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Determination of the crystal structures of some inogranic compounds by X-ray diffraction Williston, Carolyn Susan 1967-12-31

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The University of British Columbia FACULTY OF GRADUATE STUDIES PROGRAMME OF THE FINAL. ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY of CAROLYN SUSAN WILLISTON B.Sc. (Hons), The University of British Columbia, 1964 TUESDAY, MAY 9th, 1967, AT 3:30 P.M. IN ROOM 261, CHEMISTRY BUILDING COMMITTEE IN CHARGE Chairman: G. Tener J. Trotter N. Paddock ' CA. McDowell K.B. Har.vey G.G.S. Dutton W. Dalby External Examiner: D. Hall Department of Chemistry University of Alberta Edmonton, Alberta Research Supervisor: J.. Trotter SOME INORGANIC COMPOUNDS BY X-RAY DIFFRACTION ABSTRACT Dimethyltellurium diiodide is known in two forms; the crystal structure of the/ 3-form has been determined by X-ray diffraction. Mo-Ko< s c i n t i l l a t i o n counter data were used for this analysis in which the heavy atoms were located from the Patterson function, the carbon atoms by a difference synthesis and refinement was by least-squares ipethods. /3 -dimethyltellurium diiodide is ionic, [Me3Te] ^MeTel^"] , and is built up from trigonal pyramidal Me3Te+ cations with Te - C = 2.07 K, C - Te - C = 95°, and square pyramidal MeTel^" anions with Te - C = 2.15 A, Te - 1 = 2.84 - .2.98 A. The ions are bridged by four weak Te ... I interactions (distan ces 3.84, 3.88, 3.97, 4.00 A), which complete a distorted octahedral environment around each tellurium atom. The crystal and molecular structures of 2-biphenylyl- ferrocene and 4-biphenylylferrocene have been investiga ted in order to compare the configuration of the rings of the biphenyl and ferrocene groups in these two molecules. The structure of 2-biphenylylferrocene has been determined with visual Cu-Ko< data. The iron atom posi tion was found by Patterson methods, the carbon positions from successive Fourier summations'..' The positional and thermal parameters were refined by least-squares. The cyclopentadienyl rings are eclipsed, the f i r s t six- membered ring of the biphenylyl group is rotated 43° out of the cyclopentadienyl plane and the outer six-membered ring is rotated 58° out of the plane of the f i r s t six- membered ring. These rotations relieve the strain which would exist in a planar model for the C5H4 . C 6 H 4 . C6H5 group. The mean bond distances are Fe - C = 2.05 A, C - C (cyclopentadienyl) = 1.44 A. Using Fe-K°< s c i n t i l l a t i o n counter data, the structure of 4-biphenylylferrocene has been determined by Patterson and Fourier methods and refined by least-squares. The two crystallographically independent molecules in the unit c e l l have slightly different conformations. In one the cyclopentadienyl rings are oriented about midway between the eclipsed and staggered conformations and the f i r s t six-membered.ring is rotated 6° out of the plane of the cyclopentadienyl ring to which i t is bonded, with the second six-membered.ring rotated a further 9°. In the second molecule the cyclopentadienyl rings are only about 5° from the f u l l y eclipsed position and the "six-membered ring rotations are 0° and 10°.. The mean bond distances are Fe-C =2.07 A, C-C (cyclopentadienyl) =1.48 A, C-C (biphenylyl) = 1.43 A, C-C (between rings) = 1.48 A. The intermolecular separations correspond to van der Waals1 interactions. GRADUATE STUDIES Field of Study: Chemistry Topics in Physical Chemistry Topics in Inorganic Chemistry Topics in Organic'Chemistry Crystal Structures Advanced Inorganic Chemistry Chemistry of the Solid State The Chemistry of Organometallic Compounds Seminar in Special Topic Seminar in Chemistry J.A.R. Coope W.C. Lin H.C. Clark W.R. Cullen N.L. Paddock R.C. Thompson L.D. Hall F. McCapra D.E. McGreer S.A. Melzak J. Trotter R.C. Thompson L.G. Harrison W.R. Cullen J. Trotter K.B. Harvey Related Studies: Programming and Numerical Algorithms Linear Algebra A.G. Fowler H.A. Simons PUBLICATIONS Carolyn S. McCammon and James Trotter, THE STRUCTURE OF p-BROMOBENZOIC ANHYDRIDE, Acta Cryst., jL_7, 1333 (1964) . James Trotter and C.S. Williston, CRYSTALLOGRAPHIC STUD OF AN UNKNOWN COMPOUND FROM WESTERN RED CEDAR, Acta Cryst., 20, 460 (1966). " ' James Trotter and C.S. Williston, BOND LENGTHS AND THERMAL VIBRATIONS IN m-DINITROBENZENE, Acta Cryst.',-.21 285 (1966) . THE DETERMINATION OF THE CRYSTAL STRUCTURES OF SOME INORGANIC COMPOUNDS BY X-RAY DIFFRACTION by CAROLYN SUSAN WILLISTON B.Sc. (Hon.), University of British Columbia, 1964 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the Department of Chemistry We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA April, 1967 In p r e s e n t i n g 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 o f the r e q u i r e m e n t s f o r an advanced deg ree a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i 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 r e f e r e n c e and s t u d y , I f u r t h e r ag ree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e Head o f my D e p a r t m e n t o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f C hemi'sfry The U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8, Canada D a t e M d M q-,  i i ABSTRACT Supervisor: Professor James Trotter Dimethyltellurium diiodide is known in two forms; the crystal structure of the B-form has been determined by X-ray diffraction; Mo-Ka sc i n t i l l a t i o n counter data were used f o r this analysis in which the heavy atoms were located from the Patterson function, the carbon atoms by a difference synthesis and refinement was by least-squaresmethods. g-dimethyl- tellurium diiodide is ionic* [Me3Te]+ [MeTel^]", and is. built up from trigonal pyramidal Me3Te cations with Te - C = 2.07 A, C - Te - C = 95°, and square pyramidal MeTeIi+" anions with Te - C = 2.15 A, Te - I = 2.84 - o 2.98 A. The ions: are bridged by four weak Te... I interactions (distances k 3.84, 3.88, 3.97, 4.00 A), which complete a' distorted-octahedral., environment around each tellurium atom. The crystal and molecular structures of 2-biphenylylferrocene .and 4- .biphenylylferrocene have been investigated in order to compare the con figuration! of the rings of the biphenyl and ferrocene groups in these two molecules. The structure of 2-biphenylylferrocenje, has been determined with visual Gu-Ka data. The iron atom position was found by Patterson methods, the carbon positions from successive Fourier summations. The positional and thermal parameters were refined by least-squares. The cyclopentadienyl rings are eclip-sed, the f i r s t six-membered ring of the biphenyl group is rotated 43° out of the cyclopentadienyl plane and the outer six-membered ring is rotated 58° out of the plane of the f i r s t six-membered ring. These rotations relieve the strain which would exist in a planar model for the o C5H4 • CgH^ • CgH5 group. The mean bond distances are Fe - G = 2.05 A, C - C i i i (cyclopentadienyl) = 1.44 A. Using Fe-K^ scintillation counter data, the structure of 4^biphenylylferrocene has been determined by Patterson and Fourier methods and refined.by least-squares. The two crystallographically independent molecules in the unit cell have slightly different conformations. In one the cyclopentadienyl rings are oriented about midway between the eclipsed and staggered conformations and the first six-membered ring is rotated 6° out of the plane of the cyclopentadienyl ring to which i t is bonded, with the second six-membered ring rotated a further 9°. In the second molecule the cyclopentadienyl rings are only about 5° form the fully eclipsed position and the six-membered ring rotations are 0° and 10°. The mean bond distances are Fe-C = 2.07. A, C-C (cyclopentadienyl) = 1.48 A, C-C (biphenylyl) = .1.43 A , o C-C (between rings) = 1.48 A. The intermolecular separations correspond to, van der Waals' interactions. iv TABLE OF CONTENTS PAGE TITLE PAGE i ABSTRACT . . . i i TABLE OF CONTENTS iv LIST OF TABLES v i LIST OF FIGURES . . v i i ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . v i i i GENERAL INTRODUCTION 1 PART I. THE DETERMINATION OF THE STRUCTURE OF 0-DIMETHYLTELLURIUM DIIODIDE . . . . . . . . . . 3 A. INTRODUCTION . . . . . . . 4 B. THE STRUCTURE OF 6-DIMETHYLTELLURIUM DIIODIDE . . . . 6 Experimental . . . . 6 Structure Analysis ... 7 Coordinates and Molecular Dimensions 10 Discussion 12 PART II. THE DETERMINATION OF THE STRUCTURES OF 2-BIPHENYLYLFERROCENE AND 4-BIPHENYLYLFERROCENE . . . . 18 A. INTRODUCTION 19 B. THE STRUCTURE OF 2-BIPHENYLYLFERROCENE . . 22 Experimental 22 Structure Analysis 23 Coordinates,and Molecular Dimensions 27 Discussion 27 C. THE STRUCTURE OF 4-BIPHENYLYLFERROCENE . . . . . . . . 33 Experimental 33 V PAGE Structure Analysis 34 Coordinates and Molecular Dimensions 37 Discussion 40 APPENDIX I. DESCRIPTION OF SOME COMPUTER PROGRAMS WRITTEN FOR SPECIAL CALCULATIONS IN THESE ANALYSES . . 43 A. ABSORPTION CORRECTION FOR THIN FLAT CRYSTALS . . . . 44 B. ANGLE OF ROTATION FROM ECLIPSED POSITION 47 APPENDIX II. TABLES OF OBSERVED AND CALCULATED STRUCTURE;FACTORS . 50 BIBLIOGRAPHY 56 vi LIST OF TABLES TABLE PAGE g-Dimethyltellurium Diiodide I. Final positional parameters and standard.deviations, and thermal parameters and standard deviations, 11 II. Interatomic distances and angles . . . . 13 2-Biphenylylferrocene III. Final positional and thermal parameters 28 IV. Mean bond distances and valency.angles, equations of mean planes and angles, between planes 29 4-Biphenylylferrocene V. Final positional and isotropic thermal parameters . . . 38 VI. Mean bond distances and valency angles, equations of mean planes and angles between planes 39 Appendix II VII. g-Dimethyltellurium diiodide measured and calculated structure factors 51 VIII. 2-Biphenylylferrocene measured and calculated structure factors 53 IX. 4-Biphenylylferrocene measured and :calculated structure factors . . . . . . . 54 v i i LIST OF FIGURES FIGURE PAGE 3- Dimethyltellurium Diiodide 1. (a) Projected electron-density distribution 9 (b) Perspective drawing showing atom numbering 9 2. Packing diagram 15 2-Biphenylylferrocene 3. Projected electron-density distribution 25 4. ...Perspective drawing showing atom numbering 26 5. Molecular packing diagram 30 6. Projection of cyclopentadienyl rings 32 4- Biphenylylferrocene 7. Projected electron-density distribution . 35 8. Perspective drawing showing atomi numbering . . . . . . 