INTERACTIONS OF GROUP 13 LEWIS ACIDS WITH HEXACHLOROCYCLOTRIPHOSPHAZENE A Thesis Presented to The Graduate Faculty of the University of Akron In Partial Fulfillment of the Requirements for the Degree Master of Science Zin-Min Tun December, 2008 INTERACTIONS OF GROUP 13 LEWIS ACIDS WITH HEXACHLOROCYCLOTRIPHOSPHAZENE Zin-Min Tun Thesis Approved: Accepted: Advisor Dr. Claire A. Tessier Dean of the College Dr. Ronald F. Levant Co-Advisor Dr. Wiley J. Youngs Dean of the Graduate School Dr. George R. Newkome Department Chair Dr. Kim C. Calvo Date ii DEDICATION To my beloved husband iii ACKNOWLEDGEMENTS First and foremost, I would like to thank my advisor, Dr. Claire A. Tessier. She has been my inspiration not only as a scientist but also as an individual. I was not one of those people who always knew what they wanted out of life. But I was lucky enough to have taken a class from Dr. Tessier as an undergraduate student. She inspired me so much that I decided to do undergraduate research the following semester. While being a research assistant in her group, I came to the realization that I wanted to be a researcher and decided to pursue a graduate degree. To me, she is an advisor, a mentor, a friend, a parent and a role-model, and I have always been able to draw strength from her faith in my ability in times of self-doubt. I would also like to thank my co-advisor, Dr. Wiley J. Youngs for his many helpful ideas and suggestions for my research. I also received a lot of help and support throughout my graduate career from several group members, past and present. I have deep appreciation especially for Dr. Matthew J. Panzner and Dr. Monica Soler. They have always shown interest in my research and have been constant sources of knowledge and support for me. I have also found help in Dr. Khadijah Hindi, Dr. Doug Medvetz, Dr. Paul Custer and Dr. Tatiana Eliseeva. I would like to thank the former group member, Dr. Amy J. Heston who had started iv the phosphazene research in our group. I would also like to thank Brian Wright, Nikki Robishaw, and Supat Moolsin for being good friends since the undergraduate days. I am thankful to Linlin Li for all her help with the NMR and for being such a good study-partner. I am grateful to have met my host-parents, Jim and Janelle Collier. They have been kindness itself to me over the years. Their love and faith in me had seen me through many difficult times in life, including the time when I had iritis and feared that I might lose my vision. I have met many other people throughout the life who have done many random acts of kindness for me and I hope to be able to pay back their kindness one day by paying it forward. I am also thankful to my parents who believed in me and let me come to the United States for my education. I understand that letting me go is a very difficult and selfless act from their part. I would also like to thank my sister, Dr. Swe Zin Tun. She has always been there for me and has shared my pain as well as my happiness as her own. She is not only the best sister but also the best friend I could ever ask for in life. Last but not least, I would like to thank my husband, Brian Darby. In finding him, I have found myself. His love, understanding and encouragement have given me the strength and the focus to go after what I really want to be in life regardless of what other people say. While I was writing this thesis, he said, “Tell me what you need me to do. I got your back.” I thank him from the bottom of my heart for all his help and patience. I am very blessed to have him as my life partner and I can just hope to be to him what he is to me. v TABLE OF CONTENTS Page LIST OF FIGURES .............................................................................................viii LIST OF SCHEMES.............................................................................................. x CHAPTER I. INTRODUCTION ............................................................................................. 1 1.1. Introduction ................................................................................................ 1 1.2. Synthesis of Phosphazene Polymer .......................................................... 1 1.3. Interactions of [PCl2N]3 with Lewis acids.................................................... 7 II. EXPERIMENTAL ............................................................................................ 9 2.1. General Experimental Methods ................................................................. 9 2.2. Materials Used ........................................................................................... 9 2.3. Spectroscopy ........................................................................................... 10 2.4. Purification of [PCl2N]3 ............................................................................. 10 2.5. Interaction of [PCl2N]3 with AlCl3 .............................................................. 11 2.5.1. Purification of AlCl3 ............................................................................. 11 2.5.2. Synthesis of [PCl2N]3.AlCl3 .................................................................. 11 2.6. Interaction of [PCl2N]3 with AlBr3 .............................................................. 12 2.6.1. Purification of AlBr3 ............................................................................. 12 2.6.2. Synthesis of [PCl2N]3.AlBr3.................................................................. 12 vi 2.7. Interaction of [PCl2N]3 with GaCl3 ............................................................ 13 2.7.1. Purification of GaCl3 ............................................................................ 13 2.7.2. Synthesis of [PCl2N]3.GaCl3 ................................................................ 13 2.8. Interaction of [PCl2N]3 with BCl3 ............................................................... 14 2.9. Interaction of [PCl2N]3 with BBr3............................................................... 14 2.10. Interaction of [PCl2N]3 with InCl3 ............................................................ 15 III. RESULTS AND DISCUSSION..................................................................... 16 3.1. Interactions of [PCl2N]3 with Lewis Acids ................................................. 16 3.2. X-ray Crystallography .............................................................................. 17 3.2.1. [PCl2N]3.AlCl3 adduct........................................................................... 17 3.2.2. [PCl2N]3.AlBr3 adduct .......................................................................... 19 3.2.3. [PCl2N]3.GaCl3 adduct ......................................................................... 21 3.3. NMR Studies............................................................................................ 24 3.3.1. VT NMR of [PCl2N]3.AlCl3 adduct ........................................................ 26 3.3.2. VT NMR of [PCl2N]3.AlBr3 adduct........................................................ 33 3.3.3. VT NMR of [PCl2N]3.GaCl3 adduct ...................................................... 39 3.4. Comparison of [PCl2N]3.AlCl3, [PCl2N]3.AlBr3 and [PCl2N]3.GaCl3 addcuts ............................................................................ 50 IV. CONCLUSION............................................................................................. 