quickly approaches a value of-2.2 Mcps for M w =0 with variations of N and decreasing with larger M w values. Again one would not ROTATIONAL E N E R G Y L E V E L ( N ) FIGURE 1.3. P O P U L A T I O N S OF T H E R O T A T I O N A L E N E R G Y L E V E L S OF THE GROUND .STATE OF l 4 N , 6 0 AT 3 0 0 ° K , 51. expect to be able to resolve the lines corresponding to different values of N. One would expect to obtain lines, of lower intensity, closely spaced about (CT-T^ ^ ) , corresponding to the /K/=l transitions. The separation of these lines being (-p^- - If ) , may be sufficient to be resolved i n some cases. The lines, of course, again represent groups of transitions rather than individual lines. The spin rotation coupling constant . ~ - h f> 1 S/k, £ (H.33) 7 • HL. ( E * « + O ( I I- 3 4 ) • <s (e68 - ect) (U.36). and w i l l be considered next. Using the values of Bird et a l (47), € A*= 5,412.2 Mcps £ B 8 = 7.90 Mcps g c c= -95.52 Mcps one obtains values for ^ and <^ and ^ = -43.81 Mcps = (5456) K 2 Mcps N(N+1) = 25.86 Mcps P 52. For the case of K=0, the spin rotation coupling constant simply becomes ^ = ^ and under these conditions one would observe a strong central line for M N = 0 and symmetrically spaced lines of equal interval and slowly diminishing intensity for the other values of . However, when K $ 0 the situation i s more complicated since the ^ term w i l l cause a spli t t i n g of the individual M N levels, for different N values. For large values of N, the splitting between the individual N values becomes very small. Since the more highly populated rotational levels at 300°K are those with N ~ 10-20, the spectral lines w i l l probably overlap i n the majority of the cases, giving larger K 2 broadened lines ^  (^^y i s quite small for large N). The - Y extent of the spli t t i n g i s linealy dependent on MM . It also increases for increasing values of K (being proportional to 2 K ). However the intensity of the lines w i l l also decrease for the increasing values of M M and K. Thus i t can be seen i that, i n general, the spin-rotation contribution w i l l be quite complex with many individual lines of low intensity overlapping to give larger lines. Resolution of this great number of lines w i l l be extremely d i f f i c u l t , i f not impossible. In view of the above considerations, i t i s obvious that a very detailed and sophisticated treatment i s necessary i f the spectrum i s to be completely determined. Since this 53. would be beyond the scope of this thesis, only a partial analysis of the spectrum has been made, based on the spectrum of the simpler model which we have considered. A partial theoretical spectrum, based on this model and neglecting small terms and second order effects, has been determined, as shown i n f i g . IM-lcO , , ( . c ) , ^ I n this case, variations of the spin-spin coupling constant with the individual rotational levels were not taken into account but rather average values of •/}) and (-ft - "*0 were used for the different M w values considered. Similar assumptions were made i n treating the spin-rotation coupling constant. The assignments made are necessarily rough ones, i n view of the assumptions made. From the experimental spectrum and the available data the following values for the coupling constants were obtained, It should be noted that the latter value i s i n large disa obtained was comparable to f i g . I ° , i t can be seen that each of his lines was actually composed of many transitions superimposed. The value of ^  used here i s that which was determined from the coupling constants given by Bird et a l 122 - 2 Mcps (47). From the value of one may estimate P0 a 92 3 4.5 Mcps. 3100 .0 3120.0 H (GAUSS) ». 3140.0 8 10 7 -I 0 - 1 0 0 0 3160.0 3168.0 9 6 0 -I 0 0 14 16 E S R S P E C T R U M • OF GASEOUS N O g AT LOW P R E S S U R E (0.2mm. Hg) AND A P A R T I A L T H E O R E T I C A L S P E C T R U M OF THE STRONGER L I N E S . (a) REGION 3 0 7 0 . 0 G A U S S «=» 3 1 6 8 . 0 G A U S S FIGURE 1 4 ( c ) REGION 3 2 6 2 . 0 GAUSS ~ 3 3 5 7 . 3 GAUSS FIGURE: 1 4 ( d ) REGION 3 3 5 7 . 3 GAUSS — 3 4 6 3 . 3 G A U S S FIGURE 14 ( e ) REGION 3 4 6 3 3 GAUSS — 3 5 6 6 . 5 GAUSS. 54. the value of the Fermi contact constant, 0~~ . Since the orbitals involved have the same electron spin polarization, i t i s expected that <J~ and ( )\) are of the same sign (20). Therefore a value of (J~ = 128 - 2 Mcps i s obtained in these experiments. This value compares with the value of 132 Mcps as obtained by Berger (20) and 300 Mcps as obtained i n the solution work (41). The values of the Fermi contact inter-action constant obtained for NO,, i n frozen matrices, l i e i n between the gas phase and solution values. The values obtained for the low-pressure gas phase case would be expected to d i f f e r because this case corresponds closely to an unper-turbed molecular system and there i s very l i t t l e interaction from the environment (unlike the cases of the solutions and frozen matrices). One can estimate the S-character of the Fermi contact constant obtained. Dousmanis (58) has given a value for / ^ ( 0 ) / 2 for a 2S electron on nitrogen as 34 x 10 2 4cm" 3. Using this value, one obtains a Fermi contact constant of 1620 Mcps for a 2S electron of nitrogen. Thus the value of 0~ obtained i n these experiments corresponds to about 8 per cent S-character of the unpaired electron on the nitrogen nucleus. This