36 9. Projection of cyclopentadienyl rings 42 ACKNOWLEDGEMENTS I wish to express my greatest appreciation for the inspiration and guidance Professor.James Trotter has given me during the past four years. His ingenuity and personality have made working under his supervision a most rewarding and enjoyable experience. My thanks are due to Dr. F. Einstein for the g-dimethyl- tellurium diiodide sample and for much helpful discussion and advice. I am indebted to Dr. M.D. Rausch for the -crystals 0 f 2-bipheny.lylferco.cene'an!^^ Finally, I wish to thank the National Research Council of Canada for awarding me a Bursary for 1964-65 and Studentships for 1965-67. 1 GENERAL INTRODUCTION Rontgen discovered X-rays in 1895. In 1912 von Laue suggested that a diffraction pattern should result from passing X-rays through a crystal and Friedrich and Knipping experimentally confirmed his theory. Bragg developed a mathematical interpretation, of. this phenomenon which, in 1913, enabled him to determine the f i r s t crystal structure by X-ray diffraction. Before this time very l i t t l e was. known about the solid state. Properties which could be observed.could.not be explained. Knowledge of, the behaviour of atoms and molecules, in the liquid and gaseous states could be gained by observing chemical reactions.. However, i t was not even known what the basic unit of .crystals was, although their general properties indicated a regular arrangement of small, identical units. But now a method was available to investigate^the structure of crystals on an;atomic scale. Since 1913 the science of X-raycrystallography has developed rapidly and has been used to determine the crystal structures of thousands of compounds. These structures, of course, have made a primary contribution to the modern theories of structural inorganic chemistry. Atoms attain their particular arrangement in the crystal because.. the various attractive and repulsive forces acting on them are in balance. An X-ray crystal structure determines the position of each atom in the unit c e l l and the distances between the .atoms.. Also the contoured electron density maps give an idea of atomic radii and how electrons may be spread out between atoms. This information of bond lengths and angles, and electron distribution enables the inorganic chemist to deduce theories as to what type of bonding and other forces are. present in the crystal. A complete X-ray analysis can indicate whether the bonding is primarily covalent or 2 primarily ionic, whether a compound actually exists as discrete molecules as in a simple covalent compound or whether i t is completely ionic as in NaCl where there is coordination but no molecule. The crystal structure also suggests what the influence of intermolecular or interionic forces may be on the shape of a molecule or ion and shows any bridging interactions which may be present. Depending on whether the structure f a l l s into the expected pattern or whether i t has some unusual features, certain predictions can be made about related unknown compounds. Thus, the structural information made available.through the method of X-ray crystallography and from other, methods has enabled the development of an extensive theory of the chemical bond. With ,the modern automated X-ray equipment and growing computing f a c i l i t i e s the number and the accuracy of structural determinations w i l l continue to increase. And a greater understanding of the nature of molecules and crystals should be possible in the future. This thesis is concerned with the determination by single-crystal X-ray diffraction .of the structures of three inorganic compounds. These structures have been solved by.Patterson and Fourier techniques and refined by least-squares methods which are described in many reference books including those lis t e d in the Bibliography 1,2 and 3. A l l calculations were done on the IBM 7040 computer at the University of-British Columbia Computing Centre. Part I of the thesis describes the structure analysis of 6-dimethyl- tellurium diiodide. Part II consists of the investigation of the crystal and molecular structures of two arylferrocenes, 2-biphenylylferrocene and 4-biphenylylferrocene. In Appendix I two computer programs^written for special purposes in these analyses are described and listed. Appendix.II contains the tables of observed and calculated structure factors of a l l compounds in the thesis. PART I THE DETERMINATION. OF. THE STRUCTURE OF B-DIMETHYLTELLURIUM DIIODIDE 4 A, INTRODUCTION Vernon (4), in 1920, discovered that dimethyltellurium diiodide exists in tyio forms. He obtained these according to the following reactions postulating that they were trans and cis Isomers of a square-planar structure. Te + 2CH3I ^ a g f f i > Te(CH 3hI 2 Te(CH 3) 2(0H) 2 (a-dimethyltellurium diiodide) (a-base) e v a P ° r a t e Te(CH : 3) 2(0H) 2 J£L- Te(CH 3) 2I 2 (g-base) (g-dimethyltellurium diiodide) However, Drew (5), in 1929, re-examined the diiodides and suggested that the a-dimethyltellurium diiodide had. the covalent structure Me 2TeI 2, but the g-compound was not isomeric, rather i t was a complex salt-like compound. He showed that Vernon's g-diiodide can be made by mixing t r i - methyltellurium iodide (Me3TeI) and methyltellurium triiodide (MeTeI 3). Also, reaction of potassium iodide with the g-diiodide gave Me3TeI and K[MeTeIiJ . From this evidence Drew, concluded that the 6-compound was probably of the form [Me3Te] +[MeTeIi t]T The crystals of g-dimethyltellurium diiodide used in this analysis were prepared by Dr. F. Einstein using Vernon's method (4) Starting from a commercial sample of a-diiodide. They. were, shiny black plates without the strong odour of the red a-dimethyltellurium diiodide crystals. Comparison of the mass spectra (6). of the a and g-diiodides showed that a peak corresponding to a Me2TeI fragment that was present in the spectrum of the a-form was absent, in. that, of the 6-form. This would indicate that although the a-form could be simply Me 2TeI 2 the g-form probably does not contain a Me2TeI unit. Therefore, from the chemical and physical evidence i t seemed likely 5 that g-dimethyltellurium diiodide would, exist as [Me3Te]+[MeTel^] . On the basis of electron-pair repulsion theory (7) the cation, Me3Te+, with three bonding pairs of electrons around the tellurium atom would be expected to assume atrigonal pyramidal structure. The lone pair would occupy the fourth position of a tetrahedron. The anion, MeTeI4 , has five bonding pairs and one lone pair of electrons surrounding the tellurium atom. Thus, i t should exist as a square plane of iodine atoms around the tellurium atom with the methyl group above and. the lone pair below the plane. It was interesting to determine whether this was, the structure and to investigate the extent of interionic interactions which might occur. Vernon (8)-made an optical.crystallographic comparison of the two diiodideS. The results of his measurements were as follows: a-diiodide- monoclinic, a:b: c ,= 0.557.8:1;0.4310, B. = 70°21'; B-diiodide-/- monoclinic a:b:c = 0.5465:1:0.4222, B = 76°52V. Preliminary X-ray studies of a-Me2TeI2 have been made by Galloni and Pugliese (9). Their c e l l constants are similar to those obtained from our crystals of a-MejTe^ and to Vernon's data. 6 B. THE STRUCTURE OF B-DIMETHYLTELLURIUM DIIODIDE Experimental Crystals of B-dimethyltellurium diiodide are shiny black plates. elongated along £ with (010) developed The unit c e l l arid space group were determined from precession photographs, and. on the G.E. Spectrogoniometer. The density was measured by flotation in a solution of iodoform in methylene iodide. o Crystal data (X, Mo-K^  = 0.7107 A) B-dimethyltellurium diiodide, [Me3Te] + [MeTel^]"; M.W. = 823.0 . Monoclinic, a =8.12 + 0.01, b = 19.30 + 0.02, c = 10.58 + 0.02 A, B = 103°15' + 5'. U = 1614 A 3, D = 3.5 g.cm."3, Z = 4 (i.e. 8 Me 2TeI 2 units), D = 3.4 g.cm." — Jfi ~~'X F(000) = 1408. Absorption coefficient for X-rays, u(Mo-JCp = 114 cm.-1. Absent reflexions: hO^.when is odd, OkO when k_ is odd. Space group is P2i/c(CJh). The axial ratios and angle (a:b:c_. .= 0.4210:1:0.5483; 3 = 103.3°) are in agreement with those measured optically (0.4222:1:0.5465; 103.1°). The intensities of the reflexions were measured on a General Electric XRD 5 Spectrogoniometer with Single Crystal Orienter, using a s c i n t i l l a t i o n counter, approximately monochromatic Mo-jC radiation (zirconium f i l t e r and pulse height analyser), and a 0-20 scan. Of 1504 reflexions with o 20(Mo-Ka) ^ 40 (corresponding to a minimum interplanar spacing of 1.04 A), 1213 were observed. The 291 unobserved reflexions were included in the analysis with |F I =0.6 F^ , . , ,.... A l l . the intensities were corrected 3 '—o1 —threshold for background (approximately a function of 0 only). The crystal measured 7 0.42 x 0.10 x 0.75 + 0.03 mm. along a, b_, and £ respectively and was mounted with c* parallel to the <j> axis of the goniostat. Absorption was serious,, and corrections were applied by the method of Zajlkin, Forrester and Templeton (10) (see Appendix I:A); I (Corrected) = I (measured) / {1 + 9.35 exp(-0.63/m)} . The correction factor varied from 0.168 to 1.000. Lorentz and polarization... factors were applied" and the structure amplitudes were derived. Structure Analysis The positions.of the four iodine .atoms,and two tellurium atoms were determined from the three-dimensional Patterson function by considering the predicted structure, [Me3Te]+[MeTel^] . A square plane of iodine atoms was chosen from the strong near origin peaks so that '. 1(1) arid 1(3), 1(2). and 1(4) were related by a centre of symmetry at the origin. Thus, iodine ) coordinates were obtained relative to the central tellurium atom at the origin. The six peaks on the Harker line at (OJi2-2y, 1/2) and the eight. peaks on the Harker section at. (2oc, 1/2, 1/2 + 2z) were then examined to find (x, y_, z) coordinates consistent with, the relative coordinates. This was aided by the realization that the strongest peak on the Patterson map, other thjan the origin peak, was the (2x, 2y, 2z) Te(5) - Te($)' peak because i t also included 1(1) .- I (3) *, I (2)-I (4) 11.(3) - 1(1)' and 1(4) - 1(2)' peaks due to the symmetry of the square plane.. After the Harker peaks for the four iodine atoms.and the central tellurium atom were assigned, there were three remaining peaks on*the Harker section, one of which, together with the sixth peak on the Harker line; determined, the. coordinates of Te(6). A l l of the major peaks on the Patterson map could be. explained by the atomic coordinates chosen, which were a l l within 0.3 A of their f i n a l values. 