52 REFERENCES ................................................................................................... 54 APPENDIX.......................................................................................................... 56 vii LIST OF FIGURES Figure Page 1.1. The Phosphazene Polymer Backbone ....................................................... 1 1.2. Proposed Structures of the Product of Interactions between Lewis Acids and [PCl2N]3 ........................................................................... 7 3.1. Thermal Ellipsoid Plot of [PCl2N]3.AlCl3 .................................................... 18 3.2. Thermal Ellipsoid Plot of [PCl2N]3.AlBr3.................................................... 20 3.3. Thermal Ellipsoid Plot of [PCl2N]3.GaCl3 .................................................. 22 3.4. Thermal Ellipsoid Plot of the Asymmetric Unit of [PCl2N]3.AlCl3 .......................................................................................... 23 3.5. 31 3.6. 31 3.7. 31 3.8. 31 3.9. 31 3.10. 31 3.11. 1 3.12. 31 3.13. 31 P NMR Spectra of [PCl2N]3.AlCl3, [PCl2N]3.AlBr3 and [PCl2N]3.GaCl3 in CDCl3 at 25 °C ............................................................. 25 P NMR Spectra of [PCl2N]3.AlCl3 in CDCl3 at 55 °C .............................. 27 P NMR Spectra of [PCl2N]3.AlCl3 in CDCl3 at 40 °C .............................. 28 P NMR Spectra of [PCl2N]3.AlCl3 in CDCl3 at 30 °C .............................. 29 P NMR Spectra of [PCl2N]3.AlCl3 in CDCl3 at 0 °C ................................ 30 P NMR Spectra of [PCl2N]3.AlCl3 in CDCl3 at -20 °C ............................. 31 H NMR Spectra of [PCl2N]3.AlCl3 in CDCl3 at 40 °C, 30 °C, 0 °C, and -20 °C............................................................ 32 P NMR Spectra of [PCl2N]3.AlBr3 in CDCl3 at 25 °C .............................. 34 P NMR Spectra of [PCl2N]3.AlBr3 in CDCl3 at 0 °C ................................ 35 viii 3.14. 31 P NMR Spectra of [PCl2N]3.AlBr3 in CDCl3 at -20 °C............................ 36 3.15. 31 3.16. 1 3.17. 31 3.18. 31 3.19. 31 3.20. 31 3.21. 31 3.22. 31 3.23. 31 3.24. 31 3.25. 31 3.26. 1 P NMR Spectra of [PCl2N]3.AlBr3 in CDCl3 at -40 °C............................. 37 H NMR Spectra of [PCl2N]3.AlBr3 in CDCl3 at 25 °C, 0 °C, -20 °C and -40 °C............................................................ 38 P NMR Spectra of [PCl2N]3.GaCl3 in CDCl3 at 35 °C............................. 40 P NMR Spectra of [PCl2N]3.GaCl3 in CDCl3 at 30 °C............................. 41 P NMR Spectra of [PCl2N]3.GaCl3 in CDCl3 at 25 °C............................. 42 P NMR Spectra of [PCl2N]3.GaCl3 in CDCl3 at 15 °C............................. 43 P NMR Spectra of [PCl2N]3.GaCl3 in CDCl3 at 0 °C............................... 44 P NMR Spectra of [PCl2N]3.GaCl3 in CDCl3 at -20 °C............................ 45 P NMR Spectra of [PCl2N]3.GaCl3 in CDCl3 at -40 °C............................ 46 P NMR Spectra of [PCl2N]3.GaCl3 in CDCl3 at -50 °C............................ 47 P NMR Spectra of [PCl2N]3.GaCl3 in CDCl3 at -55 °C............................ 48 H NMR Spectra of [PCl2N]3.GaCl3 in CDCl3 at -55 °C,-50 °C, -40 °C, -20 °C, 0 °C, 15 °C, 25 °C, and 30 °C......................................... 49 ix LIST OF SCHEMES Scheme Page 1. Functionalization of Chlorophosphazenes ................................................. 2 2. Synthesis Routes of Chlorophosphazene Polymer .................................... 3 3. Mechanism of ROP of [PCl2N]3 Proposed by Emsley ................................ 5 4. Mechanism of ROP of [PCl2N]3 Proposed by Allcock................................. 6 x CHAPTER I INTRODUCTION 1.1. Introduction Phosphazene polymers have inorganic backbones made of alternating phosphorous and nitrogen atoms. Each phosphorous can have two substituents that are either organic or inorganic (Figure 1.1). R R' R P P N N N N P R R' R' P R R' Figure 1.1. The Phosphazene Polymer Backbone 1.2. Synthesis of Phosphazene Polymer Most functional polyphosphazenes are made by replacing chlorides on the highly reactive chlorophosphazenes with (OR) or (NR2) substituents in high yield reactions (Scheme 1).1 By varying the substituents, polyphosphazenes can be tailor-made to meet a variety of functional needs. In general, when the substituents are OR groups, the resulting phosphazene polymer is very stable and flexible and it can be used as elastomers, foams, fire-proofing, batteries, 1 contact lenses, and coatings.2 With NR2 substituents, phosphazene polymers become water degradable and can be used as coating for time released drugs.2 OR P N OR Cl OR n P N Cl NR2 n NR2 P N NR2 n Scheme 1. Functionalization of Chlorophosphazenes.1 However, synthesis of the reactive chlorophosphazenes either requires expensive starting materials or it is hard to reproduce and has low yield. Therefore, fundamental chlorophosphazene chemistry needs to be understood in order to tap into the wide range of possible applications offered by polyphosphazenes. There are several routes to synthesize chlorophosphazene polymers as shown in Scheme 2. Of the routes listed, the ring opening polymerization (ROP) of hexachlorocyclotriphosphazene, [PCl2N]3 at ~ 250 °C is the traditional route. This route has irreproducibility issues but it uses cheap starting materials. Because other routes require expensive starting materials, our goal was to study the fundamental chemistry of [PCl2N]3 in order to understand the causes of the low-yield and irreproducibility issues in its ROP. 2 3 Scheme 2. Synthesis Routes of Chlorophosphazene Polymers There are two different mechanisms of the ROP of [PCl2N]3 that were proposed by Emsley and Allcock.3,4 Scheme 3 and 4 show these two mechanisms. In Emsley’s mechanism,3 which is depicted in Scheme 3, the nitrogen on [PCl2N]3 gets protonated in the first step. The protonation weakens and breaks the bond between the nitrogen and a neighboring phosphorous, which opens the ring, leaving a lone pair on nitrogen and creating a phosphazenium cation. The lone pair on nitrogen attacks a phosphorous on another [PCl2N]3 and polymerization is started. The mechanism proposed by Allcock4 is the more commonly accepted mechanism and it is shown in Scheme 4. One chloride on [PCl2N]3 is removed in the first step, forming a phosphazenium cation. A lone pair of nitrogen on another [PCl2N]3 attacks the cation, and as a result, the second [PCl2N]3 is ring-opened, forming another phosphazenium cation and initiating the ROP process. According to this mechanism, adding a Lewis acid, which could act as a halide abstractor, in the ROP should promote the first step involving the removal of a chloride. This hypothesis is supported by one of the synthesis routes of [PCl2N]n listed in Scheme 2, where adding BCl3 lowers the ROP temperature to 210 °C compared to uncatalyzed ROP temperature at ~ 250 °C. Therefore, it is important to understand the interaction of [PCl2N]3 with Lewis acids. 