value compares approximately with the recent microwave results of Bird et aJL (47), which give a value of 9.0 per cent S-character. A theoretical treatment (59) has predicted a value of about 10.6 per cent S-character for the 55. unpaired electron on the nitrogen nucleus. The effect of increasing the pressure i s to increase the number of collisions, which results i n a mixing of the rotational and spin states. This would result i n M N no longer being a good quantum number. One then observes lines which are broadened due to the mixing of the states. In summary, the gas phase ESR spectrum of NO2 has been studied at low pressures. Even though the spectra obtained were much better resolved than by previous workers, the best resolution obtained was s t i l l insufficient to observe a l l the individual lines. The spectrum at the lowest pressures studied consisted of several hundred lines (more than five hundred incompletely resolved lines) spread over several thousand gauss. The value determined for the spin-spin coupling constant, although a l i t t l e lower, i s i n agreement with that determined in previous studies (6, 20). Since the previous workers were more concerned with the high pressure spectrum, which consists of broadened resonance lines, their values may not be as accurate. However, the value for the spin-rotation coupling constant used i n these experiments disagrees markedly with the value used i n the previous study (20). It i s f e l t that the present value i s more correct since i t was obtained from the recent microwave work on N02 and also 56. f i t s a much better resolved spectrum than the previous worker used. By considering the simplified treatment presented in this work, one can see that a complete solution to the problem of the ESR spectrum of NG2 at low pressures, w i l l be exceedingly complex and involved. The treatment presented here would not be expected to be sufficient because "higher order" effects have been neglected along with small terms. One would have to correct for the asymmetry of the molecule by using perturbation methods. The nuclear quadrupole coupling may also have to be considered. The nondiagonal matrix elements of the magnetic coupling terms may give a large contribution when the coupling effects become large. Also, a f i e l d of 3300 gauss, as used i n these experiments, i s not large enough to conform f u l l y to the strong f i e l d case and hence the vectors I, S and N are not completely decoupled with the result that second order terms of 7"(sfc and ^/Sl_ may become quite appreciable. 57. CONCLUSION The results of this work have provided a contribution to the neglected f i e l d of gas phase electron spin resonance spectroscopy. Interest i s gradually growing in this f i e l d which can provide a wealth of information on paramagnetic chemical species that are in a nearly unperturbed system. The study of the electric discharge products of ammonia in this work, indicating the presence of a radical thought to be the inline (NH) radical, has shown the possibility of detecting unstable free radicals i n the gas phase using magnetic dipole ESR spectroscopy. The imine radical would be one of the very few unstable free radicals that have ever been detected i n the gas phase using ESR. The study of the gas phase ESR spectrum of the para-magnetic molecule ^^N^O^ shows the complexity and d i f f i c u l t y that may occur when interpreting some of the gas phase spectra. The paramagnetic molecules F O^and CIO2 probably would have similar paramagnetic resonance spectra to N02 • Likely, many of the unstable polyatomic free radicals would also have spectra like that of N02 i n degree of complexity. Much further work i s definitely needed i n this f i e l d of research. For the study of the NH radical, i t would be helpful to produce and study the ND radical from deuterated ammonia. As yet, this has not been done. It would also be interesting 58. to attempt to produce the NH radical from other nitrogen-hydrogen compounds, such as hydrazine etc. Using different techniques, such as photolysis, may also provide information on the nature of this species. In the case of ^N^O^, the studies at present have been limited by the experimental apparatus, namely the sensitivity of the ESR spectrometer. No doubt i n the future this w i l l definitely be improved upon so that further studies may be carried out. However, at present i t might prove helpful to carry out an additional study on this compound by studying *""*N^ 02 • Since the nuclear spin of *""*N i s only I = 1/2, this affords several advantages over the ordinary *"4N^02 . The spectrum of ^N^C^ would consist of only two sets of lines instead of three and each of the individual lines w i l l be more intense by a factor of 3/2. The two sets of lines would exhibit the same behaviour with respect to the nuclear spin-electron spin and molecular rotation-electron spin coupling differing only in the nuclear spin sign and small variations i n some of the coupling constants (due to the change i n atomic mass of "^ N ). The nuclear spin - electron spin coupling constant would also have to be multiplied by the factor g w ( 1 5N)/ g^( 1 4N) = -1.40624, since the nuclear g-factor differs for the case of 1 5N. Thus, the ESR spectrum of *-5N1602 would be expected to be simpler to analyze than 59. that of 1 4 N 1 6 0 2 . 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