8 Structure factors were calculated using scattering factors from the 0 International Tables for X-ray Crystallography (11) and with B_ = 3.0 A for a l l six atoms, giving an R factor of 0.41. The positional and isotropic thermal parameters were then refined by block-diagonal least-squaresmethods. The function minimized was Zw(F -F ) 2 , with •/W = 0.35 for unobserved — —o —c — reflexions, v^v = 1 when I f J 4 80, and Vw = 80/l'Fj When \F^\ > 80, so that the average wfF^-F^) 2 was approximately constant over a l l values of F^ taken at intervals of 20. Two cycles of least-squares reduced R to 0.19. Refinement was continued for several more cycles, then a (F -F_ T) ' —o —Te,I difference synthesis was computed to locate the four carbon atoms. The - •• 0 , !* • largest peaks :(j.up to 6.5 e. A ) on the difference map occurred in the regions of the heavy atom positions indicating the presence of absorption and perhaps anisotropic thermal motion. The carbons were placed,partly from stereo- • • • • • • 0 3 chemical considerations, on peaks of 5.6, 5.8, 5.2, 4.3 e.A" for C(7), C(8), C(9) and C(10) respectively. These carbon atoms, with B_ = 4.5 A , were included in the next structure factor calculations. Refinement of the para meters of a l l ten atoms proceeded until R was 0.17. The small shifts for the carbon atoms indicated they had been placed correctly. At this point, an examination of the values of F^, and the absorption correction for each reflexion suggested that the correction was top severe. The intensities were then recorrected according to the equation I(corrected) = I(measured)/{1"+ 6.50 exp(-0.68/m)} so that the graph of F^/F^ versus the absorption correction was approximately a line of: zero slope. The new correction factor varied from 0.235 to 1.000. A structure factor calculation using the recorrected data gave. R = 0.15. Further refinement with isotropic thermal parameters reduced R_ Figure 1. (a) Electron-density projection along the a axis. Contours are at intervals of 1 e. A-3, s t a r r i n g at 2 e. X~ 3for C,0 and of 10 e. A"3 starting at 10 e. A - 3 for Te and I. 0 I 2 3A (b) Perspective drawing of the structure giving the numbering used. 10 to 0.12, and refinement with anisotropic thermal parameters for the tellurium and iodine atoms gave R = 0.09. At this stage, the corresponding discrepancy factors for the uncorrected and over-corrected data were 0.19 and 0.12, so that the corrections for absorption improved the structure factor agreement considerably. Analysis of the values of w(F -F.) 2 suggested — —o c 1/2 alteration of i/w~for the observed reflexions to 1/[1 + {(|F^|-50)/40}2] ; in addition the three most intense reflexions,(300, 122, 150), which were apparently affected by extinction, were removed. Further refinement then produced negligible changes in the parameters. The fi n a l measured and calculated structure factors are listed in Table VII (Appendix II), (R = .0.09 for the 1213 observed reflexions). A fina l three-dimensional Fourier series was summed and superimposed sections of the resulting electron-density distribution are shown in Figure 1, together with a drawing of the structure giving the atom numbering used in the analysis. A final difference map showed maximum fluctuations of + 2 e. A - 6 . Coordinates and Molecular Dimensions The final positional and thermal parameters are given in Table I. x, y_ and z_ are fractional coordinates referred to the monoclinic crystal axes and IJ_ are the components of the vibration tensors, written in matrix form and referred to axes a*, b* and c*.. Table I also gives the magnitudes of the principal axes of the vibration ellipsoids, which are not physically unreasonable, the vibrations being smallest along the bonds. The significant interatomic distances and angles are given in Table II. The mean plane through the four iodine atoms in the MeTel^ ion has the equation: Table I. Final positional parameters (fractional) and standard, deviations (A), and thermal parameters and standard deviations (U.. in A 2 x 102; B in A 2) ^ Atom Mean a (A) 1(2) 1(3) 1(4) Te(5) Te(6) C(7) C(8) C(9) C(10) 0.0788 0.3752 -0.0388 -0.2854 0.0334 0.3344 -0.0742 0.4251 0.-5730 0.345*8 -0.0479 0.1322 0.2109 0.0299 0.0808 0.1550 0.1266 0.0582 0.4955 0.1658 0.3215 0.3017 0.0303 0.0298 0.1673 0-6538 0.3150 0.6557 0.-J6586 0.8557 0.0053 0.0057 0.0059 0.0053 0.0041 0.0O53 0.065* 0.069 0.087 0.086 Mean Atom U 1 2 y 1 3 y 2 2 U 2 3 U 3 3 ocy: I ( D 6.1 0.6 2.4 5.2 1.2 9.3 0.3 1(2) 5.6 -1.5 1.0 5.6 -0.9 9 .6. 0.3 1(3) 9.4 -0.9 2.3 5 I 1.9 10.3 0.3 1(4) 5.6 -1.6 0.6 6.6 ' -0.1 6.5 0.3 Te(5) 4.7 -0.8 .. 1.8 3.5 -0.8 5.7 0.2 Te(6) 5.9 2.3 2.7 5.6 1.9 9.6 0.3 Atom B 0(B) c;(7) 3.7 1.3 C(8) 4.1 1.4 C(9) 6.2 . 1.9 G(10) 6.1 1.9 Magnitudes of principal axes of vibration ellipsoids: Atom y i i U '22 U '3 3 1(1) 4.8 5.8 9.7 ;i(2) 4.1 7.1 10.1 K3) 4.2 9.6 11.1 1(4) 4.3 6.6 8.1 Te(5) 3.0." 4.3 6.'2 Te(6) 3.5 6.6 10.7 12 ... -0.584 X' + 0.397 Y + 0.708 Z* = 1.963; o where X', Y and Z' are in A and referred to orthogonal axes a, b and c*. The displacements from this plane of the 1(1), 1(2), 1(3), 1(4) and Te(5) atoms are -0.10, + 0.10, -0.10, +0.12 and +0.04 A respectively, so that the iodine atoms are alternately slightly above and below the plane, the displacements being highly significant. Discussion This crystal structure analysis has shown 3-dimethyltellurium i_ _ _ diiodide to be a coordinate compound consisting of the Me3Te ion and the MeTelt! ion. However, a number of relatively short interionic I...Te contacts is evidence of some bridging interactions. The cation, Me^Te*, has a distorted trigonal pyramidal structure. Or i t could be considered as tetrahedral with the lone pair occupying the fourth position. This is the structure expected for sp_3 hybridization of the tellurium atomic orbitals. the average C-Te-G angle is 95° (a = 2°). The repulsion from the lone pair would tend to reduce the angle relative to the regular tetrahedral angle of 109.5°. It can be compared to the following bond angles (12): 0Me2- 110°; OH2- 104.5°; TeH2 - 89.5°. The small angle at Te relative to that at 0 can be explained by the fact that Te is larger and less electronegative; than 0 and thus the bonding pairs are drawn further out towards H and further apart from each other, and the bond-pair: bond-pair repulsion is less. This canalso be considered as an increase in p_ character of the bond as the electron pairs are drawn out from the nucleus. However, in TeMe3+ an angle larger than 89.5° is expected because of the size of.the three methyl groups and because of the presence of only one lone pair instead of the two in TeH2. The average Te-C bond length isV2.07 A (a = 0.06 A) Table II. Interatomic distances(A) and angles (degrees) [Me3Te]" ' Te(6) - C(8) Te(6) - C(9) Te(6) - C(10) [MeTel^]" Te(5) - C(7) 2.15 Te(5)...I(4)' 3.88 mean 2.01 2.08 2.13 2.07 Te(5) - 1(1) 2.948 Te(5) - 1(2) 2.984 Te(5) - 1(3) 2.891 Te(5) -1(4) : 2.840 Te(6)...I(l) Te(6)...I(2) Te(6)'...I(3) II III 4.00 3.84 3.97 Te(5) I - Te(5)- C 88,6,89.3,90.6 C- Te(6) - C 91.8, mean 90.0 87,88,90,92 C - Te(6)...1 C(7) - Te(5)...I(4) I - Te(5)...I(4) 1 I 166 80-106 91,97,99 mean 95 77-114(cis) 149,170,173(trans) Standard deviations Equivalent positions Te - I 0.007 Standard X y z Te - C 0.08 I -x -y -z I - Te - I 0.2 II -X -y 1-z I - Te - C 1.7 III X i 1 2+Z- C - Te - C 3.2 14 compared to 2.09 A in a-Me 2TeCl 2 (13). The anion, MeTel^ , is a distorted square pyramid. This structure can be explanied by d 2sn 3 hybridization of the tellurium orbitals, the lone pair occupying the sixth position of the octahedron opposite the methyl group. The iodine atoms are alternately above and below their mean plane by o 0.1 A, the C-Te-I angles averaging 87° and 91°. This buckling is probably caused by steric interactions between, the iodines, the mean I...I distance o o being 4.13 A. The Te-C bond distance is 2.15 A. The Te-I bond lengths o are 2.84, 2.89, 2.95 and 2.98 A; these are of the same order as those in (p-ClC 6Hi +) 2TeI 2 (2.92 and 2.95 A) (14), but the differences between the four bond lengths are highly significant and are probably related to the involve ment of the iodines in interionic interactions. The structure contains four short interionic Te-. . . I distances of 3.84, 3.88, 3.97, 4.00 A (Table II, Figures 1 and 2). The sum of the van 0 der Waals'radii of tellurium and iodine is 4.35 A (15). A l l the other interionic distances are greater than the sums of the van der Waals' r a d i i , o o o the shortest contacts being Te...1 = 4.38 A, I. . .1 = 4.43 A, I...C = 3.85 A. The four relatively short contacts suggest weak bridge-bonding between the ions. Three of these contacts are from the Me3Te+ cation to three different iodines of three neighbouring MeTelit anions and these contacts complete a distorted octahedral evironment around the tellurium atom of the Me3Te+ ion. The lone pair on this tellurium atom would be in the centre of the three iodine contacts. The distances and angles in the bridges may be summarized as follows: Te(5) - 0 I I...Tef6) I...Te(6) -C 1(1) 2.95 A 4.00 A 170° 1(2) 2.98 ' 3.84 173 1(3) 2.89 3.97 ! 149 16 where the trans I...Te-C angles are listed. The greatest deviation of these angles from the regular octahedral value of 180° is for the contact involving 1(3), 149°, and this contact is one of the longer and presumably weaker o bridges, 3.97 A. The Te-I(3) bond distance is the shortest of the three. e 1(2) is involved in the shortest and most regular contact, 3.84 A and 173°, and in the longest Te-I bond.I(1) is approximately intermediate. The Te-I...Te angles at 1(1), 1(2) and 1(3) are 118°, 103° and 110° respectively. The forces involved in these bridging interactions are probably largely electrostatic. However, there may be some donation of electrons from iodine to d-orbitals on the tellurium atom, resulting in partial neutrali zation of the positive charge on the cation. 