4 5 Scheme 3. Mechanism of ROP of [PCl2N]3 Proposed by Emsley3 6 Scheme 4. Mechanism of ROP of [PCl2N]3 Proposed by Allcock4 1.3. Interactions of [PCl2N]3 with Lewis acids The interactions of [PCl2N]3 with Lewis acids have been studied since 1940’s. Although interactions with several Lewis acids had been reported prior to our group’s work,4-8 the product of interactions were poorly characterized in some of the reports. The structures of the products of these interactions were proposed to be either 1 or 2 in Figure 1.2 or their variants.8,9 The actual structure of the adducts was still a subject of debate when our group started our research. For the Lewis acids studied here in, BCl3, AlCl3, AlBr3 and GaCl3, very different products were proposed. For BCl3, an adduct of structure 1 was proposed as an intermediate in the BCl3 initiated ROP of [PCl2N]3 at 210 °C.7, 8 AlCl3 was reported to react with [PCl2N]3 to give a bis cation related to 2.10 GaCl3 was reported not to react with [PCl2N]3.11 LA = Lewis acid LA Cl Cl LA(Cl) N Cl P P N N Cl Cl Cl N P N P Cl P Cl N P Cl Cl 1 Cl 2 Figure 1.2. Proposed Structures of the Product of Interactions between Lewis Acids and [PCl2N]3. 7 Previous work in our group had focused on the reactions between [PCl215N]3 and Lewis acids.12, 13 The purpose of using 15N labeled starting materials was to fully utilize NMR techniques in characterizing the products by introducing the NMR active 15N into the compounds. However, our group’s findings showed that there was an exchange process occurring in the Lewis acid adducts of [PCl215N]3 in solution. Due to the rapid exchange, the NMR resonances coalesced and it was difficult to assign the structure of the product in the solution state based on the NMR studies. We concluded that, in order to understand the fluxional nature of the products, it would be best to study the interactions of Lewis acids with non-labeled [PCl2N]3. Accordingly, the focus of this work was on the interactions of non-labeled [PCl2N]3 with Group 13 Lewis acids. Group 13 adducts of [PCl2N]3 previously reported were [PCl2N]3.AlBr3 and [PCl2N]3.(AlCl3)2.5, 10 GaCl3 was reported not to form adducts with [PCl2N]3.11 Although BCl3 had been used as a catalyst in the ROP process,7, 8 its adducts with [PCl2N]3 had not been isolated. The goal of this work was to investigate the interactions of [PCl2N]3 with Group 13 Lewis acids AlCl3, AlBr3, GaCl3, BCl3, BBr3, and InCl3 and to study the products, especially their fluxional natures, by using modern characterization methods. 8 CHAPTER II EXPERIMENTAL SECTION 2.1. General Experimental Methods All manipulations were carried out under vacuum or under dry and oxygen-free argon atmosphere. Standard anaerobic techniques such as Schlenk, vacuum line and glove-box techniques were applied.14-16 The vacuum line had the ultimate capacity of 2x10-4 torr. All glassware was dried in the oven overnight. The hot glassware was assembled hot and evacuated immediately, or directly placed in the port of the glove-box, evacuated and assembled in the box. 2.2. Materials Used ([PCl2N]3) (Aldrich, 99.99%) was further purified by sublimation. AlCl3, AlBr3, and GaCl3 (Alfa Aesar, ampoule, 99.999%) were sublimed before use. BCl3 was purchased from Aldrich as a 1M solution in heptane and was used without further purification. BBr3 (Aldrich) was degassed before use. InCl3 (99.999%) was used as received in an ampoule from Aldrich. The solvents hexane and chloroform were purified using a PureSolvTM system. Deuterated chloroform was purchased from Cambridge Isotopes, distilled three times from regenerated 4 Å molecular sieves and stored under argon. 9 2.3. Spectroscopy Proton and 31P NMR spectra were taken on Varian INOVA 400 MHz or Varian 500 MHz spectrometers. Proton NMR spectra were referenced to the residual proton resonance in the deuterated solvent, and 31P NMR spectra were externally referenced to phosphoric acid (0 ppm). In order to exclude moisture from the samples, NMR tubes were flame sealed under vacuum. Variable Temperature NMR (VT NMR) studies were performed by Dr. Deepa Savant and the author. For X-ray crystallographic analysis, crystals were placed on a slide and covered with paratone oil. The slide was transported from the glove-box to the diffractometer in a desiccator that was covered with aluminum foil. Crystals were immediately mounted in the dark. Crystallographic data were acquired on a Bruker SMART Apex CCD diffractometer and structure solution and refinement were done using the Bruker SHELXTL package. Crystal structure analyses were done by Dr. Matthew J. Panzner, Dr. Doug Medvetz, and Brian Wright. 2.4. Purification of [PCl2N]3 [PCl2N]3 (5 g) was placed in a sublimator. The sublimation was carried out on the high vacuum line overnight at ~60 °C. The sublimate (4.7 g) was collected in the glove box and stored in an amber vial in the glove box until use. 10 2.5. Interaction of [PCl2N]3 with AlCl3 In order to avoid protonated impurities, high vacuum line and glove box techniques were used instead of the Schlenk line. Because the [PCl2N]3.AlCl3 adduct was light sensitive, exposure to light was minimized throughout all phases of the work. 2.5.1. Purification of AlCl3 The sealed glass ampoule containing AlCl3 (5 g) was scored open in the glove box. AlCl3 was put in a sublimator and a thin layer of glass wool that had been pre-dried in an oven was placed on top of AlCl3. The function of the glass wool layer was to prevent Al2O3 impurities from rising with the sublimate and contaminating it. The sublimation was done on the high vacuum line overnight at ~85 °C. Sublimed AlCl3 (~ 4.5 g) was collected in the glove box and stored in an amber vial in the box until further use. 2.5.2. Synthesis of [PCl2N]3.AlCl3 In the glove box, [PCl2N]3 (0.69 g, 2.0 mmol) was dissolved in hexane (~ 20 mL) to give a colorless solution. AlCl3 (0.27 g, 2.0 mmol) was added and colorless crystals instantly formed on the wall of the flask. Due to light-sensitivity of the solution, the reaction flask was wrapped in aluminum foil and stored in the dark for 10 days as more crystals grew. The solution was filtered to collect the first batch of crystals, which were characterized to be [PCl2N]3.AlCl3. Yield: ~89%. 11 MP: 128-130 °C. 31P NMR (CDCl3) at 0 °C: δ 26.8 ppm (d), 16.6 ppm (t). See the Appendix for X-ray crystallographic information. 2.6. Interaction of [PCl2N]3 with AlBr3 In order to avoid protonated impurities, high vacuum line and glove box techniques were used instead of the Schlenk line. Because the [PCl2N]3.AlBr3 adduct was light sensitive, exposure to light was minimized throughout all phases of the work. 2.6.1. Purification of AlBr3 The sealed glass ampoule container of AlBr3 was scored open in the glove box. AlBr3 (5 g) was put in a sublimator and sublimation was conducted on the high vacuum line overnight at ~ 70 °C. Sublimed AlBr3 (4.8 g) was collected in the glove box and stored in an amber vial in the box. 2.6.2. Synthesis of [PCl2N]3.AlBr3 In the glove box, [PCl2N]3 (0.69 g, 2.0 mmol) was dissolved in hexane (~ 20 mL) to give a colorless solution. AlBr3 (0.53 g, 2.0 mmol) was added and the flask was swirled. The solution turned cloudy and needle-like colorless crystals formed on the wall of the flask. Due to light-sensitivity of the solution, the reaction flask was wrapped in aluminum foil and stored in the dark for 7 days. The volatiles were slowly removed with the reaction flask chilled in a methanol/ice slush bath. The crystals were characterized to be [PCl2N]3.AlBr3. Yield: ~87%. 12 MP: 174-175 °C. 31P NMR (CDCl3) at 0 °C: δ 26.7 ppm (d), 16.7 ppm (t). See the Appendix for X-ray crystallographic information. 