0 The fourth short "'interionic Te... I distance, 3.88 A, occurs between MeTelt^- anions, these anions being joined by two such contacts to form o centrosymmetrical dimers (Figure 2). The Te(5)-I(4) bond distance, 2.84 A, is the shortest of the four Te-I lengths and the Te(5)...I(4) interionic contact, 3.88 A, is also one of the shorter interionic distances. The Te-I(4)...Te angle is 86°. . This bridging occurs to the region where the lone pair electrons of the tellurium atom are expected to be, the C-Te...I angle being 166°. Therefore, the interionic bonding1 in the anion likely involves donation of electrons from the tellurium lone pair into d-orbitals of the iodine atom. This is in contrast to the cation in which the positive charge means its non-bonding lone pair is influenced by a. relatively strong f i e l d and as a result does not appear to be directly involved in the bonding. On the other; hand, the lone pair on the negatively charged anion is more weakly held and is more available for interionic bonding. Thus the structure of 8-dimethyltellurium diiodide consists, essentially of trigonal pyramidal Me3Te+ cations and square pyramidal MeTe11+ anions. The interionic:bridge-bonds which; occur indicate that i t cannot be regarded 17 as a purely ionic compound. PART II THE DETERMINATION OF THE STRUCTURES OF 2-BIPHENYLYLFERROCENE AND 4-BIPHENYLYLFERROCENE 19 A. INTRODUCTION Both 2-biphenylylferrocene and 4-biphenylylferrocene consist of a biphenylyl ligand attached to ferrocene. The structures of biphenyl and of ferrocene in the solid and in the vapour states have been studied because the configurations they assume are important in relation to possible explana tions of bonding in these compounds. It was of interest to determine the crystal structures of 2-biphenylylferrocene and 4-biphenylylferrocene to compare the orientations of the biphenylyl rings and the arrangement of the cyclopentadienyl rings with those of biphenyl and ferrocene. These structures analyses sh'ould provide further evidence as to the relative importance of intermdlecular packing forces and intramolecular bonding forces in determining the orientations of the molecules. Electron diffraction studies (16) indicated that in the vapour the angle between the planes of the two rings of biphenyl was 45°. However, X-ray analyses (17) showed that biphenyl was almost completely planar in the solid state'. Even the ortho hydrogens which would be expected to be pushed out of the molecular plane by steric repulsion, remained in the o o plane. The distance between them was increased from 1.80 A to 2.07 A by the opening of the C-C-H valency angle from 120°, thus relieving the strain without sacrificing planarity. However, because of the long inter-ring C-C bond length and its non-planarity in the vappur state, i t seems unlikely that there is much derealization of electrons between the two rings but rather i t is intermolecular packing forces which are. the main cause of biphenyl's planarity in the crystalline state. It is quite possible then, that under the different packing forces experienced in the 2-biphenylylferrocene and 4-biphenylylferrocene molecules the strain of 'the ortho hydrogens would cause the rings to be rotated from a CPplanar position. 20 Dicyclopentadienyl iron ( f i r s t written as I) was discovered accidentally in 1951 (18). To explain i t s remarkable st a b i l i t y i t was proposed that there were important contrihu'tions from the resonance form (II) and intermediates and the cyclopentadienyl group tends to become "aromatic". CH \ CH-Fe-CH CH 'CH . CH :-CH CH CH ^ CH CH I* CH CH / CH ^ \(") •(+)(+) (-) / ^ Fe CH CH '•CH I CH II This compound's unusual character and structure created great interest and further chemical and physical investigations immediately followed. The X-ray analysis (19) showed its structure to consist of the iron atom sand wiched between two parallel cyclopentadienyl rings. Various theories were put forth to explain the bonding. These theories had to allow for the experimentally observed features of equivalent bonding to a l l five carbons in each ring and free rotation of the rirtgs, which had been shown to occur in the vapour (20). The two cyclopentadienyl rings in ferrocene are staggered (19) as they are in the corresponding Co(21), Ni(21), V(22) and Cr(22) compounds. However,, in ruthenocene (23) and osmocene (24) the rings are in the eclipsed configuration. This suggests that i t is probably lattice forces, rather than the metal-ring' bonding forces, which determine the ring orientations. Although, possibly the fact that the rings in ruthenocene (inter-ring O . ' . distance 3.68 A (23)) are futher apart than in ferrocene (inter-ring distance 3.32 A (19)) could explain why the fomer compound more<easily assumes an eclipsed configuration, when the staggered one would be expected to be more stable. However, ferrocene, biferrocenyl (25) and differocenyl ketone (26) 21 o 0 o have inter-ring distances of 3.32 A, 3.32 A and 3.30 A respectively, yet, whereas the rings in ferrocene are staggered (36° rotation from eclipsed position), those in biferrocenyl are rotated 17° and the rings in differocenyl are rotated only 5.2° from an eclipsed position. This further indicates that the packing forces are most important in determining the rotational configu ration of the cyclopentadienyl rings. - It is also interesting that the cyclopentadienyl rings in these compounds are not always parallel. Although the rings in ferrocene are essentially parallel,-''those in 1,1'-tetramethylene-ferrocjsne (27), for example, are t i l t e d 23° with respect to one another. 2-biphenylylferrocene and 4-biphenylylferrocene were prepared by Dr. M.D. Rausch (28) by simultaneous decomposition of , differocenylmercury and the corresponding di-biphenylylmercury compound in the presence of silver. He also synthesized 4-biphenylylferrocene by reaction of 4-biphenyl- yldiazonium chloride and ferrocene. 22 B. THE STRUCTURE OF 2-BIPHENYLYLFERROCENE Experimental Crystals of 2-biphenylylferrocene (28) are orange-yellow needles elongated along b_. The density was measured by flotation in aqueous potassium iodide and the unit c e l l dimensions and space group were determined from rotation and Weissenberg photographs. Crystal data (X, Cu-K^ = 1.5418 A) 2-Biphenylylferrocene, C 2 2H 1 8Fe; M.W. = 338.2; m.p.=133-134°. Orthohombic, a. = 23.16, b = 5.92, £ = 11.56 A. °3 o U = 1585 A , D = 1.40, Z = 4, D = 1.42 g.cm.~i. — ~2L 21 F(000) = 704. Absorption coefficient for X-rays, ufCu-K^) = 77 cm.-1 Absent reflexions: Ok £ when £ is odd, hJH when ih is odd. Space group is 5 1 1 Pca2j (C_2V) or Pcam (D2h) • Pca2j from structure analysis. A l l the crystals were very small and poorly formed and gave poor diffraction patterns w:hich exhibited a rapid decrease in intensity with increasing Bragg angle. Nevertheless, interest in the general structure of the molecule prompted the continuation of the analysis, although the paucity of experimental data.precluded the accurate measurement of bond distances. The best diffraction patterns were obtained with Cu-K^ radiation, which was therefore used in preference to molybdenum or iron radiations. The intensities of the reflexions were estimated visually from hK£ Weissenberg films (K = 0 —+ 3); only 313 reflexions were observed. The crystal used had cross-section 0.05 x 0.05 mm., so that absorption errots were not serious and no corrections were applied. Lorentz and polarization corrections were made and the structure, amplitudes were derived. The scale factors between 23 the layers were i n i t i a l l y estimated by timing the exposures and were later adjusted slightly from comparisons of measured and calculated structure factors. Structure Analysis A preliminary study was made of the two-dimensional hOfc projection. The Fe-Fe peaks in the Patterson function implied Fe coordinates of either (0.15, 0) or (1/4-0.15,0), the two positions giving the same vector map. From the Fourier synthesis summed with phases based on the iron atom only, a possible molecular outline could be distinguished which indicated that the mirror plane which occurred at z = 0 was spurious. When the twenty-two carbon atoms- were approximately located and structure factors then calculated using Fe artd C scattering factors i of the International Tables for X-ray Crystallography (11) with B = 6.0 A 2 for Fe and B = 4.5. A.2 for C, the discrepancy index, R, was 0.26. Therefore, i t was decided to continue the analysis in three-dimensions. ;• < •  • The three-dimensional Patterson could be interpreted in terms of space group Pcam with iron coordinates (0.15,0,0) or (1/4-0.15,0,0). Two three-|dimensional electron-density distributions were computed with phases based on the two possible iron positions. The resulting maps had, of course, Pcam symmetry, but again the mirror plane was spurious (the mirror symmetry could have been retainer! by allowing a disordered arrangement of molecules, but at no stage in the analysis was there any evidence to suggest disorder). Both maps showed chemically reasonable molecuLfes and revealed the positions, of the seventeen carbon atoms in the biphenylylcyciopentadienyl group,, based on space group Pca2i. Since structure factor calculations gave R = 0.30 and 0.34 for the two possible structures and also the f i r s t gave better 24 packing of the molecules in the unit c e l l , i t seems to be the correct arrangement. From the Fourier summed using the iron coordinates of (0.15,0,0) and the corresponding biphenylylcyclopentadienyl carbon coordinates (i.e. the f i r s t structure), the other cyclopentadienyl ring carbon atoms could be unambiguously located. Refinement of the positional and isotropic thermal parameters proceeded by block diagonal least-squares methods, minimizing E w t l F j - l F ^ J ) 2 , with *fa = |Fj/50 when IfJ < 50 and /w = 5 0 / I F J when I F ^ I 5. 50. The layer line scaling was adjusted by equating ^1^1 and z l F ^ I for each layer after each least-squares cycle. After several cycles of least^squares the R value was 0.19. Then, since the calculated structure factors corresponding to the more intense reflexions were consistently higher than the observed, the~se reflexions, (400, 600, 201, 202, 402, 602, 410, 211) were corrected for extinction before f-urther refinement. This was done according to the empirical method of Pinnock, Taylor and Lipson (29) using equation 1c/1o =. 1 + .Cfc/lO Ic where I 0 is the observed intensity I c is the calculated intensity y is the absorption coefficient g is a constant. This procedure is regarding secondary extinction as equivalent to an increase in the absorption coefficient of each reflexion. Refinement was continued until the shifts became small and were in random directions. The f i n a l R value was 0.15 for the 313 observed Figure 3. Superimposed sections of the three-dimensional, electron-density distribution, through the atomic centres parallel to (010). Contours are at intervals of 0.7 g. A"3, starting at 1.4 g. A - 3 for C, and 3.5 e. A - 3, starting at 7.0 e. A - 3 for Fe. 26 0_ 4 Figure 4. A perspective drawing of the molecule giving the atom numbering used. reflexions. Measured and calculated structure factors are listed in Table VIII (Appendix II). A f i n a l three-dimensional Fourier series was summed and superimposed sections of the resulting .electron-density distribution are shown in Figure 3. Figure 4 is a drawing of the molecule giving the atom numbering used for convenience in the analysis. A final difference map showed no ' 0 3 significant spurious detail,, the maximum fluctuation being + 0.6 e. A"* . Coordinates and Molecular Dimensions The final, positional and thermal parameters are given in Table III. o The individual bond distances and angles are not very accurate (a ~0.07 A and 5°), and the average values only are given in Table IV. Table IV also gives the equations of-the mean planes of the various rings and the angles between the planes. A l l the intermolecular contacts correspond to van der 0 Waals' interactions or greater, the shortest C...C distance being 3.3 A. The arrangement of the molecules in the crystal is shown in :Figure 5. Discussion In the 2-biphenylylferrocene molecule the iron atom is sandwiched between the two cyclopentadienyl rings. These rings appear to be not quite parallel, although the angle between the normals, 8°, is not really significantly different from zero. The three rings of the 2-biphenylyl- cyclopentadienyl group exhibit large deviations from coplanarity which relieve the strain which would exist in a planar configuration. The cyclo pentadienyl ring is rotated about the C(2)-C(7) bond 43° out of the plane of the -CgHif ring and the outer six-membered ring is rotated about the i C(8)-C(13> bond by 58° from the -Cgt^- plane. The two rotations are in Table III Final positional (fractional x 10 ) and thermal (A) parameters. Mean standard deviations are a(x) = a(y) = a(z) = 0.009 A for Fe, 0;05 A for C; a(B) = 0.2 A2 for Fe, 1.5 A2 for C. Atom X I z B Fe(l) 152.2 -029.7 0 6.8 C(2) 118 012 156 1.5 3 101 -203 105 4.8 4 172 -289 104 8.6 5 203 -106 143 3.5 6 169 066 167 1.7 7 060 135 173 2.4 8 053 299 265 4.2 9 016 499 286 2.0 10 -036 523 198 5.9 11' -028 358 102 4.5 12 010 155 095 5.2 13 098 294 358 3.7 14 108 084 430 8.3 15 142 112 538 5.7 16 182 333 550 6.7 17 •• 174 515 488 7.9 18 139 529 392 5.7 19 118 195 -121 4.5 20 174 . 247 -121 6.2 21 203 061 -127 4.9 22 157 -135 -168 6.9 . 23 097 -038 -148 . 2.7 Table IV. Mean bond distances (a -0.07 A) and valency angles (a - 5°), equations of mean planes and angles between planes. Distances and angles Fe-C 2.05. C-C(5-rings) 1.44 C-C(6-rings) 1.50 C-C(between rings) 1.52 C-C-C(5-rings) 108 C-C-G(6-rings) 120 Equations of mean planes, in the form. IX' + mY + nZ' + p_ = 0, where X',Y,Z' are coordinates in A referred to orthogonal axes a,b,c*. Angles between planes Maximum Plane Atoms .1 m n E displac 5(1) 2-6 . 0. .072 0. .351 -0. .934 1, .416 0.04 5 (2) 19-23 : 0. 028 0. .228 -0. .973 -1. .733 0.08 6 (1) 7-12 0. .598 0. .626 -0. .500 -0, .333 0.16 6 (2) 13-18 0. .736 -0. .335 -0, .588 1 .348 0.10 Planes 5(l)-5(2) 5(1)-6(1) 5(l)-6(2) 6(D-6(2) Angle 8° 43 61 58 o p p o s i t e d i r e c t i o n s a n d i n c r e a s e t h e C ( 6 ) . . . C ( 1 8 ) d i s t a n c e o f a b o u t 1.5 A o i n a p l a n a r m o d e l t o 3.84 A. T h e r e l a t i o n b e t w e e n t h e c y c l o p e n t a d i e n y l r i n g s c a n be s e e n i n F i g u r e 6, w h i c h shows a v i e w a l o n g t h e n o r m a l t o t h e i r p l a n e s . T h e r i n g s a r e a p p r o x i m a t e l y e c l i p s e d , t h e a v e r a g e a n g l e o f r o t a t i o n f r o m t h e e c l i p s e d p o s i t i o n ( c a l c u l a t i o n i n A p p e n d i x I:B) b e i n g a b o u t 0 ° . T h e mean b o n d d i s t a n c e s a n d v a l e n c y a n g l e s a r e w i t h i n t h e l i m i t s o f e x p e r i m e n t a l e r r o r , s i m i l a r t o t h o s e . i n r e l a t e d c o m p o u n d s . 3 2 3 Fe 19 6 2 0 Figure 6 . View of the cyclopentadienyl rings normal to their planes Heavier lines are nearer the viewer. 33 C. THE STRUCTURE OF ,4-BIPHENYLYLFERROCENE Experimental Crystals of 4-biphertylylferrocene (28) are orange-yellow plates elongated along b. The density was measured by flotation in aqueous potassium iodide and the unit cell parameters and space group! were deter mined from rotation and Weissenberg photographs and on a,G.E. Spectrogonio- meter. o o Crystal data (X, Cu-IT = 1.54jl8 A; X, Fe-K^ = 1.9373 A). 4-Biphenylyl- ! ferrocene, C 2 2H 1 8Fe; M.W. = 338.2; m.p. = 164-165°. Monoclinic, a = 19.18/b = :7.79^ c = 10.85 A, g = 91.8°. 03 I 3 U = 1620 A , D m=l.38, Z .= 4, D = .1.39 g.cm." . F(000) = 704. ; Absorption coefficients for X-rays, y(Cu-Ka) =76 cm."1, y(Fe-Ka) =25 cm.-1. 2 Absent reflexions: OkO when k is odd. Space group is P2i (C2) or P2i/m 2 . (C2jh) . P2i from structure analysis. The intensities were measured on a General Electric XRD 5 Spectrogoniometer with Single Crystal Orienter, using a scintillation counter, approximately monochromatic ^e~^-a radiation (manganese fil t e r and pulse height analyser), and a 0-20 scan. All reflexions with 20(Fe-Ka)^: 148°. o (minimum.d = 1.0 A) were examined and 1579 (87%) had measurable intensities. The intensities were corrected for background, which was approximately a function of 0 only. The crystal used was mounted with b parallel to the <j) axis of the goniostat and had cross-section 0.4 x 0.01 mm. Crystals of more uniform,cross-section were not obtainable so that i t was necessary to consider possible absorption errors. Because of the extreme thinness of the i t 34 crystal plate, absorption is serious only for planes in a few very narrow regions of reciprocal space (2), the maximum possible error in structure factor being about 30%. Since only a few planes have errors as large as th and because of the d i f f i c u l t y of making accurate estimations of the absorption, no corrections were applied. The possible errors could have been reduced to about half by using molybdenum.radiation, but only at the expense of weaker, and hence, less reliable intensities. Lorentz and polarization factors were applied and the strueure amplitudes were derived. Structure Analysis The Fe-Fe vectors,in the three-dimensional Patterson function could be interpreted in therms of space group A2/m with one independent iron atom situated on the mirror plane. A three-dimensional electron-density distribution computed with phases based on this arrangement had, of course, the corresponding symmetry, but the positions of possible carbon atom peaks indicated clearly that some of the symmetry elements were spurious (alternatively i t would have been possible to retain mirror symmetry by allowing a disordered arrangement of molecules, but neither at this nor any other stage of the analysis was their any evidence to suggest ;disorder) The ambiguities were resolved by,using chemical knowledge'and' by' defining the positive direction of the y-axis by arbitrarily choosing one of the two possible molecular arrangements around one iron atom. There were then four possible arrangements.;around the second iron atom. Two of these could immediately be discarded since, they corresponded to A2 and £2i/c symmetries The other two each had space group P_2i with two molecules in the asymmetric unit; Structure factors were calculated for both of•these latter arrange ments using scattering factors.of the International Tables for X-ray l l M l l l l M l I I I I 0 1 2 3 4 5 6 & Figure 7. Superimposed sections of the three-dimensional electron-density distribution, through the atomic centres parallel to (010). Contours are at intervals of 1 e. A - 3, starting at 2 e. A ~ 3 o a Figure 8. View of the structure giving the atom numbering used.. In both Figure 7 and Figure 8 only the molecules with ixon. atoms at y -0 are shown and the iron atoms, which are sandwiched between the five-membered rings, are omitted for clarity. 37 0 Crystallography (11) with IJ-=-4.0 A for a l l atoms; the R_ factors were 0.38 and 0.43 for the two arrangements. Three cycles of least-squares refinement reduced these values to 0.20 and 0.31, so that the f i r s t arrangement seemed correct. A three-dimensional electron-density map confirmed the derived structure and further refinement proceeded.by block-diagonal least-squares methods, minimizing Ew(|F |-|F |) 2,with/w = |F 1/20 when | F | < 20 and •=. 1 when >-20. Refinement was continued, i n i t i a l l y with isotropic and f i n a l l y with anisotropic thermal parameters, until the shifts were small and in random directions, the fin a l R being 0.15 for the observed reflexions. Final measured and calculated structure factors are listed in Table IX (Appendix II). A fi n a l three-dimensional :Fourier series was summed and superimposed sections of the resulting electron-density distribution are shown in Figure 7. Figure 8 is a drawing of the structure giving the atom numbering used for convenience in the analysis. A final difference map showed no ° 3 significant spurious•detail, the maximum fluctuations being + 0.7 e. A Coordinates and Molecular Dimensions The final positional parameters are given in Table V. As a result of the possible absorption errors the individual values of the anisotropic thermal parameters probably have no real physical significance, and Table V includes only the final isotropic values. The individual"bond distances and angles are also not very accurate o (a - 0.04 A and 3 ) and the average values only are given in Table VI. Table VI also gives the equations of the mean planes of the various rings; these were computed with inclusion of the atoms listed in.the Table to Table V. Final positional (fractional x 10 ) and isotropic.thermal (A ) parameters. Mean standard deviations are o(x) = a(y) = a(z) = 0.004 A for Fe, 0.03 A for C; o(B) = 0.1 A2 for Fe, 0.8 A for C. Atom x 1 z ' B Fe(l) 135.4 0 385.5 5.4 2 126.7 -486.5 -119.2 5.7 C(3) 208 150 305 4.5 4 168 060 211 5.8 5 091 086 212 5.4 6 086 220 308 3.6 7 158 248 356 4.7 8 194 -108 524 6.2 9 128 -038 ' 577 5.9 10 069 -129 496 4.9 11 091 -241 422 7.5 12 173 -251 419 7.1 13 197 -651 -199' 6.2 14 167 -540 -288 4.2 15 096 -573 -285 5.2 16 072 -689 -197 6.0 17 138 -754 -125 7,1 18 180 -333 008 4.6 19 125 -424 062 6.5 20 055 -396 017 3.4 21 069 -260 -082 6.8 22 147 -237 -086 5.2 23 283 149 325 4.6 2# 312 247 420 5.0 25 386 245 445 6.1 26 432 135 356 4.9 27 395 046 262 4.4 28 325 053 241 5.6 29 506 138 377 3.3 30 537 212 484 3.7 31 610 209 499 5.8 32 657 . 133 414 7.3 33 622 061 307 4.4 34 549 055 282 5.6 35 260 -346 037 4,3 36 281 -459 133 4.7 37 352 -474 160 6.8 38 . 