2.7. Interaction of [PCl2N]3 with GaCl3 In order to avoid protonated impurities, high vacuum line and glove box techniques were used instead of the Schlenk line. Because the PCl2N]3.GaCl3 adduct was light sensitive, exposure to light was minimized throughout all phases of the work. 2.7.1. Purification of GaCl3 The sealed glass ampoule containing GaCl3 was scored open in the glove box. GaCl3 (5 g) was placed in a sublimator. The overnight sublimation conducted on the high vacuum line at 45 °C afforded 4.5 g of pure GaCl3. The sublimate was collected in the glove box and stored in an amber vial in the box until use. 2.7.2. Synthesis of [PCl2N]3.GaCl3 In the glove box, [PCl2N]3 (0.69 g, 2.0 mmol) was dissolved in hexane (~ 20 mL) to give a colorless solution. GaCl3 (0.35 g, 2.0 mmol) was added. The flask was swirled and all dissolved. Due to light-sensitivity of the solution, the reaction flask was wrapped in aluminum foil and stored in the dark for 2 days. The volatiles were slowly removed and colorless crystals were collected. The product was characterized to be [PCl2N]3.GaCl3. Yield: ~83%. MP: 126-127 °C. 13 31 P NMR (CDCl3) at -55 °C: δ 25.28 ppm (d), δ 16.08 ppm (t). See the Appendix for X-ray crystallographic information. 2.8. Interaction of [PCl2N]3 with BCl3 In the glove box, [PCl2N]3 (0.49 g, 1.5 mmol) was put in a Schlenk flask. BCl3 solution in heptane (1M, 1.5 mL, 1.5 mmol) was added via syringe. With the reaction mixture being stirred constantly, hexane was added drop-wise until all of the solids dissolved. The flask was wrapped in aluminum foil and stored in the dark for 7 days. The volatiles were slowly removed to give colorless crystals which were characterized to be the starting material, [PCl2N]3. 31P NMR (CDCl3): δ 20.0 ppm (s). 2.9. Interaction of [PCl2N]3 with BBr3 In the glove box, [PCl2N]3 (0.34 g, 1.1 mmol) was dissolved in hexane (~ 20 mL). BBr3 (1M, 1.1 mL, 1.1 mmol) was added via syringe. The reaction flask was swirled to mix the contents. No change was observed. The flask was wrapped in aluminum foil and stored in the dark for 30 minutes. Clear, colorless crystals formed on the wall of the flask. The flask was stored in the dark for 7 days to promote crystal growth. X-ray crystallographic characterization of the crystals showed that they were the starting material, [PCl2N]3. 31P NMR (CDCl3): δ 20.0 ppm (s). 14 2.10. Interaction of [PCl2N]3 with InCl3 In the glove box, InCl3 (0.44 g, 2.0 mmol) was put in a Schlenk flask containing hexane (~ 20 mL). InCl3 did not dissolve in hexane. [PCl2N]3 (0.69 g, 2.0 mmol) was added and the flask was wrapped in aluminum foil. The reaction mixture was stirred overnight. The volatiles were slowly removed under vacuum. The resulting white solid was characterized to be the starting material, [PCl2N]3. 31 P NMR (CDCl3): δ 20.0 ppm (s). 15 CHAPTER III RESULTS AND DISCUSSION As stated in the introduction, even though several interactions of Lewis acids with [PCl2N]3 had previously been reported, the products were poorly characterized by modern standards and their structures were not agreed upon. The focus of this research was to synthesize complexes of [PCl2N]3 with Lewis acids of interest and to characterize the products using modern techniques that were not common at the times of previous reports, most importantly by using VT NMR studies. 3.1. Interactions of [PCl2N]3 with Lewis acids Cl Cl P N N Cl Cl P P Cl N Cl Cl MX3 hexane Cl MX3 N N Cl Cl P P Cl N Cl MX3= AlCl3, AlBr3or GaCl3 P (Eq. 3.1) The 1:1 reaction of [PCl2N]3 with Lewis acids AlCl3, AlBr3 and GaCl3 can be described by the equation 3.1. [PCl2N]3.AlCl3 adducts are plate-like crystals with the melting point 128-130 °C. [PCl2N]3.AlBr3 adducts are needle-like crystals and have the melting point 174-175 °C. The melting point of [PCl2N]3.AlBr3 was previously reported to be 174 °C.5 [PCl2N]3.GaCl3 adducts are needle-like crystals having the melting point 126-127 °C. 16 The adducts were extremely moisture sensitive, and protonated impurities tended to develop. Vigorous anaerobic techniques were required in all stages of handling. Exposure to light needed to be limited, especially in solutions of chloronated hydrocarbons. The reactions of [PCl2N]3 with BCl3, BBr3 and InCl3 did not give adducts. This means that the nitrogen atoms on [PCl2N]3 are very poor bases and that only the interactions with very strong Lewis acids lead to adduct formations. 3.2. X-ray crystallography The crystals of the [PCl2N]3.AlCl3, [PCl2N]3.AlBr3 and [PCl2N]3.GaCl3 adducts suitable for single crystal x-ray diffraction analysis were grown from dry hexane. 3.2.1. [PCl2N]3.AlCl3 adduct The thermal ellipsoid plot of [PCl2N]3.AlCl3 can be seen in Figure 3.1. The asymmetric unit of [PCl2N]3.AlCl3 contains half of two molecules and an aluminum atom was bound to one nitrogen atom on each molecule. The bond lengths of AlN pairs are 1.982(3) Å and 1.970(3) Å. The bond distances between the nitrogen atom that is bound to the aluminum atom and the two neighboring phosphorous atoms are 1.6521(14) Å and 1.6530(14) Å. These bond distances are longer than the P-N bonds in the starting material [PCl2N]317 and they show single bond character. The remaining P-N bond distances of the adduct fall between 1.560(2) Å and 1.573(2) Å and they are comparable to the P-N bonds of [PCl2N]3.17 17 18 Figure 3.1. Thermal Ellipsoid Plot of [PCl2N]3.AlCl3 3.2.2. [PCl2N]3.AlBr3 adduct The thermal ellipsoid plot of [PCl2N]3.AlBr3 is shown in Figure 3.2. There is no halogen exchange between AlBr3 and [PCl2N]3. The asymmetric unit contains half of two [PCl2N]3.AlBr3 molecules and an aluminum atom was bound to one nitrogen atom on each molecule. The bond lengths of Al-N pairs are 1.994(3) Å and 1.992(3) Å. The bond distances between the nitrogen atom that is bound to the aluminum atom and the two neighboring phosphorous atoms are 1.6532(15) Å and 1.6517(15) Å. These bond distances are longer than the P-N bonds in the starting material [PCl2N]317 and they show single bond character. The remaining P-N bond distances of the adduct fall between 1.562(2) Å and 1.577(2) Å and they are comparable to the P-N bonds of [PCl2N]3.17 19 20 Figure 3.2. Thermal Ellipsoid Plot of [PCl2N]3.AlBr3 3.2.3. [PCl2N]3.GaCl3 adduct The thermal ellipsoid plot of [PCl2N]3.GaCl3 is shown in Figure 3.3. The asymmetric unit contains two [PCl2N]3.GaCl3 molecules and a gallium atom was bound to one nitrogen atom on each molecule (Figure 3.4). The bond lengths of Al-N pairs are 1.994(3) Å and 1.992(3) Å. The bond distances between the nitrogen atom that is bound to the gallium atom and the two neighboring phosphorous atoms are 1.6532(15) Å and 1.6517(15) Å. These bond distances are longer than the P-N bonds in the starting material [PCl2N]317 and they show single bond character. The remaining P-N bond distances of in the adduct fall between 1.562(2) Å and 1.577(2) Å and they are comparable to the P-N bonds of [PCl2N]3.17 21 Figure 3.3. Thermal Ellipsoid Plot of [PCl2N]3.GaCl3 22 23 Figure 3.4. Thermal Ellipsoid Plot of the Asymmetric Unit of [PCl2N]3.GaCl3 3.3. NMR Studies The 31P spectra of [PCl2N]3.AlCl3, [PCl2N]3.AlBr3, and [PCl2N]3.GaCl3 obtained in CDCl3 at 25 °C are shown in Figure 3.5. It can be seen in the spectra that all three adducts are fluxional at this temperature. In order to better understand the fluxional nature, VT NMR studies of the adducts were performed in CDCl3. 24 25 Figure 3.5. 