403 -370- 088 5,3 ; 39 377 -253 -010 4.5 40 306 -249 -034 4.9 41 480 -373 120 4.2 42 501 -462 228 4.4 43 573 -456 257 5.7 44 622 -384 184 6.5 45 599 -295 076 5.2 46 523 -297 043 4.6 39 Table VI. o Mean bond distances (a ~ 0.04 A) and valency angles (a ~ 3 ), equations of mean planes and angles between planes. Distances and angles Fe-G 2.07 A C-C (5-rings) 1.48 C-C (6-rings) 1.43 C-C (between rings) 1.48 C-C-C (5-rings) 108c C-C-C (6-rings) 120 Equations , of mean planes in Jhe form XV + mY + nZ' + p_ = 0, where X', Y, Z' are coordinates in A referredto orthogonal axes a,b,c*. Maximum Plane Atoms 1 m n E Displacement 5(1) 3-7 0. .135 0. .725 -0.675 0.860 0.04 5(2) 8-12 0. .032 0. .718 -0.696 4.502 0.03 5(3) 18-22 0. ,106 -0, .742 -0.662 -2.302 0.03 5(4) 13-17 0. .094 -0. .744 -0.662 -5.577 0.03 6(1) 23-28 0. ,100 0, .790 -0.604 0.716 0.03 6(2) 29-34 0. .070 0, .875 -0.479 0.408 0.01 6(3) 35-40 0. .095 -0, .748 -0.657 -2.279 0.03 6(4) 41-46 0. ,113 -0, .851 -0.513 -2.891 0.02 Angles between planes Planes Angle Planes Angle 5(1)-S(2) 6° 5(3)-5(4) 0° 5(1)-6(1) 6 5(3)-6(3) 0 5(l)-6(2) 15 5(3)-6(4) 11 6(l)-6(2) 9 6(3)-6(4) 10 40 define the rings and the atoms bonded directly to each ring. The maximum displacements from the. planes are also given. All the intermolecular contacts correspond to van der Waals' interactions, the shortest C...C 0 distances being 3.44 A. Discussion , The crystal structure analysis of 4-biphenylylferrocene has shown that the unit cell contains two crystallographically independent molecules. All four.rings in each molecule are/approximately parallel, but with small twists which appear to be significant. In molecule 1 (containing Fe (1) and five-membered ringsC(3)-C(7) and C(8)-C(12)) the angle between the two cyclopentadienyl rings is about 6°, the first six-membered ring of the biphenylyl group is rotated about the C-C bond 6° out of the plane of.the cyclopentadienyl ring to which i t - i s bonded and the outer benzene ring is rotated by a further 9°. In molecule .2 the corresponding angles are 0°, 0° and 10°., The general arrangement in each molecule is therefore rather similar;, the.cyclopentadienyl rings are approximately parallel, the -CgH^ - ring is perhaps slightly rotated from the five-membered ring plane and the -CgH5 ring exhibits a somewhat larger, but s t i l l relatively small displace ment." So the biphenylyl group in this molecule compares with the planar arrangement of biphenyl in the solid state (17), although there is a slight rotation of one ring plane with respect to the other. In 2-biphenylyl- ferrocene the angle of 58° between the planes of the two benzene rings can be compared with the 45° angle in biphenyl vapour,(16). Thus, by their ring rotations the strain resulting from the close,contact of the ortho> . hydrogens in completely planar biphenyl is relieved in both 4- and 2- biphenylylferrocene, especially in the latter compound. One of the principal objects of the investigation was the 41 determination of the arrangements of the cyclopentadienyl rings, which is illustrated in.Figure 8 and more clearly in Figure 9, which shows views approximately along,the normals to the ring planes. If the orientations are described in terms of the rotation of one.of the rings from the fully eclipsed position, then molecule 1, with a rotation of about 15° (calculation in Appendix I:B), is approximately midway between the fully eclipsed (0°) and fully staggered (36°) arrangements and molecule 2, rotation about 5°, is nearly eclipsed (Figure 9). The observation of these two different arrangements in the same crystal supports the view that the orientations must be strongly dependent on intermplecular forces (26). Also the displacements from cpplanarity in the biphenylyl groups in 4-biphenylylferrocene and in 2-biphenylylferrocene.are further indication, that there is no conjugation between the two phenyl rings, but probably i t is the interactions between molecules which determine the biphenyl configuration. The mean bond distances and valency:angles are* within the limits of experimental error, similar to those,in related molecules. 9 17 Figure 9. Views of- the cyclopentadienyl rings normalto t h e i r planes. Heavier lines are nearer the viewer. A P P E N D I X I D E S C R I P T I O N OF SOME COMPUTER PROGRAMS WRITTEN FOR S P E C I A L CALCULATIONS I N THESE ANALYSES 44 A. ABSORPTION CORRECTION FOR THIN FLAT CRYSTALS In the crystal structure analysis of 3-dimethyltellurium diiodide a l l the reflexions were corrected for absorption according to the method of Zalkin, Forrester and Templeton (10) for thin, f l a t crystals. The approximation is made that the absorption correction depends on the harmonic mean value m of: | cos P_| and . | cos Oj , where P_ and Q are the angles between the incident and diffracted beams, respectively, and the normal to the f l a t plate. Thus; 2 _ .1 1 m ~ | cos Pj + | cos 0^  | (I) and m is inversely proportional to the path length of a beam scattered at the centre of the crystal. By spherical trigonometry | cos Pj = | cos 0 cos <j> + .• sin 0 sin $ cos x| (2) | cos pj =• | cos 0 cos <J> - sin ,0 sin <f>. cos x| CD i f the crystal is perpendicular to the, incident beam when 0 = <j> = 0. 0, $ and x are respectively, the Bragg angle, polar angle and inclination angle., settings for the goniostat. The equation used for the correction was I (measured) , I (corrected) = 1 + a exp(-—/m) (4) The intensities of the,reflexions from the 002 and 006 planes which have x = 90° (and thus m = • | cos PJ = | eqs Oj =. | cos 0 cos, <j>|) were measured for <}) = 0° to 360° at intervals of .10°. The constants a_ and b_ were then determined from the graph of 45 I(measured) , \ — — - 1 versus In \ I (minimum) J \ cos 0 cos $ J This method, then, reduces the intensities of all reflexions with less than maximum absorption. The following computer program calculates the absorption correction for each reflexion according to equation (4). The input required includes a_ and b_, the constants obtained from the graph and <s)Q, the value of n) when I(measured) is maximum (i.e. when the crystal is perpendicular to the incident beam). The program also must read in the goniostat settings 9, X and <j> for each plane. The value of <J> used in equation (4_) is a) = <}> (input) - <(>o so that 4> = - 0 when I (measured) is maximum. 46 SFORTRAN C ABSORPTION CORRECTION - THIN FLAT CRYSTALS READ (5.1) A»B»PHIA 1 FORMAT(3F10.5 ) 3 READ (5.8) LFH.LFK>LFL.I NT,SC»TWOTH,CHI,PHI 8 FORMAT(10X.3I3.2X.I5,3X.F6.2»11X.F8.3»2(1X.F8.3)) TH=TWOTH/(2.*57.29578) PHE=(PHI + (3 60.-PHI A)1/57.29578 22 CTCP=COS(TH)*COS(PHE> STSPC=SIN(TH)*SIN(PHE)*COS(CH1/57.29578 ) CSP = ABS(CTCP+STSPC ) CSQ=ABS(CTCP-STSPC ) CM=2.*CSP*CSQ/(CSQ+CSP) SCA=1./(1.+A*EXP(-B/CM> ) SC=SC*SCA*10. WRITE (6.8) LFH.LFK.LFL.INT.SC. TWOTH» CHI »PH I WRITE (7,8) LFH.LFK.LFLtlNT.SC.TWOTH.CHI.PHI GO TO 3 END SENTRY 47 B. ANGLE OF ROTATION FROM ECLIPSED POSITION The following program was written to calculate the angle of rotation of the cyclopentadienyl rings from the fully eclipsed position in 2-biphenylylferrocene and in 4-biphenylylferrocene. This involves projecting the two rings of aferrocene group onto one plane, the direction cosines of which are the average of those of the ring planes, the rings being approximately parallel. The equation of the average plane is Ax .+ yy + vz + d = 0. (1_) A.set of orthogonal axes is calculated so that two axes are in the plane and one is perpendicular to i t . Their direction ,cosines (A^y^ . v p are as follows: ( > 3 > u 3 > v 3 ) = C^.M.v) (2) where x^, y^, z^  are coordinates, with respect to the orthogonal axes a_, b_ and c*, of a,point on the plane, l = /(xx - x2V •+ (yi - y 2)2 + O i - z 2)2 . (A2,y2,v2) = ( yivs - y$vi vi ^ 3 - v.3*i AiiL3_l_i3JLL ) (!) \ r 2 ' r 2 ' r 2 . / where r 2 = /(uiV3 ~ P 3 v l ) 2 + (^l x 3 " v 3 ^ i ) 2 •+ (A1V3 - A 3yi ) 2 . ; Each ring atom is projected onto the average plane by finding its new coordinates (y^, y 2, 0) with respect to the ,above orthogonal axes from its original coordinates (xi, x2, x3) with respect to the orthogonal axes a, b and c*. 48 yz>. vi) - ( xi> X2» X3), x2 *3 u i P3 v 2 3^ \ If the angle of rotation of one ring with respect to the other is defined as the angle 0 between the projected Fe-G bond to a carbon atom on one ring and the projected Fe-C bond to the corresponding carbon on the other ring, then i t is calculated as follows: cos 0 = (yi (Fe) - y i (Cx)). ( y i (Fe) - y i (C2)) + (y 2 (Fe)-y2 (0^)) (y 2 (Fe)-y2 (C2)) (6J /[ (y 1 (Fe) - y i (CO) 2+(y2 (Fe) -y2 (d)) 2] [ ( y i (Fe) - y i (G2)) 2+ (y 2 (Fe) -y2 (C2)) 2] where Cj is a carbon atom in ring 1, C 2 is the corresponding carbon atom in ring 2. 49 SFORTRAN C ROTATION FROM ECLIPSED DIMENSION XI ( 11 ) , X2( 11 ) »X3 (11). Yl(ll), Y2 ( 11). iY3(ll)»Al(ll), 31(11) DIMENSION Rl(11) DO 25 1=1.11 READ (5.8) XI(I)» X2(I) » X3(I) 8 FORMATUF8.5) 25 CONTINUE READ (5.8) WL.WU.WV.D' WL3=WL WU3=WU WV3=WV X3 2=-(D+WL»X1(2)+WU*X2(2))/WV X35 = -(D+WL*XK5)+WU*X2(5) )/WV AX=X1(2)-X1(5) BX=X2(2)-X2(5) C1=X32-X35 RX»SQRT(AX*AX+BX*BX+C1*C1.) WL1=AX/RX WU1=BX/RX WV1=C1/RX A2=WU1*WV3-WU3*WV1 B2=WV1*WL3-WV3*WL1 C2=WL1*WU3-WL3*WU1 R2=SQRT(A2*A2+B2*B2+C2*C2) WL2=A2/R2 WU2=B2/R2 WV2=C2/R2 DO 28 1=1.11 Yl(I) = X 1(I) *WL1+X2(I)*WU1+X3(I)*WV1 Y2(I)=X1< I)#WL2+X2(I)*WU2+X3(I)*WV2 WRITE (6.8) YI( I ) »Y2( I ) 28 CONTINUE DO 30 1=2.6 Al( I )»Y1<1)-Yl(I) Bl ( I )*Y2(1>-Y2<I) Rl(I)oSQRT< Al(I)*A1(I>+81(I)*B1(I)> 30 CONTINUE DO 35 J»7.11 AllJ)=Y1(1l-Yl<J> Bl (J)=Y2(1)-Y2(J) Rl(J)=SQRT(A1(J)*A1(J)+B1(J)*B1(J)) 35 CONTINUE DO 38 1=2.6 J=I+5 C=(Al(I>*A1(J)+B1(I)*B1(J))/(Rl(I)*R1(J)) ANG°57.296»ATAN(SQRT<I1.0-C*C)/(C*C))) WRITE (6.9) I.J.ANG 9 FORMATI2I4.F10.5) 38 CONTINUE END SENTRY APPENDIX II TABLES OF OBSERVED AND CALCULATED STRUCTURE FACTORS 51 Table VII. 8-Dimethyltellurium diiodide measured and calculated structure factors h k i F 0 h a Q" 2 127.4" - 1 0 9 . 6 0 a 4 - 6 . 7 9 . 1 0 0 6 3 2 9 . 4 3 6 6 . 6 0 0 n 1 2 3 . 6 - 1 0 1 . 1 0 1 1 1 1 * . 3 1 2 4 . 9 0 2 2 4 7 . 9 - 2 9 2 . ) 0 3 2 8 2 . 6 3 6 7 . 0 0 4 - 1 3 . 0 - 2 6 . 8 0 1 S 3 3 . 0 - 2 0 . 7 ft 6 - 1 7 . 7 - 1 B . O 0 7 64 .1 3 3 . 4 0 8 126 .4 - 1 3 2 . 6 0 9 - 2 1 . 9 - 1 5 . 5 0 0 173 .3 1 8 0 . 6 0 1 8 2 . 5 - 9 4 . 3 0 2 92 .1 - B 3 . f i 0 2 3 7 2 . 3 4 7 . 3 D 2 4 - 1 4 . 1 - 1 2 . 1 0 2 S 102 .8 - 1 1 7 . 3 0 2 6 8 9 . 2 9 4 . 8 0 7 OS.8 . - 9 3 . 7 D a 4i.a - 4 4 . 3 0 2 9 - 2 2 . 0 13 .0 0 I 1 4 3 . 6 ' 132.1 0 2 2 1 2 . 2 - 2 1 0 . 2 0 3 127 .4 - 1 2 8 . 9 0 3 4 1 3 3 . 0 168 .3 0 •I A 1 . 3 7 1 . n 0 3 b - 1 7 . 6 33.1 0 7 - 1 9 . 2 9 . 9 0 8 8 0 . 2 - 9 1 . 2 0 9 -22.2 - 7 . 0 0 0 112 .4 - 1 1 6 . 1 g 1 9 1 . 3 - 6 5 . 3 0 2 3 1 2 . 3 3 7 7 . 6 0 3 7 2 . 9 - 6 1 . 1 D 4 4 137.6 169 .0 0 4 3 9 7 . 0 103 .0 0 6 5 2 . 2 - 9 4 . 0 0 7 - 1 9 . 4 - 1 1 . 7 0 4 B - 2 0 . 9 3 0 . 1 0 9 - 2 2 . 4 - 3 T . 8 0 I 2 0 1 . 8 1 9 9 . 9 0 2 2 5 3 . 3 - 2 4 0 . 6 0 5 3 2 5 6 . 9 2 6 6 . 3 0 5 4 126.P 113 .7 0 5 9 1 . 9 8 2 . 4 0 6 1 9 9 . 8 - 2 0 9 . 6 0 7 - 1 9 . 7 - 3 7 . 3 n ft 4 9 . 7 - 3 1 . 7 0 9 9 3 5 . 8 4 4 . 7 0 D 6 1 . 9 5 1 . 6 0 1 2 4 5 . 3 196.1 a 2 9 8 . 2 6 3 . 4 0 3 2 1 9 . 1 - 2 4 3 . 5 n * 4 6 . ] 1 7 . * 0 <, 3 102 .3 - 1 7 2 . 8 0 6 3 4 . 8 - 2 0 . 7 0 7 - 2 0 . 0 - 2 3 . 9 0 8 3 3 . 9 4 3 . 6 a 9 1 0 9 . 9 - 1 0 3 . 4 0 1 2 2 6 . 3 - 7 3 1 . 1 0 T 2 2 2 9 . 1 - 2 0 3 . U 0 7 3 172 .9 161.8 0 4 9 2 . 4 6 9 . 7 0 T 5 130 .2 - 1 2 4 . 4 0 6 134.6 - 1 1 6 . 7 0 7 - 2 0 . 4 - 3 7 . 2 . 0 7 B 9 9 . 7 - 6 0 . 3 0 9 - 2 3 . 2 . 41 .2 0 0 126.7 - 1 1 4 . 6 0 I 2 7 5 . 5 233 .1 0 b I - 1 5 . 2 - 2 2 . 3 0 3 4 6 . 6 4 1 . 9 0 8 4 3 2 . 0 32 .2 0 tt 3 2 0 5 . 7 - 1 9 6 . 0 0 6 8 9 . 4 - 9 0 . 9 0 6 7 9 0 . 7 7 6 . 8 0 u 8 - 2 2 . 1 14 .8 0 •J 1 1 9 4 . 2 161 .3 0 V 2 8 4 . 7 3 7 . 3 0 9 3 7 5 . 9 - 6 0 . 5 0 9 4 156.1 - 1 4 8 . 2 0 9 5 5 3 . 2 4 9 . 6 0 9 6 5 1 . 0 3 8 . 3 0 9 7 1 3 . 6 1 4 . t 0 9 8 - 2 2 . 5 - 2 0 . 6 0 10 0 1 7 8 . 9 - 1 7 9 . 0 0 10 1 104 .5 - 6 7 . 4 0 10 2 183 .9 173 .7 0 10 3 3 4 . 9 - 3 9 . 4 ID 4 8 4 . 9 76 .1 0 10 5 198 .7 - 1 4 1 . 4 o 10 6 9 9 . 6 - 5 3 . 6 0 10 7 9 0 . 7 - 3 7 . 6 0 10 8 - 2 2 . B 2 9 . 3 0 11 1 7 4 . 9 3 7 . 6 0 11 7 173 .3 1 11.1 0 u 3 3 2 0 . 2 - 3 2 1 . 2 ' 0 u 4 2 3 2 . 8 - 2 2 9 . 9 0 u 5 113 .1 1 0 2 . 6 0 11 6 6 7 . 1 - 6 9 . 2 . 0 11 J -21..» 13.2 5 5 . 1 108 .6 74 .4 1 4 9 . 3 - ' • 3 - 9 - 2 0 . 8 - 2 1 . 9 1 9 . A 31 .2 9 0 . 7 71-7 - 5 3 . 1 1 4 9 . 6 5 6 . 4 - 2 0 . 8 - 2 1 . 8 1 2 6 . 0 4 7 . 4 4ft -3 - 0 . 2 - 2 3 . 4 - 2 2 . 3 - 1 6 . 0 144 .8 37.2 -19.2 -19.9 3 3 . 6 - 1 3 . 0 - 1 9 . 9 1 2 3 . 7 - 1 4 . 9 4Z.Q - 2 0 . 0 - 1 7 . 5 1 0 . 3 3 0 . 3 - 1 5 . 0 •106 .7 134.8 163 .3 1 0 1 - 9 - 1 8 . 6 - 1 9 . 1 31 .2 1 1 6 . 8 7 4 . 5 3 4 . 9 - 1 2 . 2 - 6 . 7 - 1 6 . 7 - 1 1 7 . 1 - 1 6 2 . 0 - 9 7 . 6 8 6 . 0 124 .1 - 1 8 . 3 2 3 7 . 2 138 .6 1 7 . 3 7 6 . 6 56 .1 2 7 7 . 6 7 0 . 3 2 1 . 9 7 2 . 9 2 9 . 9 5 . 8 4 0 . 4 106.1 74 .1 2 9 . 4 - 7 2 . 7 109 .1 2 . 4 2 4 7 . 4 122 .8 _ L 1 5 9 . 9 175 .6 1 9 . 3 134 .7 5 0 . 8 7 2 . 2 - 9 0 . 0 2 8 7 . 1 - 7 4 . 9 - 2 9 . 7 - f t " - * 9 9 . 6 197.1 1 0 . 8 5 0 . 1 153 .3 6 9 . 8 6 6 . 8 >3.4 » . 3 6 1 . 1 5 1 . 8 112 .7 - 1 1 . 6 104 .0 103 -3 2 2 9 . 9 3 6 0 . 4 • 199.2 157 .3 7 0 . 5 191 .4 140 .4 18 .7 132 .2 2 1 . 6 }j,e 4 0 . 1 - 1 1 . 7 1 1 7 . 6 • 3 7 . 9 3 6 . 3 3 0 . 8 2 1 . 2 2 7 9 . 8 ' 2 0 9 . 2 0 8 . 5 276 .2 frfr.T 101.1 2 8 9 . 0 2 4 5 . 6 - 1 0 . 3 2 9 0 . 9 - H - 2 - 9 . 4 - 1 2 . 2 4 9 . 8 - 1 3 . 2 3 5 . 2 - 1 4 . 2 4 3 . 8 2 B 4 . 7 116 .6 - 7 3 . 1 1 1 8 . 9 -36^4_ •151 .9 - 7 5 . 4 5 5 . 8 4 . 3 - 1 8 . 0 - 4 7 . 8 4 6 . 2 •110 .6 2 2 0 . 7 •433.2 1 9 9 . 8 •131-8 •189.7 1 3 1 . 0 15 .8 137 .3 2 5 . 8 - 2 6 . 9 - 5 7 . 2 1 1 . 0 - 1 1 3 . 1 - 3 7 . B - 5 1 . 5 - l ? t ? - 2 8 . 3 - 3 1 8 . 8 - 2 0 4 . 3 - 9 3 . 0 - 3 0 0 . 3 7 7 - 0 108 .8 3 3 8 . 3 2 6 6 . 3 19 .8 - 3 2 2 . 0 - 6 . 3 4 . 4 1 7 . 3 - 4 3 . 0 - 6 . 9 - 2 2 . 1 23 .1 7 4 . 6 67.0 194.4 218.6 5 6 . 6 4 6 . 9 61.0 63.4 -133.3 233.4 276.8 132.6 -139.1 94.4 109.9 39.9 -38.6 lo9.6 ll3." -12.9 2 2 . 9 21.5 22.4 - 1 4 . 0 31.0 61.iL 6 3 . 5 6 6 . 7 107.5 - 1 1 4 . 4 3 0 . 6 4 2 . 2 - 1 2 . 6 - 3 . 1 3 9 9 . 8 4 4 7 . 0 " 7 . 7 156.9, 5 5 . 1 - 6 1 . 4 167 .2 - 2 1 2 . 2 1 6 3 . 9 - 1 7 7 . 9 2 2 6 . 3 2 5 1 . 3 197 .3 2 0 8 . 6 " 3 - 0 137 .7 109.1 106 .9 - 1 3 . 9 1 2 . 6 6 0 . 9 - 6 7 . 1 103 .6 112 .6 109 .7 - 1 1 2 . 0 80 . 1 7 3 . 9 5 4 . 4 3 6 . 0 - 1 3 . 6 2 8 9 - 3 - 8 7 . 6 - 8 1 . 9 - 5 3 . 7 4 8 . 3 16 .8 -32 .1 ,7 r t . j 6 6 . 2 6 4 . 5 - 6 6 . 4 8 9 . 5 85 .7 155 .1 161 .4 2 4 7 . 7 2 6 5 . 8 Z6Q.fi -HI.1 1 1 3 . 8 1 2 1 . 3 2 9 . 6 3 4 . 7 102 .3 - 1 0 8 . 1 7 2 . 9 - 6 0 . 1 53 .1 - 6 3 . 6 ) 6 7 . 7 - 1 8 7 . 3 - 1 9 . 0 33 .2 3 2 . 3 4 9 . 9 - 1 4 . 8 191 .3 6 . 9 - 3 9 . 2 4 4 . 3 5 2 . 0 - 1 7 . 9 !"-« 73 .1 - 6 6 . 8 1 9 0 . 3 - 1 9 6 . 3 133.7 1 1 9 . 6 31.1 - 3 4 . 4 4 6 . 7 - 3 2 . 7 163.1 - I f l Z . ? 8 1 . 3 8 5 . 4 9 3 . 3 - 1 0 3 . 9 68 .2 - 8 9 . 8 6 8 . 1 7 5 . 3 3 3 . 6 4 3 . 1 4 6 . 7 - 4 7 ^ - 2 0 . 8 - 2 9 . 4 7 2 . 5 - 7 6 . 9 - 2 2 . 3 6 . 1 2 9 . 9 3 9 . 6 - 1 0 . 0 H . 4 100 .4 333 . 0 - 1 0 . 0 128 .9 6 1 . 2 - l f c - f t 5 4 . 8 4 3 . 0 - 1 2 . 4 6 9 . 1 3 7 . 5 ftQ-2 147.2 159.1 8 1 . 2 - 2 2 . 7 5 4 . 0 -Hi* - 1 5 . 6 7 7 . 1 162 .9 2 4 4 . 2 4 9 . 4 35 .9 - 1 7 . 3 - 2 8 3 . 4 3 1 7 . 4 12 .1 113 .2 6 4 . 9 , a*a 5 3 . 2 -49,» 19 ,8 7 0 . 6 . - 4 0 . 2 . - 3 7 . 8 - 1 4 3 . 0 139 .1 8 4 . 2 i 3 9 . 1 ! 3 9 . ) Hit 1.8 71 .4 161 .6 2 1 2 . 4 - 5 3 . 3 3 7 . i 18 .0 8 2 . 3 3 3 . 1 - 3 7 , l 1 1 1 . 6 104,7 3 6 . 0 3 3 . 6 -».a a*i_ - 1 9 . 6 - 2 0 , 5 - 2 1 . 6 - 2 0 . 0 , . - l f c . 7 _ . r 2 1 . 0 2 12 6 - 2 2 . 9 33.7 - 2 12 6 - 1 5 . 4 2 . 5 - 7 1 ? 7 3 3 . 6 n .1 2 X3 0 2 1 4 . 0 - 1 7 1 . 3 1 79 .2 6 0 . 2 1 166 .9 174 .3 2 EI2.2 6 4 . 3 2 - 1 4 . 8 - 4 . 3 1 177 .4 - 9 6 . 1 - 2 V3 3 1 1 9 . 6 - 1 1 7 . 9 2 13 4 - 2 1 . 6 15 .0 4 9 0 . 3 9 0 . 5 5 1 3 3 . 9 117 .9 5 - 1 6 . 2 - 9 . 3 6 - 2 3 . 4 2 b . 7 - 2 13 6 123 .4 1 2 3 . 2 7 - 1 7 . 8 36 .6 2 (4 0 145 .8 112 .0 1 130.1 - 1 0 1 . 3 1 9 1 . 3 - 8 4 . 8 7 6 8 . 7 ! 5 B . l - 2 14 2 106 .1 105 .4 2 14 3 - 2 1 . 2 - 1 7 . 2 1 9 3 . 3 5 1 . 7 2 14 4 184 .2 136 .6 4 - 1 7 . 4 - 1 4 . 2 3 150 .0 113 .9 - 2 14 9 54 .1 9 6 . 6 6 3 7 . 6 4 7 . 6 0 39 .7 - 2 1 . 9 1 2 1 3 . 3 167.2 1 - 1 8 . 5 - 1 0 . 6 2 3 8 . 1 35 .4 - 2 13 2 6 6 . 0 - 8 2 . 9 3 - 2 0 . 8 15 .4 3 6 1 . 6 6 4 . 0 2 19 4 - 2 1 . 4 8 . 4 4 - 1 9 . 5 - 1 2 . 8 5 53 .4 5 1 . 2 2 16 1 89 .1 - 7 4 . 7 - 2 16 I U 9 . 9 - 1 0 2 . 4 2 6 8 . 4 - 6 1 . 7 2 6 0 . 9 6 1 . 3 2 16 3 - 2 0 . 1 13.8 3 - 2 1 . 2 - 1 1 . 4 - 2 16 * - 2 1 . 7 - 3 8 . 9 0 9 9 . 4 - 3 7 . 6 1 3 5 . 4 - 2 6 . 3 1 6 7 . 6 - 6 2 . 7 2 - 1 9 . 2 - 6 . 6 7 - 7 7 . 7 - 1 7 . 3 - 2 17 3 4 8 . B 5 1 . 0 0 0 4 9 9 . 7 3 8 1 . 4 0 2 3 6 . 8 4 0 . 8 0 2 10T .5 - 1 0 8 . 6 ft 4 i m . Q - i n i . n - 3 0 4 8 4 . 3 110 .9 0 6 1 7 3 . 9 1 7 5 . 0 0 4 171 .5 163 .0 0 8 7 3 . 8 - 7 3 . 0 a 6 - 1 0 . 1 0 . 8 n i n 1.* - 7 * . l 3 0 - 6 . 7 - 0 . 7 3 i 1 156.8 - 1 5 3 . 9 - 3 l 1 328 .2 361 .4 2 3 3 . 6 - 3 0 . 5 2 2 3 9 . 6 - 2 5 4 . 5 1 1C17.T m i . * - 1 i 3 101.9 9 5 . 3 4 2 0 . 4 5 . 2 4 4 7 . 7 - 4 3 . 7 9 9 2 . 8 3 0 . 6 5 19 .0 - 1 8 . 6 h - i n . o - 1 . 7 - 3 i 6 2 0 . 5 B.7 7 8 2 . 7 - 7 5 . 9 7 184 .0 I B 7 . 3 8 4 6 . 7 - 3 0 . 1 fl I Z J . O - 1 1 6 . 8 9 4 1 . 8 - 1 6 . 9 - 3 i 10 - 1 1 . 9 6 . 6 0 - 6 . 9 - O . Q 3 1 120 .0 - 1 1 8 . 8 1 4 0 . 8 - 3 6 . 6 2 3 5 . 2 - 3 2 . 1 7 7 6 . 3 19.n 3 2 3 8 0 . 6 06 .2 3 4 0 . 6 - 3 5 . B 4 104 .3 - 1 0 1 . 6 4 140 .1 149 .3 5 4 5 . 2 - 4 7 . 9 3 3 3 . 0 - 3 3 . 3 3 2 6 ' 4 1 . 3 - 3 4 . 5 6 9 3 . 9 88 .1 7 9 3 . 0 - 9 0 . 8 7 4 6 . 4 - 3 6 . 7 B 5 5 . 4 - 5 4 . 6 fl 5 2 . 7 4 4 . 6 - 3 2 9 3 2 . 3 - 2 7 . 2 0 177 .7 - 1 6 0 . 3 I 7 1 . 6 6 0 . 5 1 138 .9 140.4 2 136 .2 - 1 3 1 . 9 7 - 7 . 0 -*. 1 3 3 3 180 .6 - 2 0 0 . 2 4 14 .4 5 . 0 - 3 3 4 139 .2 136 .8 3 } 5 2 3 . 0 17.7 52 Table VII. C O N T I N U E D : h k I F„ - 3 " 3 3 1 0 6 . 0 108 .0 3 1 * II * * • t - 1 1 . 7 fa 8 3 . 4 8 4 . 6 7 4 8 . e - 4 9 . 0 - 3 3 7 1 1 0 . 3 113 .3 8 4 6 . 3 - 3 B . 7 6 (17.1 - 6 2 . 1 - 3 3 9 2 8 . 0 1 6 . 0 0 143 .9 - 1 4 1 . 4 3 4 1 304 .S - 3 3 3 . 4 1 B 6 . 9 8 5 - 2 2 144 .2 217 . 2 2 110.0 197 .3 3 4 J 3 7 . 7 3 1 . 1 - 3 4 3 1 0 1 . 6 - 9 9 . 7 * 7 8 . 2 8 3 . 9 - 3 4 4 148 .2 1 4 6 . 0 3 3 3 . 9 - 2 7 . 9 4 274 .1 2 9 9 . 4 3 4 6 9 4 . 1 - 9 3 . 7 6 3 0 . 3 - 2 9 . 9 3 4 7 6 b . 3 - 6 1 . 3 7 3 1 . 1 - 1 6 . 3 3 4 6. 2 * . 7 2 3 . 7 8 - 1 0 . 3 3 . 2 - 3 4 9'. 73 .7 - 6 9 . 2 3 S 0 9 2 . 0 91 .1 3 5. I 164 .3 171.1 1 13 .1 - 5 . 9 ?. 1 6 4 . 7 - 1 6 7 . 2 ? I0>».9 117 .0 3 3 3 101 .4 107 .9 , 3 1 7 6 . 7 181 .8 4 1 0 . 6 - 1 4 . 9 4 15 .7 9 . 3 ' 3 9 5 - 1 0 . 6 - 4 . 4 3 7 7 . 4 70 .7 3 3 6 6 1 . 7 - 8 1 . 7 6 144 .1 - 1 4 7 . 3 3 3 7 - 1 2 . 1 1.2 7 6 3 . 3 - 6 3 . 3 e 4 3 . 2 3 8 . 3 9 5 3 . 2 5 1 . 3 3 6 0 6 7 .6 3 6 . 7 1 6 9 . 6 - 7 1 . 3 1 9 2 . 9 9 1 . 7 2 4 0 . 4 4 0 . 0 2 7 9 . 3 - 2 2 . 1 1 - 4 . 4 8 . 9 - 3 6 3 2 6 9 . 6 - 2 8 8 . 4 4 5 4 . 2 - 6 0 . 3 4 79 .4 8 3 . 4 5 1 2 7 . 0 - 1 3 6 . 9 5 7 3 . 3 71 .0 6 31 .6 - 2 9 . 9 - 3 6 6 3 4 . 8 3 1 . 6 7 - 1 2 . 7 - 1 8 . 3 7 7 7 . 7 - 7 4 . 4 - 3 ' 4 B 3 0 . 3 2 3 . 6 9 9 7 . 9 - 8 9 . 0 n A ft - A 70 .2 3 7 1 147 .7 - 1 4 9 . 6 1 2 1 3 . 7 - 2 1 9 . 2 2 1B2 .0 - 196.1 2 103 .3 1 0 4 . 3 i m i . e 117 .4 - 3 7 3 194 .7 2 0 3 . 3 4 3 3 . 6 - 6 2 . 6 4 4 9 . 2 32 .1 3 7 3 151 .3 - 1 6 3 . 0 3 - 9 . 7 B . 4 f. - i s . A - ! > . ? - 3 7 6 111.7 - 1 1 2 . 5 7 2 6 . 3 - 2 4 . 2 7 3 2 . 8 - 5 2 . 6 b - 1 1 . 3 1 3 . 3 9 7 9 . 3 7 8 . 3 0 74 .7 - 7 2 . 3 3 8 1 - 1 0 . b - 1 0 . 3 I 2 1 4 . 3 2 7 3 . 3 2 - 1 0 . 9 - 2 1 . 2 2 7 1 . 2 - 6 9 . 9 3 6 1 . 3 - 6 1 . 1 i i i o . n 119 . 1 3 8 4 42 .B - 3 8 . 9 4 3 5 . 7 4 0 . 3 5 128 .1 - 1 4 1 . 3 3 7 0 . 2 - 7 3 . 3 3 8 6 2 3 . 3 - 2 8 . 5 6 1 7 . 1 - 3 3 . 4 J 8 7 - 1 4 . 4 18 .1 7 6 3 . 8 6 4 . 2 8 - 1 2 . 0 12 .1 0 4 9 . 0 - 3 4 . 2 1 107 .9 120 .9 1 7 0 . 4 4 . 1 3 9 2 4 7 . 3 - 3 2 . 9 • 3 9 2 1 3 2 . 0 161 .6 3 - 1 2 . 3 - 3 . 4 3 3 9 . 8 - 3 6 . 3 3 9 4 1 7 7 . 7 - 1 9 1 . 8 4 7 A . 7 9 3 . 1 3 9 3 - 1 3 . 9 3 . 3 9 - 1 0 . 7 3 . 8 3 9 . f t . . . - M i * . - 3 9 6 1 9 . 6 1 4 . 3 9 7 3 2 . 6 - 1 2 . 9 4 8 71.A 1 4 . 7 ] 10 0 6 8 . 0 - 7 1 . 3 10 1 - 1 3 . 0 - 3 1 . 7 - 3 10 1 3 2 . 3 - 3 7 . 0 10 2 - 1 3 . 4 - 1 . 6 10 2 135 .1 1 4 6 . 9 10 3 «A.n - 1 0 1 . 3 - 3 10 1 7 1 . 0 7 1 . 3 10 4 116 .4 1 2 3 . 7 10 4 6 9 . 2 - 7 4 . 7 3 10 3 2 6 . 6 - 3 2 . 6 10 3 116 .6 - 1 1 9 . 4 10 A -IA.7 - 3 10 6 - 1 1 . 9 - 1 1 . 4 10 7 - 1 2 . 5 - 7 . 3 - 3 10 8 - 1 3 . 2 - 3 . 3 0 - 1 4 . 4 8 . 2 1 i n n . 7 107 . 1 - 3 11 1 6 8 . B - 7 4 . 3 3 11 2 6 1 . 4 6 3 . 1 2 8 8 . 1 ' 9 8 . 3 3 11 3 170 .B - 1 7 8 . 3 3 113 .2 - 1 1 7 . 8 4 141.4 - 1 4 * . ? - 3 11 4 1 0 1 . 6 - 1 1 1 . 1 5 - 1 7 . 2 2 2 . 3 - 3 11 5 3 7 . 1 6 0 . 6 6 - 1 8 . 1 - 2 4 . 0 b 74 .7 - 8 1 . 3 7 - 1 1 . 7 - 1 1 . 1 3 12 0 - 1 6 . 6 - 1 0 . 2 1 5 0 . 8 - 3 4 . 3 1 2 3 . 1 3 0 . 4 2 [74 . 6 - 2 1 3 . 7 2 3 0 . 4 3 8 . 2 3 100.1 - 1 0 1 . 9 - 3 12 3 3 2 . 1 3 1 . 3 4 - 1 8 . 7 9 . 4 - 3 12 4 2 2 3 . 0 - 2 4 5 . 2 3 - 1 9 . 6 13 .6 3 3 6 . 5 33 .7 6 8 2 . 9 87 .1 - 3 12 7 - 1 4 . 1 - 6 . 3 3 13 0 1 1 6 . 9 - 1 0 8 . 0 1 - 1 9 . 5 - 1 8 . 0 - 3 13 I 6 1 . 3 - 7 3 . 5 2 1 0 J . 7 - 9 5 . 8 2 2 7 . 3 2 9 . 9 3 13 3 - 2 0 . 6 - 2 6 . 2 3 5 1 . 1 - 3 3 . 2 4 - 2 1 . 4 4 4 . 5 4 S B . 4 9 5 . 4 3 - 2 2 . 3 2 1 . 7 5 - 1 3 . 8 -74.A - 3 13 6 3 6 . 7 4 0 . 8 3 ' • 14 ' v 0 126 .6 106.1 1 - 2 1 . 3 - 5 . 6 1 3 9 . 7 6 2 . 5 2 4 3 . 6 - 3 0 . 9 2 34 .2 - 3 4 . 9 3 14 3 - 2 2 . 4 - 3 0 . 0 3 - 1 4 . 2 23 .1 4 - 2 3 . 1 33 .2 4 9 4 . 6 - 1 0 2 . 2 3 - 1 4 . 9 1 2 . 7 6 - 1 3 . 3 - 3 . 1 3 15 0 72 .7 - 6 4 . 3 3 13 1 3 6 . 3 - 4 6 . 7 1 40 .1 3 3 . 7 2 3 0 . 3 - 4 3 . 0 4! 153 .6 - 1 6 7 . 1 1 - 7 1 . 1 1 2 . 4 :j 13 1 \v.y 4 - 1 3 . 8 - 4 4 . 1 1 0 . 0 3 - 1 6 . 3 - 1 7 . 0 3 16 0 1 0 9 . 9 - 9 1 . 1 1 7 7 . 7 - 6 7 . 7 . 3 16 1 8 1 . 1 - 8 4 . 3 3 16 2 - 2 3 . 3 - 1 2 . 2 2 3 9 . 3 - 6 1 . 3 • 3 16 3 - 1 7 . 0 12 .7 4 1 4 . 8 4 3 . 4 ft 1*4 .4 - i o n . n - 3 (7 1 6 4 . 6 - 6 2 . 8 2 - 1 0 . 7 - 8 . 4 0 0 - 7 . 8 - 2 7 . 