31P NMR Spectra of [PCl2N]3.AlCl3, [PCl2N]3.AlBr3, and [PCl2N]3.GaCl3 in CDCl3 at 25 °C 3.3.1. VT NMR of [PCl2N]3.AlCl3 31 P VT NMR spectra of [PCl2N]3.AlCl3 in CDCl3 were obtained at 55 °C, 40 °C, 30 °C, 0 °C, and -20 °C. Two single resonances were observed at 27.5 ppm and 17.3 ppm at 55 °C (Figure 3.16) and 17.2 ppm and 17.0 ppm for 40 °C (Figure 3.17). At 30 °C, the resonance at 27.3 ppm had resolved into a doublet. However, the resonance at 16.9 ppm had not resolved into a triplet yet, although it did have two side shoulders (Figure 3.18). At 0 °C, a well resolved doublet at 26.8 ppm and a triplet at 16.6 ppm were observed, along with a singlet at 18.9 ppm (Figure 3.19). At -20 ppm, the doublet was seen at 26.5 ppm, where as the triplet was at 16.4 ppm and the singlet was at 18.7 ppm. The singlet was due to protonated impurities in the product (Figure 3.20). Similar resonance had been observed in the reaction of [PCl2N]3 and AlBr3 in the presence of water.13 H VT NMR spectra of the [PCl2N]3.AlCl3 in CDCl3 were also obtained at 1 40 °C, 30 °C, 0 °C, and -20 °C. A singlet was observed at 10.1 ppm at all temperatures studied (Figure 3.21). The presence of the singlet in this ppm region confirmed our hypothesis that there were protonated impurities in the product. 26 27 Figure 3.6. 31P NMR Spectrum of [PCl2N]3.AlCl3 in CDCl3 at 55 °C 28 Figure 3.7. 31P NMR Spectrum of [PCl2N]3.AlCl3 in CDCl3 at 40 °C 29 Figure 3.8. 31P NMR Spectrum of [PCl2N]3.AlCl3 in CDCl3 at 30 °C 30 Figure 3.9. 31P NMR Spectrum of [PCl2N]3.AlCl3 in CDCl3 at 0 °C 31 Figure 3.10. 31P NMR Spectrum of [PCl2N]3.AlCl3 in CDCl3 at -20 °C 32 Figure 3.11. 1H NMR Spectra of [PCl2N]3.AlCl3 in CDCl3 at 40 °C, 30 °C, 0 °C, and -20 °C 3.3.2. VT NMR of [PCl2N]3.AlBr3 P VT NMR of [PCl2N]3.AlBr3 in CDCl3 were obtained at 25 °C, 0 °C, -20 31 °C, and -40 °C. At 25 °C, two single resonances at 27.1 ppm and 16.9 ppm were observed (Figure 3.22). At 0 °C, the resonance at 26.7 ppm had resolved into a doublet. However, the resonance at 16.7 ppm had not resolved into a triplet yet, although it did have two side shoulders. A small broad feature was also seen at the base of this resonance (Figure 3.23). At -20 °C, a well resolved doublet at 26.5 ppm and a triplet at 16.5 ppm were observed, along with a singlet at 17.6 ppm (Figure 3.24). At -40 ppm, the doublet was seen at 26.2 ppm, where as the triplet was at 16.2 ppm and the singlet was at 17.3 ppm. The singlet was due to protonated impurities in the product (Figure 3.25). Similar resonance had been observed in the reaction of [PCl2N]3 and AlBr3 in the presence of water.13 H VT NMR spectra of [PCl2N]3.AlBr3 in CDCl3 were also obtained at 25 1 °C, 0 °C, -20 °C, and -40 °C (Figure 3.26). At 25 °C and 0 °C, a singlet was observed at 9.4 ppm. At -20 °C and -40 °C, the resonance had moved to 9.3 ppm and 9.2 ppm respectively. The presence of the singlet in this ppm region confirmed our hypothesis that there were protonated impurities in the product. 33 34 Figure 3.12. 31P NMR Spectrum of [PCl2N]3.AlBr3 in CDCl3 at 25 °C 35 Figure 3.13. 31P NMR Spectrum of [PCl2N]3.AlBr3 in CDCl3 at 0 °C 36 Figure 3.14. 31P NMR Spectrum of [PCl2N]3.AlBr3 in CDCl3 at -20 °C 37 Figure 3.15. 31P NMR Spectrum of [PCl2N]3.AlBr3 in CDCl3 at -40 °C 38 Figure 3.16. 1H NMR Spectra of [PCl2N]3.AlBr3 in CDCl3 at 25 °C, 0 °C, -20 °C, and -40 °C 3.3.3. VT NMR of [PCl2N]3.GaCl3 31 P VT NMR spectra of [PCl2N]3.GaCl3 in CDCl3 were obtained at 35 °C, 30 °C, 25 °C, 15 °C, 0 °C, -20 °C, -40 °C, -50 °C, and -55 °C. At 35 °C, the exchange was very rapid and a sharp singlet was observed at 22.1 ppm (Figure 3.6). At 30 °C (Figure 3.7), 25 °C (Figure 3.8), and 15 °C (Figure 3.9), a gradually broader singlet at 22.9 ppm, 23.9 ppm, and 23.7 ppm were observed respectively. At 0 °C (Figure 3.10), two single resonances were observed at 26.2 ppm and 17.1 ppm. At -20 °C (Figure 3.11), the two resonances became sharper (25.6 ppm and 16.5 ppm), but the individual peaks were still not resolved. At -40 °C, the resonance at 25.4 ppm had taken the form of a doublet. Although the resonance at 16.2 ppm had developed two shoulders, it had not resolved into a triplet. A new peak at 19.8 ppm was also observed at this temperature (Figure 3.12). At -50 °C (Figure 3.13) and -55 °C (Figure 3.14), a doublet at 25.3 ppm a singlet at 19.7 ppm, and a triplet at 16.1 ppm were observed. The singlet appears to be due to protonated impurities in the product. Similar resonance had been observed in the reaction of [PCl2N]3 and AlBr3 in the presence of water.13 H VT NMR spectra of [PCl2N]3.GaCl3 in CDCl3 were also obtained at 35 1 °C, 30 °C, 25 °C, 15 °C, 0 °C, -20 °C, -40 °C, -50 °C, and -55 °C. A singlet was observed at 9.8 ppm for all temperatures. However the peak became sharper as the temperature decreased (Figure 3.15). The presence of the singlet in this ppm region confirmed our hypothesis that there were protonated impurities in the product. 39 40 Figure 3.17. 31P NMR Spectrum of [PCl2N]3.GaCl3 in CDCl3 at 35 °C 41 Figure 3.18. 31P NMR Spectrum of [PCl2N]3.GaCl3 in CDCl3 at 30 °C 42 Figure 3.19. 31P NMR Spectrum of [PCl2N]3.GaCl3 in CDCl3 at 25 °C 43 Figure 3.20. 31P NMR Spectrum of [PCl2N]3.GaCl3 in CDCl3 at 15 °C 44 Figure 3.21. 31P NMR Spectrum of [PCl2N]3.GaCl3 in CDCl3 at 0 °C 45 Figure 3.22. 31P NMR Spectrum of [PCl2N]3.GaCl3 in CDCl3 at -20 °C 46 Figure 3.23. 31P NMR Spectrum of [PCl2N]3.GaCl3 in CDCl3 at -40 °C 47 Figure 3.24. 31P NMR Spectrum of [PCl2N]3.GaCl3 in CDCl3 at -50 °C 48 Figure 3.25. 31P NMR Spectrum of [PCl2N]3.GaCl3 in CDCl3 at -55 °C 49 Figure 3.26. 1H NMR Spectra of [PCl2N]3.GaCl3 in CDCl3 at -55 °C, -50 °C, -40 °C, -20 °C, 0 °C, 15 °C, 25 °C and 30 °C 3.4. Comparison of [PCl2N]3.AlCl3, [PCl2N]3.AlBr3 and [PCl2N]3.GaCl3 The x-ray crystallographic data of all three adducts show that the P-N bonds containing the nitrogen atom that is bound to the Lewis acids are longer than the rest of the P-N bonds in the ring. This lengthening, and therefore weakening, of the ring bonds due to the adduct formation might facilitate bond breakage in the ROP process. The bond distances between Al-N (1.970(3) Å 1.994(3) Å) and Ga-N (2.040(3) Å -2.048(3) Å) are comparable to the dative bond distances between nitrogen and group 13 metals.12, 13 The Al-N distance in [PCl2N]3.AlCl3 is shorter that that in [PCl2N]3.AlBr3. This suggests that AlCl3 binds more tightly than AlBr3 does to [PCl2N]3. In comparing the 31P NMR spectra of [PCl2N]3.AlCl3, [PCl2N]3.AlBr3, and [PCl2N]3.GaCl3, it was seen that the rate of the exchange process was not the same for all three adducts. The expected doublet and triplet resonances were well resolved at 0 °C for [PCl2N]3.AlCl3, and at -20 °C for [PCl2N]3.AlBr3. For [PCl2N]3.GaCl3, however, it was not until -50 °C that the expected peaks became resolved. This indicates that the rate of exchange of [PCl2N]3.GaCl3 is faster than those of [PCl2N]3.AlCl3 and [PCl2N]3.AlBr3. The peaks did not coalesce in 31P NMR spectra for [PCl2N]3.AlCl3 and [PCl2N]3.AlBr3 even at the boiling point temperature of CDCl3. Therefore, VT NMR studies need to be done in a solvent that has a higher boiling point than CDCl3, in order to calculate the rate of exchange of [PCl2N]3.AlCl3 and [PCl2N]3.AlBr3 adducts. From 1H VT NMR spectra of the three adducts, the singlet was observed more and more down-field going from [PCl2N]3.AlBr3 to [PCl2N]3.GaCl3 and [PCl2N]3.AlCl3. Therefore, the acidities 50 of the protonated impurities in the adducts can be ranked in the increasing order from [PCl2N]3.AlBr3 to [PCl2N]3.GaCl3 and [PCl2N]3.AlCl3. 51 CHAPTER IV CONCLUSION Adducts of [PCl2N]3 with AlCl3, AlBr3, and GaCl3 were successfully synthesized and characterized by X-ray crystallography and 31P and 1H VT NMR. The adducts assume the structure of the variant 1 depicted in Figure 1.2. The adduct formation lengthens the bonds between the nitrogen atom that is interacting with the Lewis acid and its two phosphorous neighbors in the ring. Because this bond weakening might promote the bond breakage in the initial step of the ROP of [PCl2N]3, potential catalytic abilities of these adducts in the ROP process should be explored. The [PCl2N]3.AlCl3, [PCl2N]3.AlBr3, [PCl2N]3.GaCl3 adducts are light sensitive, especially in solutions of chloronated hydrocarbons. The adducts are also extremely moisture sensitive, and vigorous anaerobic techniques are required in order to prevent the formation of protonated impurities. The involvement of these protonated species both in the ROP process and in the gradual degradation of the chlorophosphazene polymer in storage needs to be studied. The exchange process in solution for all three adducts were investigated using 1H and 31P VT NMR studies. At 0 °C, the resonance peaks in the 31P NMR 52 spectra of [PCl2N]3.AlCl3 and [PCl2N]3.AlBr3 resolve into the expected pattern consisting of one doublet and one triplet. In the 31P NMR spectra of [PCl2N]3.GaCl3, the resonance peaks resolve into a doublet and a triplet at -50 °C. The fact that the resonances for [PCl2N]3.GaCl3 resolve at lower temperature than [PCl2N]3.AlCl3 and [PCl2N]3.AlBr3 indicates that the exchange in [PCl2N]3.GaCl3 is faster than that in [PCl2N]3.AlCl3 and [PCl2N]3.AlBr3. In 31P NMR spectra of [PCl2N]3.AlCl3 and [PCl2N]3.AlBr3, the peaks do not coalesce at the boiling point temperature of CDCl3. Therefore, in order to calculate the rates of exchange of these adducts, VT NMR studies need to be done in a solvent that has a higher boiling temperature than CDCl3. Of the interactions studied, the reactions of [PCl2N]3 with BCl3, BBr3 and InCl3 did not lead to adduct formation. This indicates that the nitrogen atoms on [PCl2N]3 are very poor bases and that very strong Lewis acids are needed to form adducts. The interactions of [PCl2N]3 with other strong Lewis acids involving both main group and transition metals should be studied. 53 REFERENCES (1) de Jaeger, R.; Gleria, M. Progress in Polymer Science 1998, 23, 179-276. (2) Allcock, H. R. Chemistry and Applications of Polyphosphazenes; WileyInterscience: New York, 2003; pp 109-187. (3) Emsley, J.; Udy, P. B. Polymer, 1972, 13, 593-594. (4) Allcock, H. R. Phosphorous-Nitrogen Compounds; Academic Press: New York, 1972; pp 230-248. (5) Coxon, G. E.; Sowerb, D. B. Journal of the Chemical Society A: Inorganic, Physical, Theoretical 1969, 1969, 3012-3014. (6) Kravchenko, E. A.; Levin, B. V.; Bananyarly, S. I.; Toktomatov, T. A. Koord. Khim. 1977, 3, 374-379. (7) Sennett, M. S.; Hagnauer, G. L.; Singler, R. E.; Davies, G. Macromolecules 1986, 19, 959-964. (8) Potts, M. K.; Hagnauer, G. L.; Sennett, M. S.; Davies, G. Macromolecules 1989, 22, 4235-4239. (9) Schacht, E.; Vandorpe, J.; Dejardin, S.; Lemmouchi, Y.; Seymour, L. Biotechnology and bioengineering 1996, 52, 102-108. (10) Bode, H.; Bütow, K.; Lienau, G. Chem. Ber 1948, 81, 547-552. (11) Rivard, E.; Lough, A. J.; Chivers, T.; Manners, I. Inorg. Chem. 2004, 43, 802-811. (12) Heston, A. J.; Panzner, M. J.; Youngs, W. J.; Tessier, C. A. Inorg. Chem. 2005, 44, 6518-6520. (13) Heston, A. J.; Tessier, C. A.; Panzner, M. J.; Youngs, W. J. Phosphorus, Sulfur Silicon Relat. Elem. 2004, 179, 831-837. (14) Shriver, D. F.; Drexdon, M. A. The Manipulation of Air-Sensitive Compounds; Wiley: New York, 1986. 54 (15) Plesch, P. H. High Vacuum Techniques for Chemical Syntheses and Measurement ; Cambridge University Press: New York, 1989. (16) Sanderson, R. T. Vacuum Manipulation of Volatile Compounds; John Wiley & Sons: New York, 1948. (17) Allcock, H. R. Chem. Rev. 1972, 72, 315-356. 55 APPENDIX SUPPLEMENTARY MATERIALS FOR ALL X-RAY CRYSTAL STRUCTURES Adduct: [PCl2N]3.AlCl3 56 Table 1. Crystal data and structure refinement for [PCl2N]3.AlCl3. Empirical formula Al Cl9 N3 P3 Formula weight 480.97 Temperature 100(2) K Wavelength 0.71073 Å Crystal system Orthorhombic Space group Pmn2(1) Unit cell dimensions a = 11.992(2) Å = 90° b = 11.713(2) Å = 90° c = 10.7730(19) Å = 90° Volume 1513.3(5) Å3 Z 4 Density (calculated) 2.111 Mg/m3 Absorption coefficient 2.014 mm-1 F (000) 928 Crystal size 0.27 x 0.10 x 0.04 mm3 Theta range for data collection 1.74 to 28.24°. Index ranges -15<=h<=15, -15<=k<=15, -14<=l<=14 Reflections collected 12759 Independent reflections 3732 [R (int) = 0.0259] Completeness to theta = 28.24° 97.5 % Absorption correction Semi-empirical from equivalents Max. and min. transmission 0.923 and 0.733 Refinement method Full-matrix least-squares on F2 Data / restraints / parameters 3732 / 1 / 163 Goodness-of-fit on F2 1.093 Final R indices [I>2sigma(I)] R1 = 0.0226, wR2 = 0.0526 R indices (all data) R1 = 0.0234, wR2 = 0.0529 Absolute structure parameter 0.15(6) Largest diff. peak and hole 0.417 and -0.260 e.Å-3 57 Table 2. Atomic coordinates (x 104) and equivalent isotropic displacement parameters (Å2x 103) for [PCl2N]3.AlCl3. U(eq) is defined as one third of the trace of the orthogonalized Uij tensor. _____________________________________________________________________________ x y z U(eq) _____________________________________________________________________________ Cl(1) 0 1326(1) 6532(1) 34(1) Cl(2) 0 3284(1) 4612(1) 26(1) Cl(3) 1830(1) -1227(1) 3813(1) 26(1) Cl(4) 2241(1) 673(1) 1838(1) 26(1) Cl(5) 0 357(1) -537(1) 33(1) Cl(6) 1442(1) -1990(1) 744(1) 27(1) Cl(7) 1789(1) 3953(1) 7399(1) 22(1) Cl(8) 2268(1) 6488(1) 8100(1) 22(1) Cl(9) 0 3019(1) 10894(1) 40(1) Cl(10) 0 5414(1) 12106(1) 23(1) Cl(11) 0 8278(1) 6680(1) 20(1) Cl(12) 1423(1) 6085(1) 5095(1) 24(1) P(1) 0 1599(1) 4725(1) 17(1) P(2) 1179(1) 184(1) 3117(1) 16(1) P(3) 1176(1) 5261(1) 8347(1) 15(1) P(4) 0 4673(1) 10469(1) 17(1) Al(1) 0 -963(1) 798(1) 18(1) Al(2) 0 6552(1) 6125(1) 14(1) N(1) 0 -153(2) 2414(2) 15(1) N(2) 1108(2) 1124(2) 4141(2) 27(1) N(3) 0 5657(2) 7673(2) 14(1) N(4) 1110(2) 4966(2) 9757(2) 23(1) _____________________________________________________________________________ 58 Table 3. Bond lengths [Å] and angles [°] for [PCl2N]3.AlCl3. _____________________________________________________ Cl(1)-P(1) 1.9730(12) Cl(2)-P(1) 1.9772(12) Cl(3)-P(2) 1.9748(8) Cl(4)-P(2) 1.9625(8) Cl(5)-Al(1) 2.1118(13) Cl(6)-Al(1) 2.1077(8) Cl(7)-P(3) 1.9827(8) Cl(8)-P(3) 1.9620(8) Cl(9)-P(4) 1.9907(13) Cl(10)-P(4) 1.9660(11) Cl(11)-Al(2) 2.1089(12) Cl(12)-Al(2) 2.1082(8) P(1)-N(2)#1 1.572(2) P(1)-N(2) 1.572(2) P(2)-N(2) 1.561(2) P(2)-N(1) 1.6521(14) P(3)-N(4) 1.560(2) P(3)-N(3) 1.6530(14) P(4)-N(4)#1 1.573(2) P(4)-N(4) 1.573(2) Al(1)-N(1) 1.982(3) Al(1)-Cl(6)#1 2.1077(8) Al(2)-N(3) 1.970(3) Al(2)-Cl(12)#1 2.1082(8) N(1)-P(2)#1 1.6521(14) N(3)-P(3)#1 1.6530(14) N(2)#1-P(1)-N(2) 115.42(15) N(2)#1-P(1)-Cl(1) 109.74(9) N(2)-P(1)-Cl(1) 109.74(9) N(2)#1-P(1)-Cl(2) 109.17(9) N(2)-P(1)-Cl(2) 109.17(9) Cl(1)-P(1)-Cl(2) 102.84(5) 59 Table 3. Bond lengths [Å] and angles [°] for [PCl2N]3.AlCl3 (continued). N(2)-P(2)-N(1) 116.51(11) N(2)-P(2)-Cl(4) 108.97(9) N(1)-P(2)-Cl(4) 107.63(9) N(2)-P(2)-Cl(3) 110.11(9) N(1)-P(2)-Cl(3) 108.20(9) Cl(4)-P(2)-Cl(3) 104.75(4) N(4)-P(3)-N(3) 116.50(11) N(4)-P(3)-Cl(8) 109.22(8) N(3)-P(3)-Cl(8) 107.72(9) N(4)-P(3)-Cl(7) 110.42(8) N(3)-P(3)-Cl(7) 107.84(9) Cl(8)-P(3)-Cl(7) 104.43(4) N(4)#1-P(4)-N(4) 115.50(15) N(4)#1-P(4)-Cl(10) 109.94(8) N(4)-P(4)-Cl(10) 109.94(8) N(4)#1-P(4)-Cl(9) 108.91(8) N(4)-P(4)-Cl(9) 108.91(8) Cl(10)-P(4)-Cl(9) 102.88(5) N(1)-Al(1)-Cl(6)#1 107.31(5) N(1)-Al(1)-Cl(6) 107.31(5) Cl(6)#1-Al(1)-Cl(6) 110.29(5) N(1)-Al(1)-Cl(5) 104.35(9) Cl(6)#1-Al(1)-Cl(5) 113.51(4) Cl(6)-Al(1)-Cl(5) 113.51(4) N(3)-Al(2)-Cl(12)#1 107.91(5) N(3)-Al(2)-Cl(12) 107.91(5) Cl(12)#1-Al(2)-Cl(12) 108.10(5) N(3)-Al(2)-Cl(11) 105.69(9) Cl(12)#1-Al(2)-Cl(11) 113.47(3) Cl(12)-Al(2)-Cl(11) 113.47(3) P(2)-N(1)-P(2)#1 117.68(16) P(2)-N(1)-Al(1) 121.15(8) P(2)#1-N(1)-Al(1) 121.15(8) 60 Table 3. Bond lengths [Å] and angles [°] for [PCl2N]3.AlCl3 (continued). P(2)-N(2)-P(1) 125.33(13) P(3)-N(3)-P(3)#1 117.18(15) P(3)-N(3)-Al(2) 121.41(8) P(3)#1-N(3)-Al(2) 121.41(8) P(3)-N(4)-P(4) 124.48(13) _____________________________________________________________ Symmetry transformations used to generate equivalent atoms: #1 -x,y,z 61 Table 4. Anisotropic displacement parameters (Å2x 103) for [PCl2N]3.AlCl3. The anisotropic displacement factor exponent takes the form: -2 2[ h2 a*2U11 + ... + 2 h k a* b* U12 ] _____________________________________________________________________________ U11 U22 U33 U23 U13 U12 _____________________________________________________________________________ Cl(1) 68(1) 20(1) 14(1) 1(1) 0 0 Cl(2) 41(1) 18(1) 19(1) 1(1) 0 0 Cl(3) 26(1) 29(1) 22(1) 3(1) -5(1) 7(1) Cl(4) 23(1) 27(1) 30(1) -1(1) 9(1) -7(1) Cl(5) 61(1) 24(1) 14(1) 3(1) 0 0 Cl(6) 29(1) 25(1) 27(1) -8(1) 7(1) 5(1) Cl(7) 24(1) 20(1) 23(1) -5(1) -3(1) 7(1) Cl(8) 16(1) 24(1) 25(1) -4(1) 1(1) -5(1) Cl(9) 70(1) 17(1) 33(1) 5(1) 0 0 Cl(10) 31(1) 24(1) 14(1) -1(1) 0 0 Cl(11) 20(1) 14(1) 28(1) -2(1) 0 0 Cl(12) 27(1) 26(1) 20(1) 3(1) 9(1) 7(1) P(1) 21(1) 18(1) 12(1) -4(1) 0 0 P(2) 14(1) 19(1) 15(1) -4(1) 0(1) 0(1) P(3) 13(1) 17(1) 14(1) -1(1) 0(1) 1(1) P(4) 21(1) 16(1) 14(1) 1(1) 0 0 Al(1) 25(1) 16(1) 12(1) -2(1) 0 0 Al(2) 16(1) 14(1) 13(1) 0(1) 0 0 N(1) 14(1) 18(1) 14(1) -4(1) 0 0 N(2) 18(1) 34(1) 29(1) -19(1) -5(1) 1(1) N(3) 12(1) 17(1) 14(1) 1(1) 0 0 N(4) 15(1) 35(1) 19(1) 5(1) -3(1) 5(1) 62 Adduct: [PCl2N]3.AlBr3 63 Table 5. Crystal data and structure refinement for [PCl2N]3.AlBr3. Empirical formula Al2 Br6 Cl12 N6 P6 Formula weight 1228.71 Temperature 100(2) K Wavelength 0.71073 Å Crystal system Monoclinic Space group P2(1)/m Unit cell dimensions a = 10.8919(12) Å = 90° b = 12.1067(14) Å = 91.898(2)° c = 12.1387(14) Å = 90° Volume 1599.8(3) Å3 Z 4 Density (calculated) 2.551 Mg/m3 Absorption coefficient 8.898 mm-1 F (000) 1144 Crystal size 0.15 x 0.07 x 0.03 mm3 Theta range for data collection 1.68 to 28.28°. Index ranges -14<=h<=14, -15<=k<=16, -15<=l<=16 Reflections collected 13941 Independent reflections 3951 [R (int) = 0.0249] Completeness to theta = 28.28° 95.1 % Absorption correction Semi-empirical from equivalents Max. and min. transmission 0.766 and 0.547 Refinement method Full-matrix least-squares on F2 Data / restraints / parameters 3951 / 0 / 163 Goodness-of-fit on F2 1.000 Final R indices [I>2sigma(I)] R1 = 0.0220, wR2 = 0.0482 R indices (all data) R1 = 0.0283, wR2 = 0.0503 Largest diff. peak and hole 0.574 and -0.457 e.Å-3 64 Table 6. Atomic coordinates (x 104) and equivalent isotropic displacement parameters (Å2x 103) for [PCl2N]3.AlBr3. U(eq) is defined as one third of the trace of the orthogonalized Uij tensor. _____________________________________________________________________________ __________________________x___________y____________z_____________U(eq)________ Br(1) 55(1) 9005(1) 3832(1) 20(1) Br(2) 1831(1) 7500 1634(1) 18(1) Br(3) 4138(1) 4017(1) -1936(1) 20(1) Br(4) 5615(1) 2500 511(1) 21(1) P(1) 3418(1) 8664(1) 4696(1) 12(1) P(2) 5531(1) 7500 5268(1) 13(1) P(3) 1912(1) 1331(1) 362(1) 14(1) P(4) 434(1) 2500 1779(1) 17(1) Al(1) 1186(1) 7500 3390(1) 13(1) Al(2) 4114(1) 2500 -834(1) 14(1) N(1) 4828(2) 8602(2) 4966(2) 16(1) N(2) 2740(2) 7500 4305(2) 13(1) N(3) 1025(2) 1400(2) 1346(2) 23(1) N(4) 2572(2) 2500 4(2) 12(1) Cl(1) 2547(1) 9241(1) 5982(1) 22(1) Cl(2) 3109(1) 9752(1) 3526(1) 18(1) Cl(3) 5945(1) 7500 6885(1) 20(1) Cl(4) 7138(1) 7500 4584(1) 20(1) Cl(5) 1049(1) 713(1) -954(1) 23(1) Cl(6) 3225(1) 274(1) 738(1) 21(1) Cl(7) 511(1) 2500 3402(1) 29(1) Cl(8) -1358(1) 2500 1438(1) 31(1) _____________________________________________________________________________ 65 Table 7. Bond lengths [Å] and angles [°] for [PCl2N]3.AlBr3. _____________________________________________________ Br(1)-Al(1) 2.2737(6) Br(2)-Al(1) 2.2661(10) Br(3)-Al(2) 2.2731(6) Br(4)-Al(2) 2.2707(10) P(1)-N(1) 1.562(2) P(1)-N(2) 1.6532(15) P(1)-Cl(2) 1.9575(8) P(1)-Cl(1) 1.9791(8) P(2)-N(1)#1 1.575(2) P(2)-N(1) 1.575(2) P(2)-Cl(4) 1.9622(12) P(2)-Cl(3) 1.9988(12) P(3)-N(3) 1.564(2) P(3)-N(4) 1.6517(15) P(3)-Cl(6) 1.9620(9) P(3)-Cl(5) 1.9736(9) P(4)-N(3) 1.577(2) P(4)-N(3)#2 1.577(2) P(4)-Cl(7) 1.9703(12) P(4)-Cl(8) 1.9820(12) Al(1)-N(2) 1.994(3) Al(1)-Br(1)#1 2.2737(6) Al(2)-N(4) 1.992(3) Al(2)-Br(3)#2 2.2731(6) N(2)-P(1)#1 1.6532(15) N(4)-P(3)#2 1.6517(15) N(1)-P(1)-N(2) 116.46(11) N(1)-P(1)-Cl(2) 109.16(8) N(2)-P(1)-Cl(2) 107.51(9) N(1)-P(1)-Cl(1) 110.18(8) N(2)-P(1)-Cl(1) 107.84(10) Cl(2)-P(1)-Cl(1) 105.05(4) 66 Table 7. Bond lengths [Å] and angles [°] for [PCl2N]3.AlBr3 (continued). N(1)#1-P(2)-N(1) 115.75(15) N(1)#1-P(2)-Cl(4) 109.56(8) N(1)-P(2)-Cl(4) 109.56(8) N(1)#1-P(2)-Cl(3) 108.70(8) N(1)-P(2)-Cl(3) 108.70(8) Cl(4)-P(2)-Cl(3) 103.92(5) N(3)-P(3)-N(4) 116.15(12) N(3)-P(3)-Cl(6) 108.69(9) N(4)-P(3)-Cl(6) 107.45(9) N(3)-P(3)-Cl(5) 110.42(9) N(4)-P(3)-Cl(5) 108.20(10) Cl(6)-P(3)-Cl(5) 105.36(4) N(3)-P(4)-N(3)#2 115.28(15) N(3)-P(4)-Cl(7) 109.18(9) N(3)#2-P(4)-Cl(7) 109.18(9) N(3)-P(4)-Cl(8) 109.93(9) N(3)#2-P(4)-Cl(8) 109.93(9) Cl(7)-P(4)-Cl(8) 102.58(5) N(2)-Al(1)-Br(2) 103.90(9) N(2)-Al(1)-Br(1)#1 108.97(5) Br(2)-Al(1)-Br(1)#1 114.16(3) N(2)-Al(1)-Br(1) 108.97(5) Br(2)-Al(1)-Br(1) 114.16(3) Br(1)#1-Al(1)-Br(1) 106.52(4) N(4)-Al(2)-Br(4) 103.42(9) N(4)-Al(2)-Br(3)#2 109.06(5) Br(4)-Al(2)-Br(3)#2 113.65(3) N(4)-Al(2)-Br(3) 109.06(5) Br(4)-Al(2)-Br(3) 113.65(3) Br(3)#2-Al(2)-Br(3) 107.81(4) P(1)-N(1)-P(2) 123.82(13) P(1)-N(2)-P(1)#1 116.98(16) P(1)-N(2)-Al(1) 121.51(8) 67 Table 7. Bond lengths [Å] and angles [°] for [PCl2N]3.AlBr3 (continued). P(1)#1-N(2)-Al(1) 121.51(8) P(3)-N(3)-P(4) 124.65(14) P(3)-N(4)-P(3)#2 117.89(16) P(3)-N(4)-Al(2) 121.06(8) P(3)#2-N(4)-Al(2) 121.06(8) _____________________________________________________________ Symmetry transformations used to generate equivalent atoms: #1 x,-y+3/2,z #2 x,-y+1/2,z 68 Table 8. Anisotropic displacement parameters (Å2x 103) for [PCl2N]3.AlBr3. The anisotropic displacement factor exponent takes the form: -2 2[ h2 a*2U11 + ... + 2 h k a* b* U12 ] _____________________________________________________________________________ U11 U22 U33 U23 U13 U12 _____________________________________________________________________________ Br(1) 15(1) 23(1) 22(1) -5(1) -1(1) 7(1) Br(2) 20(1) 22(1) 12(1) 0 3(1) 0 Br(3) 21(1) 23(1) 17(1) 5(1) 2(1) -4(1) Br(4) 11(1) 36(1) 16(1) 0 -1(1) 0 P(1) 12(1) 11(1) 14(1) 0(1) -1(1) 0(1) P(2) 11(1) 13(1) 15(1) 0 -1(1) 0 P(3) 13(1) 14(1) 16(1) 1(1) 2(1) -2(1) P(4) 10(1) 26(1) 14(1) 0 3(1) 0 Al(1) 11(1) 16(1) 12(1) 0 0(1) 0 Al(2) 11(1) 19(1) 13(1) 0 2(1) 0 N(1) 14(1) 13(1) 22(1) 0(1) -3(1) -3(1) N(2) 11(1) 13(1) 14(1) 0 1(1) 0 N(3) 22(1) 19(1) 27(1) 2(1) 11(1) -3(1) N(4) 12(1) 11(1) 14(1) 0 1(1) 0 Cl(1) 22(1) 25(1) 18(1) -8(1) 2(1) 2(1) Cl(2) 19(1) 14(1) 21(1) 5(1) -4(1) -1(1) Cl(3) 25(1) 21(1) 13(1) 0 -1(1) 0 Cl(4) 11(1) 31(1) 18(1) 0 1(1) 0 Cl(5) 20(1) 24(1) 25(1) -4(1) -4(1) -7(1) Cl(6) 23(1) 19(1) 22(1) 6(1) 2(1) 6(1) Cl(7) 21(1) 53(1) 13(1) 0 1(1) 0 Cl(8) 12(1) 59(1) 23(1) 0 -1(1) 0 69 Adduct: PCl2N]3.GaCl3 70 Asymmetric Unit: [PCl2N]3.GaCl3 71 Table 9. Crystal data and structure refinement for [PCl2N]3.GaCl3. Empirical formula Cl9 Ga N3 P3 Formula weight 523.71 Temperature 100(2) K Wavelength 0.71073 Å Crystal system Monoclinic Space group P2(1)/c Unit cell dimensions a = 11.776(3) Å = 90° b = 10.830(3) Å = 92.011(4)° c = 23.865(6) Å = 90° Volume 3041.6(12) Å3 Z 7 Density (calculated) 2.001 Mg/m3 Absorption coefficient 3.220 mm-1 F (000) 1750 Crystal size 0.11 x 0.08 x 0.07 mm3 Theta range for data collection 1.71 to 28.33°. Index ranges -15<=h<=15, -13<=k<=14, -31<=l<=31 Reflections collected 25603 Independent reflections 7155 [R (int) = 0.0719] Completeness to theta = 28.33° 94.4 % Absorption correction Semi-empirical from equivalents Max. and min. transmission 0.8060 and 0.7066 Refinement method Full-matrix least-squares on F2 Data / restraints / parameters 7155 / 0 / 289 Goodness-of-fit on F2 0.963 Final R indices [I>2sigma(I)] R1 = 0.0397, wR2 = 0.0751 R indices (all data) R1 = 0.0722, wR2 = 0.0797 Largest diff. peak and hole 0.627 and -0.552 e.Å-3 72 Table 10. Atomic coordinates (x 104) and equivalent isotropic displacement parameters (Å2x 103) for [PCl2N]3.GaCl3. U(eq) is defined as one third of the trace of the orthogonalized Uij tensor. _____________________________________________________________________________ x y z U(eq) _____________________________________________________________________________ Ga(1) 3402(1) 6117(1) 1182(1) 15(1) Ga(2) 10959(1) 740(1) 1310(1) 17(1) Cl(1) 12003(1) 669(1) 589(1) 25(1) Cl(2) 9626(1) -611(1) 1308(1) 29(1) Cl(3) 12011(1) 777(1) 2062(1) 27(1) Cl(4) 11121(1) 3787(1) 371(1) 26(1) Cl(5) 9345(1) 1685(1) 141(1) 24(1) Cl(6) 11182(1) 3882(1) 2161(1) 28(1) Cl(7) 9367(1) 1882(1) 2415(1) 25(1) Cl(8) 6641(1) 4550(1) 1205(1) 32(1) Cl(9) 8625(1) 6422(1) 1194(1) 29(1) Cl(10) 6946(1) 10876(1) 1349(1) 26(1) Cl(11) 4571(1) 12124(1) 1289(1) 22(1) Cl(12) 3481(1) 8015(1) 2357(1) 22(1) Cl(13) 6018(1) 7392(1) 2151(1) 24(1) Cl(14) 6064(1) 7524(1) 365(1) 22(1) Cl(15) 3531(1) 8153(1) 78(1) 19(1) Cl(16) 1677(1) 6743(1) 1177(1) 23(1) Cl(17) 3899(1) 5035(1) 1905(1) 24(1) Cl(18) 3865(1) 5125(1) 445(1) 23(1) P(1) 4737(1) 8415(1) 653(1) 14(1) P(2) 4703(1) 8331(1) 1837(1) 16(1) P(3) 5291(1) 10485(1) 1289(1) 16(1) P(4) 9744(1) 3019(1) 669(1) 17(1) P(5) 9774(1) 3112(1) 1852(1) 18(1) P(6) 8316(1) 4625(1) 1218(1) 20(1) N(1) 5019(3) 9823(3) 712(1) 17(1) N(2) 4331(3) 7715(3) 1225(1) 15(1) N(3) 4961(3) 9749(3) 1827(1) 18(1) 73 Table 10. Atomic coordinates (x 104) and equivalent isotropic displacement parameters (Å2x 103) for [PCl2N]3.GaCl3. U(eq) is defined as one third of the trace of the orthogonalized Uij tensor (continued). N(4) 10093(3) 2372(3) 1275(1) 15(1) N(5) 8796(3) 4082(4) 1794(2) 30(1) N(6) 8750(3) 3976(3) 679(2) 22(1) 74 Table 11. Bond lengths [Å] and angles [°] for [PCl2N]3.GaCl3. _____________________________________________________ Ga(1)-N(2) 2.048(3) Ga(1)-Cl(16) 2.1410(12) Ga(1)-Cl(18) 2.1473(12) Ga(1)-Cl(17) 2.1514(12) Ga(2)-N(4) 2.040(3) Ga(2)-Cl(3) 2.1446(13) Ga(2)-Cl(2) 2.1466(13) Ga(2)-Cl(1) 2.1517(13) Cl(4)-P(4) 1.9774(16) Cl(5)-P(4) 1.9642(16) Cl(6)-P(5) 1.9757(17) Cl(7)-P(5) 1.9637(16) Cl(8)-P(6) 1.9730(17) Cl(9)-P(6) 1.9810(17) Cl(10)-P(3) 1.9952(16) Cl(11)-P(3) 1.9671(16) Cl(12)-P(2) 1.9616(16) Cl(13)-P(2) 1.9787(16) Cl(14)-P(1) 1.9796(15) Cl(15)-P(1) 1.9603(15) P(1)-N(1) 1.567(4) P(1)-N(2) 1.648(3) P(2)-N(3) 1.566(4) P(2)-N(2) 1.650(3) P(3)-N(3) 1.572(4) P(3)-N(1) 1.576(3) P(4)-N(6) 1.563(4) P(4)-N(4) 1.646(3) P(5)-N(5) 1.561(4) P(5)-N(4) 1.649(3) P(6)-N(6) 1.569(4) P(6)-N(5) 1.580(4) N(2)-Ga(1)-Cl(16) 103.77(10) 75 Table 11. Bond lengths [Å] and angles [°] for [PCl2N]3.GaCl3 (continued) N(2)-Ga(1)-Cl(18) 108.32(10) Cl(16)-Ga(1)-Cl(18) 114.93(5) N(2)-Ga(1)-Cl(17) 106.83(10) Cl(16)-Ga(1)-Cl(17) 114.08(5) Cl(18)-Ga(1)-Cl(17) 108.38(5) N(4)-Ga(2)-Cl(3) 106.95(10) N(4)-Ga(2)-Cl(2) 103.05(10) Cl(3)-Ga(2)-Cl(2) 114.53(5) N(4)-Ga(2)-Cl(1) 107.25(10) Cl(3)-Ga(2)-Cl(1) 109.97(5) Cl(2)-Ga(2)-Cl(1) 114.33(5) N(1)-P(1)-N(2) 116.13(18) N(1)-P(1)-Cl(15) 110.45(14) N(2)-P(1)-Cl(15) 106.86(13) N(1)-P(1)-Cl(14) 109.76(14) N(2)-P(1)-Cl(14) 108.59(14) Cl(15)-P(1)-Cl(14) 104.37(7) N(3)-P(2)-N(2) 115.42(18) N(3)-P(2)-Cl(12) 109.10(14) N(2)-P(2)-Cl(12) 108.12(13) N(3)-P(2)-Cl(13) 111.07(14) N(2)-P(2)-Cl(13) 107.91(13) Cl(12)-P(2)-Cl(13) 104.63(7) N(3)-P(3)-N(1) 115.84(19) N(3)-P(3)-Cl(11) 109.82(14) N(1)-P(3)-Cl(11) 109.62(14) N(3)-P(3)-Cl(10) 108.54(14) N(1)-P(3)-Cl(10) 109.06(15) Cl(11)-P(3)-Cl(10) 103.21(7) N(6)-P(4)-N(4) 115.74(19) N(6)-P(4)-Cl(5) 109.55(15) N(4)-P(4)-Cl(5) 107.31(13) N(6)-P(4)-Cl(4) 110.47(15) 76 Table 11. Bond lengths [Å] and angles [°] for [PCl2N]3.GaCl3 (continued) N(4)-P(4)-Cl(4) 108.19(13) Cl(5)-P(4)-Cl(4) 105.00(7) N(5)-P(5)-N(4) 116.20(19) N(5)-P(5)-Cl(7) 108.72(17) N(4)-P(5)-Cl(7) 108.06(13) N(5)-P(5)-Cl(6) 110.85(17) N(4)-P(5)-Cl(6) 107.70(13) Cl(7)-P(5)-Cl(6) 104.66(7) N(6)-P(6)-N(5) 115.42(19) N(6)-P(6)-Cl(8) 108.86(15) N(5)-P(6)-Cl(8) 109.03(16) N(6)-P(6)-Cl(9) 110.48(15) N(5)-P(6)-Cl(9) 109.30(17) Cl(8)-P(6)-Cl(9) 103.00(7) P(1)-N(1)-P(3) 123.8(2) P(1)-N(2)-P(2) 118.2(2) P(1)-N(2)-Ga(1) 121.08(18) P(2)-N(2)-Ga(1) 120.76(18) P(2)-N(3)-P(3) 124.3(2) P(4)-N(4)-P(5) 118.0(2) P(4)-N(4)-Ga(2) 120.97(18) P(5)-N(4)-Ga(2) 121.00(18) P(5)-N(5)-P(6) 124.7(2) P(4)-N(6)-P(6) 125.1(2) _____________________________________________________________ Symmetry transformations used to generate equivalent atoms: 77 Table 12. Anisotropic displacement parameters (Å2x 103) for [PCl2N]3.GaCl3. The anisotropic displacement factor exponent takes the form: -2 2[ h2 a*2U11 + ... + 2 h k a* b* U12 ____________________________________________________________________________ U11 U22 U33 U23 U13 U12 _____________________________________________________________________________ Ga(1) 16(1) 15(1) 16(1) 1(1) 1(1) 0(1) Ga(2) 16(1) 14(1) 22(1) -1(1) 1(1) 2(1) Cl(1) 19(1) 27(1) 28(1) -8(1) 6(1) 2(1) Cl(2) 24(1) 17(1) 45(1) -4(1) 5(1) -4(1) Cl(3) 26(1) 29(1) 26(1) 4(1) -6(1) 7(1) Cl(4) 30(1) 26(1) 23(1) 2(1) 8(1) -8(1) Cl(5) 24(1) 26(1) 21(1) -8(1) -5(1) 2(1) Cl(6) 37(1) 22(1) 26(1) -5(1) -4(1) -7(1) Cl(7) 28(1) 27(1) 20(1) 6(1) 7(1) 2(1) Cl(8) 20(1) 23(1) 54(1) 6(1) 7(1) 1(1) Cl(9) 25(1) 17(1) 46(1) -1(1) 2(1) 0(1) Cl(10) 17(1) 31(1) 30(1) 0(1) -2(1) -3(1) Cl(11) 25(1) 14(1) 28(1) -3(1) 1(1) 1(1) Cl(12) 25(1) 23(1) 17(1) 2(1) 7(1) 1(1) Cl(13) 24(1) 25(1) 21(1) -2(1) -5(1) 5(1) Cl(14) 18(1) 24(1) 25(1) 0(1) 7(1) 3(1) Cl(15) 19(1) 21(1) 15(1) 1(1) -3(1) -3(1) Cl(16) 17(1) 27(1) 24(1) 1(1) 2(1) 1(1) Cl(17) 29(1) 20(1) 24(1) 8(1) -4(1) -1(1) Cl(18) 26(1) 19(1) 25(1) -7(1) 7(1) -2(1) P(1) 16(1) 14(1) 13(1) 0(1) 1(1) 0(1) P(2) 19(1) 16(1) 13(1) 0(1) 1(1) 1(1) P(3) 18(1) 15(1) 16(1) 0(1) 0(1) -1(1) P(4) 19(1) 17(1) 14(1) 0(1) 0(1) 1(1) P(5) 24(1) 16(1) 15(1) -1(1) 2(1) 4(1) P(6) 21(1) 16(1) 22(1) 3(1) 4(1) 5(1) N(1) 23(2) 16(2) 13(2) -1(2) 1(2) -1(2) N(2) 19(2) 15(2) 12(2) 2(2) 1(2) -3(2) N(3) 28(2) 13(2) 14(2) 0(2) -2(2) -4(2) 78 Table 12. Anisotropic displacement parameters (Å2x 103) for [PCl2N]3 GaCl3. The anisotropic . displacement factor exponent takes the form: -2 2[ h2 a*2U11 + ... + 2 h k a* b* U12 (continued) N(4) 18(2) 12(2) 14(2) 0(2) 1(2) 2(2) N(5) 38(3) 35(3) 18(2) -4(2) 1(2) 22(2) N(6) 30(2) 21(2) 15(2) 3(2) 0(2) 12(2) ______________________________________________________________________________ 79
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