4 0 2 173 .6 1 7 4 . 3 0 2 2 4 4 . 2 2 3 4 . 8 ft 4 130 .7 144 .4 - 4 0 4 7 4 . 7 - 7 1 . 6 4 0 6 9 8 . 7 9 4 . 6 0 6 1 3 8 . 4 • 1 9 9 . 6 0 a 4 2 . 3 17.2 0 - 7 . 8 3 . J 1 4 3 . 1 41 . 1 - 4 1 t 2 7 1 . 0 2 8 3 . 9 Z 54 .1 4 6 . 6 2 176 . 8 - 1 7 8 . 7 3 2 9 . 0 - 2 8 . 3 3 2 2 5 . 3 • 2 2 3 . 2 4 1 0 7 . 8 108 .6 . 4 I 4 114 . 8 - 1 1 1 . 6 3 191 . 6 193 .2 3 10 .2 2 4 . 8 6 75 .1 - 7 3 . 1 - 4 1 6 . .52.2 . - 3 1 . 7 4 1 7 7 1 . 4 3 . ? - 4 8 3 3 3 . 6 3 8 . 2 4 B 4 - 1 2 . 0 - 5 . 0 - 4 8 4 3 1 . 4 - 3 9 . 3 4 B 5 - 1 2 . 6 10 .4 - 4 8 3 - 1 0 . 1 - 7 . 7 - 4 1 7 5 1 . 4 5 2 . 6 - 4 1 8 1 9 . 5 - 1 . 1 - 4 1 9 114 .3 - 1 0 9 . 3 4 2 0 7 4 . 9 6 3 . 8 4 2 1 3 0 . 9 2 4 . 3 - 4 7 1 «n.7 - 8 7 . 0 4 8 6 2 4 . 9 - 3 0 . 3 - 4 6 6 - 1 0 . B - 9 . 3 - 4 8 7 4 3 . 9 - 4 4 . 9 - 4 8 8 3 3 . 7 2 1 . 3 4 9 0 7 6 . 9 6 0 . 9 4 9 1 3 4 . 4 AO.4 4 2 2 6 4 . 3 6 0 . 5 - 4 2 2 7 0 . 3 - 6 6 . 4 4 2 3 2 9 . 2 18 .7 - 4 2 3 2 0 5 . 6 - 2 1 0 . 3 4 2 4 2 4 . 6 - 2 0 . 1 - 4 2 4 3 0 . 3 4 2 . 7 - 4 9 1 3 0 . 2 - 5 2 . 1 4 9 2 - 1 1 . 7 11 .1 - 4 9 2 4 2 . 3 4 3 . 9 4 9 3 32 .2 34kB - 4 9 1 7 7 . 4 8 0 . 8 4 4 4 - 1 2 . 7 - 8 . 1 4 2 3 27 .1 2 0 . 5 - 4 2 3 106.4 109 .0 4 • 2 6 4 7 . 4 4 4 . 0 - 4 2 6 - 9 . 3 15 .6 4 2 7 1 8 . 3 - 1 4 . 9 - 4 2 7 R6.8 - B 4 . 0 - 4 9 4 2 B . S - 3 1 . 1 4 9 5 - 1 1 . 3 11 .5 - 4 9 9 - 1 0 . 7 - 1 5 . 2 - 4 9 6 112 .0 - 1 1 3 . 2 - 4 9 7 7 2 . 4 - 7 4 . 8 - 4 9 8 8 1 . 7 8 4 . 3 - 4 2 8 2 3 . 4 - 1 9 . 6 - 4 2 9 7 9 . 0 - 7 5 . 3 4 3 0 2 1 . 2 - 1 9 . 9 4 3 I 14B.4 - 1 5 2 . 6 - 4 3 1 128.6 131 .7 4 1 7 7fc.rt - 7 7 . 7 4 10 0 137 .0 132 .0 4 10 1 193 .9 2 1 2 . 3 - 4 10 " 1 - 1 0 . 4 1 0 . 9 4 10 2 5 3 . 3 - S B . 5 - 4 10 2 16 .6 - 2 2 . 3 4 10 1 1 1 . 1 - 1 1 . 1 - 4 3 2 6 0 . 3 - 5 4 . 9 4 3 3 9B .2 4 6 . 9 - 4 3 1 105 .8 107 .8 4 3 4 9 3 . 9 9 4 . 8 - 4 3 4 4 A . 7 «.*. 7 - 4 10 3 9 4 . 2 - 9 9 . 7 4 10 4 - 1 1 . 6 2 6 . 9 - 4 10 4 6 7 . 6 - 7 3 . 6 4 10 3 2 8 . 6 - 3 7 . 1 - 4 10 5 142.2 - 1 4 7 . 5 - 4 10 A 4 4 . 1 107 .3 - 4 10 7 - 1 2 . 2 3 . 7 4 11 0 1A3.0 181 .1 4 11 1 4 0 . 0 - 3 8 . 0 - 4 11 I - 1 1 . 0 - 2 3 . 2 4 II 7 - 1 1 . 7 - 1 0 . 0 4 3 5 3 4 . 2 56 .1 - 4 3 3 167 .3 - 1 6 9 . 2 4 3 6 4 2 . 9 - 3 7 . 0 - 4 3 6 14 .9 - 6 . 2 4 3 7 - 1 1 . 8 - 0 . 4 - 4 1 7 1 4 . 0 IX.A - 4 3 8 7 1 . 1 - 1 0 . 2 - 4 3 9 19.4 - 3 . 3 4 4 0 184 .3 1 7 4 . 8 4 4 1 184.2 - 1 7 8 . 2 - 4 4 1 4 0 . 1 3 0 . 3 4 4 7 l*O.I 1 4 1 . 3 • 4 11 2 2 9 . 2 - B 6 . 4 4 11 3 3 3 . 1 - 3 2 . 3 - 4 11 1 6 6 . 6 7 0 . 7 4 1 1 . 4 - 1 4 . 7 - 1 4 , 1 - 4 11 4 2 6 . 9 - 3 3 . 4 - 4 11 3 78.4 - 7 5 . 1 - 4 4 2 159 .3 - 1 6 9 . 1 4 4 3 1B7.4 197 .4 - 4 4 } 192 .9 - 2 0 1 . 2 4 4 4 4 4 , 1 3 2 . 7 - 4 4 4 107.2 10B.2 4 4 3 4 0 . 7 - 4 3 . 7 - 4 11 6 126 .1 - 1 2 8 . 3 - 4 11 7 3 2 . 7 3 8 . 2 4 12 0 4 7 . 9 5 0 . 8 4 12 1 - 1 4 . 7 - 3 . 0 - 4 12 1 - 1 1 . 6 - 2 0 . 6 4 12 2 7 0 7 . 7 - 7 1 1 . 1 - 4 4 5 139 .4 138 . 9 4 4 6 4 9 . 3 4 9 . B - 4 - 4 6 2 4 . 4 - 2 2 . 4 4 4 7 4 9 . 6 - 5 6 . 6 - 4 4 7 - 1 0 . 1 - 2 . 0 - 4 4 0 I f l f l .4 - 1 0 7 . 7 - 4 12 2 - 1 1 . 7 2 1 . 0 4 12 3 - 1 3 . 6 2 3 . 6 - 4 12 1 2 0 . 3 - 1 3 . 9 4 12 4 - 1 6 . 2 12 .6 - 4 12 4 8 4 . 6 - 8 7 . 3 - 4 12 3 7 B . 6 - 7 9 . 0 - 4 4 9 5 4 . 3 - 3 3 . 0 4 5 0 2 3 7 . 6 2 1 9 . 4 4 5 1 11B.8 121 .4 - 4 5 1 7 7 . 8 - 2 8 . 5 4 3 2 16 .4 1 2 . 3 - 4 3 7 4 0 . 0 - 3 3 . 2 - 4 12 6 9 1 . 9 B 6 . 0 4 13 0 6 3 . 6 - 7 1 . 6 4 13 1 - 1 4 . 4 4 . 6 - 4 13 I - 1 2 . 3 - 1 4 . 2 4 13 2 2 6 . 6 31 .4 - 4 11 2 - 1 2 . 4 1 .0 4 3 1 162 .7 1 7 1 . 6 - 4 3 1 103 . 6 1 0 0 . 6 4 3 4 3 4 . 8 - 6 0 . 3 - 4 5 4 7 8 . 6 - 7 4 . 7 4 3 3 - 1 1 . 0 - 4 . 3 - 4 3 3 1 4 . 8 - 2 8 . 1 4 13 3 3 8 . 9 - 4 8 . 3 - 4 11 3 3 8 . 8 - 6 3 . 3 - 4 13 4 7 0 . 2 - 2 1 . 2 - 4 13 3 2 4 . 6 2 3 . 9 - 4 19 6 3 4 . 3 7 0 . 3 4 14 0 - I B . 4 6 . 4 4 3 6 6 4 . 7 6 3 . 4 - 4 5 6 6 0 . 4 - 6 0 . 3 - 4 3 7 7 5 . 0 - 7 7 . 3 - 4 3 8 3 7 . 9 - 3 7 . 6 - 4 3 9 - 1 1 . 6 - 1 6 . 1 4 6 0 118.7 - 1 1 3 . 7 4 14 1 SA.2 - 3 6 . 6 - 4 14 1 9 9 , 8 - 1 1 4 . 9 4 14 2 6 3 . 6 - 6 0 . 6 - 4 14 2 6 9 . 1 7 5 . 3 - 4 14 3 4 7 . 2 4 4 . 6 - 4 14 4 6 6 . 6 - B O . l 4 6 1 6 3 . 9 - 6 3 . 7 - 4 6 1 2 1 1 . 6 - 2 2 1 . 7 4' 6 2 8 8 . 7 6 8 . 9 - 4 6 2 1 0 B . 1 1 1 6 . 0 4 6 3 162 .3 189 .1 —4 A 1 2 1 1 . 0 - 7 7 3 . 4 - 4 14 3 - 1 3 . 9 14 .4 4 15 0 101 .7 - 1 0 4 . 4 4 15 I - 2 1 . 4 - 2 7 . 2 - 4 13 1 - 1 4 . 1 I B . 9 - 4 13 2 110 .4 - 1 5 0 . 2 - 4 15 3 - 1 4 . 2 -11.« 4 6 4 3 1 . 6 36 .2 - 4 6 4 8 1 . B 8 1 . 1 4 6 3 - 1 1 . 5 - 1 5 . 3 - 4 6 3 5 2 . 2 - 3 3 . 4 4 6 6 32 .1 - 2 3 . 6 - 4 A A Rft.l - 4 4 . 7 - 4 15 4 5 4 . 3 - 6 0 . 8 3 0 0 6 1 . 0 - 3 4 . 2 3 0 2 4 7 . 2 - 4 8 . 3 - 3 0 2 1 1 3 . 9 - 1 0 8 . 7 3 0 4 6 3 . 1 6 1 . 4 - 3 0 4 101.7 - 1 0 0 . 7 - 4 6 7 9 3 . 1 - 9 2 . 4 - 4 6 6 2 2 . 4 12 .1 - 4 6 9 2 9 . 0 - 2 0 . 9 4 7 0 137.8 1 2 9 . 1 5 0 6 - 1 1 . 3 - 4 . 2 - 3 0 6 4 1 . 5 - 5 0 . 4 - 3 0 8 6 9 . 3 - 6 2 . 3 3 1 0 171 .9 166 .9 5 1 1 119 .8 - 1 1 0 . 3 - 9 1 1 7 8 . 4 7A . 6 5 1 2 4 1 . 4 4 0 . 6 - 3 1 2 39 .1 36 .2 9 1 1 104.7 - 1 0 6 . 6 - 3 1 3 141 .8 - 1 6 3 . 6 4 1 4 7 3 . 5 - 1 4 . 4 - 4 7 1 1 6 1 . 9 - 1 7 4 . 9 4 7 2 U 4 . 0 117 .8 - 4 7 2 9 9 . 3 3 4 . 6 4 7 3 4 1 . 3 - 4 0 . 0 - 4 7 3 - 9 . 2 - 1 0 . 3 4 7 4 7 4 . A - 7 4 . 3 • 4 7 4 173.1 - 1 8 6 . 3 4 7 5 7 3 . 8 - 7 9 . 9 - 4 7 3 1 6 0 . 0 173 .8 4 7 6 3 1 . 0 2 8 . 2 - 4 7 6 79 .1 - 7 B . 6 - 4 T 7 HI.4 - 8 7 . 4 - 9 I 4 76 .7 - 7 6 . 4 9 I 5 7 0 . 5 7 1 . 6 - 5 1 3 149.2 - 1 4 9 . 2 9 1 . 6 4 1 . 2 3 7 . 1 - 9 1 6 38 .1 - 3 9 . 2 - 4 1 7 7 1 . 7 77 .A T 4 7 8 2 9 . B 2 1 . 9 4 8 0 98 .1 - 9 0 . 4 4 8 1 5 9 . 3 6 9 . 9 - 4 8 I 4 6 . 4 - 4 2 . B 4 8 2 2 6 . 0 2 2 . 9 - 4 8 7 A7 .A A T . II - 3 1 8 - 1 0 . 9 - 2 . 7 - 5 1 9 5 7 . 4 - 3 2 . 8 5 . 2 0. 1 2 6 . 6 . - 1 2 0 . 8 4 8 3 6 4 . 2 - 7 1 . 1 2 0 2 . 5 - 2 0 4 . 6 9 0 . 0 - 6 9 . 5 41.ft -411.7 3 0 . 4 - 2 4 . 8 2 1 4 . 0 2 1 4 . 9 2 0 8 . 9 - 4 1 . 9 - 4 2 . 5 7 2 . 0 - 7 1 . 0 182 .4 - 1 1 . 7 4 9 . 4 3 8 . 8 5 0 . 0 4 0 - 8 181.9 - 7 . 5 - 4 8 . 0 2 3 . 4 66 .1 5 0 . 7 2 1 . 4 K i l l . 4 32.4, - 2 4 . 1 - B 3 . 6 - 3 5 . 3 13 .9 104 .1 4 3 . 4 138.6 - 1 6 1 . 0 - 1 0 . 7 2 7 . 7 - 1 8 . 8 - 1 1 . 2 - 1 0 . 9 A 6 . 4 6 6 . 5 104.4 44.7 31 . 4 - 1 1 . 0 - 2 8 . 2 7 .1 119 .0 - 1 1 5 . 0 9 6 . 0 - 9 1 . - 9 . 0 - 2 . 0 7 3 - P 4*-« - 4 3 . 5 6 5 . 5 2 4 . 2 - 3 6 . 5 - 2 5 . 3 3 1 - 5 150 .6 152 .4 132 .9 - 1 1 3 . 2 2 1 . 2 - 6 . 6 17 .6 9 9 . 2 5 6 . 1 7 7 . 7 116 .1 - 3 5 . * 5 5 . 4 9 5 . 9 37 .1 - 1 1 . 7 39 .0 9 6 . 0 an.5. - 2 4 . 6 9 8 . 0 • 8 9 . 3 2 3 . 3 I I . B - 7 6 . 7 1 1 4 . 4 - 6 3 . 6 8 0 . 9 - 1 1 4 . 4 5 0 . 5 4 1 . 3 2 3 . 0 9 9 . 0 5 8 . 4 -mil 1 1 . 6 - I t . O 71 .2 1 1 7 . 0 31 . 6 " 9 . 6 - 5 4 . 3 7 2 . 2 19 .8 5 1 . 1 - 4 2 . ; - 2 1 . 1 104 . 2 5 4 . 7 - 2 4 . 2 1.7 3 4 . 3 7 3 . 3 - 2 6 . 3 1 0 * . 2 - 6 . 2 1 5 . 7 71 .1 - 7 2 . 3 3 6 . 9 4 5 . 8 2 3 . 2 6 b . * 3 3 . 7 26 .8 33 .2 4 3 . 8 5 / . 7 i!ti - 3 4 . 3 -48.a •19 .5 63 .7 S 4 . 6 - 3 9 . 1 17 .6 - 3 9 . 2 - 4 0 . 7 6 1 . 1 4 3 . 3 4 1 . 4 2 2 . 2 - 1 4 . 0 8 7 . 6 9 1 . 0 3 9 . 1 4 1 . 8 3 9 . 7 1 1 . 9 131 . 6 1 3 7 . 9 0 8 . 9 9 1 . 6 113 .4 - 1 2 4 . 0 4 1 . 7 41.a 2 0 4 . 3 2 2 4 . 8 7 9 . 9 7 9 . 3 17.1 - 8 . 7 - 1 1 . 1 - 3 . 9 4. r U . 118.6 3 8 . 8 9 6 . 1 4 6 . 7 6 0 . B " . 4 3 7 . 4 04 .1 3 2 . 7 ? 4 . 7 6 3 . 9 6 2 . 0 41 .1 - 1 J . 9 18 .2 it.O 2 8 . 1 - 1 2 . 3 4 4 . 1 9 0 . 8 - 1 1 . 9 -n.» 4 1 . 3 !>9.5 19 .1 53 .1 6 9 . 4 - 1 5 . 4 9 6 . 4 6 1 . 8 6 2 . 4 3 7 . 2 1 9 . 3 - 9 . 9 . 2 7 . 6 37 .7 5 4 . 7 4 0 . 3 2 8 . 0 9 9 . 4 5!>.8 L 0 f . 7 • 117.8 4 1 . 9 - 7 2 . 7 1 2 2 . 8 6 0 . 6 102 .0 - 4 9 . 9 5B .B 1 0 . 5 40 .1 - 9 6 . 5 - 1 9 . 9 3 2 . 9 3 0 . 7 - 3 P . J 72 .1 6 2 . 0 - 4 7 . 4 2 4 . 1 2 4 . 5 - 5 1 . 1 2 6 . 4 0 . 3 4 7 . 8 9 9 . 2 3 .3 - l f i - 4 4 0 . 7 6 9 . 9 - 1 4 . - 3 6 . 0 - 7 0 . 2 - 1 2 . ' _ 109.2 - 7 3 . 9 0 .4 9 6 . 2 64 .1 3 2 . 3 3 0 . 8 3 .8 - 1 6 . 7 9 3 .6 - 5 A . 5 105.0 112.7 3 3 . B 136.6 - l i B . l - 5 2 . 4 - 6 9 . 6 2 6 . 4 - 6 . 0 •m- 6 2 . 0 - 3 3 . 1 - 9 2 . 2 - 1 5 - 5 19 . » - 3 6 . e 6 8 . 3 17.6 6 6 . * 2 8 . 9 - 1 0 . 0 -m- 6 J . 3 sr.i 94 . 2 » - » 19 .6 3 8 . 2 9 0 . 0 2 4 . 3 13 .5 74.5 5 3 . 4 3 3 . L 1A9.3 - 1 A 7 . 0 3 4 . 6 2 2 . 1 - 1 0 . 7 2 0 . 9 130 .0 4 9 . 6 2 8 . 3 2 3 . 6 19B.2 • 2 B . 3 17 .2 3 4 . 3 2 6 . 0 174.4 2 6 . 3 31 .7 10.1 6 3 . 9 121.9 2 4 . 9 199. 1 - 1 1 . 3 5 3 . 6 6 8 . 1 3 6 . 8 3 9 . 3 6 4 . 4 11 .0 - 1 2 7 . 0 - 4 6 . 0 - 2 1 . 2 14.4 6 3 . 9 1 0 3 . H 7 2 . 3 - 4 1 . 0 •203.1 2 Z . i - 8 . 0 3 9 , 8 19 .8 - 3 1 . 4 2 9 . 1 2 6 . 2 1B5.2 - 1 6 . 9 - 2 2 . 8 - 9 - 0 6 2 . 7 •119.1 2 0 . 6 170 .3 2 . 2 - 8 7 . 7 31 .0 3 0 . 3 - 6 1 . 2 4 1 . 0 104 .1 53 Table VIII. •Biphenylylferrocene measured and calculated structure factors. h k I Fo * 0 0 1 6 6 . 1 1 7 4 . 9 6 0 0 1 3 1 . 5 1 5 0 . 0 ft 0 0 0 . 0 0 . 7 10 0 0 2 6 . 7 2 6 . 2 1 ! 0 0 1 4 . 5 1 0 . 6 u 0 0 0 , 0 1 1 . 0 16 0 0 2 3 . 5 2 8 . 6 IB 0 0 1 8 . 0 1 4 . 2 20 0 0 1 3 . 4 1 9 . 0 22 0 0 1 1 . 4 1 9 . 2 7 0 1 1 0 7 . 7 1 1 6 . 6 4 0 1 7 4 . 2 8 1 . 9 6 0 1 1 6 . 1 3 1 . 6 a 0 I 2 9 . 9 3 2 . 6 10 0 1 1 7 . 1 2 0 . 2 12 0 1 2 6 . 9 3 0 . 2 1 * 0 W . J 2 1 . 1 16 c I 0 . 0 3 . 2 IP 0 I I S . 1 2 2 . 5 20 0 1 1 f t . 9 2 8 . 1 0 0 2 7 « . l 7 9 . 6 2 0 2 6 T . I 9 3 . 1 * 0 1 2 1 . 6 1 2 0 . 0 6 0 2 9 0 . 6 9 4 . 6 ft 0 2 3 2 . 4 3 6 . 1 10 0 7 4 0 . 2 4 1 . 2 12 c 2 2 2 . 2 31i .9 U 0 2 1 9 . 0 2 2 . 4 16 a 2 4 . 0 2 4 . 6 U 0 1 2 . 9 1 1 . 1 2 0 3 4 3 . 0 4 6 . 1 4 c J 3 2 . 4 3 3 . 7 6 c 3 4 8 . 1 4 5 . 6 ft 0 3 6 7 . 6 6 6 . 9 ID 0 2 6 . 1 2 5 . 5 12 0 3 3 8 . T 4 0 . 1 14 0 3 3 3 . 3 9 3 . 7 14 0 3 2 1 . 1 2 4 . 6 16 0 3 2 2 . 7 2 1 . 5 0 0 4 5 2 . 5 4 9 . 7 2 0 7 . 5 1 2 . 4 0 4 7 . 9 1 2 . 9 6 0 4 6 3 . 2 5 6 . 7 e 0 4 2 2 . 5 1 3 . 7 10 0 4 7 7 , 5 6 2 . 7 12 0 4 2 7 . 6 2 7 . 9 u 0 2 5 . 4 3 2 . 0 16 0 4 1 7 . S 1 6 . 0 16 0 4 1 6 . 6 1 1 . 7 2 0 5 3 3 . 2 3 4 . 8 4 0 5 1 9 . 8 2 7 . 3 6 c 5 4 2 . 9 4 3 . 9 6 0 3 6 . 6 3 8 . 4 10 0 5 1 5 . 2 9 . 1 12 0 s 4 7 . 7 4 7 . 5 14 0 1 2 . 4 1 4 . 8 0 0 6 6 6 . 9 6 4 . 1 2 0 6 3 8 . 6 4 0 . 5 4 0 6 5 . 1 6 2 . 6 6 0 6 3 1 . 1 2 8 . 8 e 0 0 . 0 9 . 9 10 0 6 2 5 . 9 3 0 . 0 12 0 6 1 7 . 3 1 4 . 4 14 0 1 2 . 9 9 . 5 Z 0 7 7 6 . 1 6 7 . 6 * 0 7 1 6 . 3 2 2 . 0 b 0 7 0 . 0 1 0 . 6 B 0 7 1 9 . 1 2 6 . 2 10 0 T 9 . 6 6 . 1 12 0 7 1 0 . 0 6 . 8 0 0 4 7 . 1 4 3 . 7 2 0 1 5 . 9 1 8 . 9 4 0 s 2 4 . 1 2 7 . 5 6 0 B 2 1 . 4 1 7 . 8 a 0 9 . 8 6 . 1 2 c 9 1 7 . 2 9 . 0 4 0 2 5 . B 2 1 . 5 6 u 9 2 1 . 9 1 7 .B 0 0 10 ^ 8 . 7 2 5 . 1 2 0 10 1 8 . 9 9 . 1 4 0 10 1 2 . 0 4 . 6 2 0 11 2 6 . 9 1 6 . 8 4 0 11 0 . 0 0 . 4 6 0 11 IB.7 4 . 5 2 1 0 6 4 . 1 7 4 . 2 9 1 0 3 9 . 6 4 0 . 1 4 1 0 1 3 4 . 6 1 3 2 . 8 5 I 0 1 5 . 2 2 0 . 9 6 1 0 1 7 . 1 2 4 . 5 T 1 0 6 . 2 1 .1 B 1 0 1 0 . 5 1 9 . 9 9 I 0 1 2 . 8 1 2 . 6 10 1 0 1 3 . 6 1 7 . 2 11 I 0 1 4 . 5 3 . 4 12 I 0 1 9 . 6 1 4 . 3 19 1 0 1 6 . 3 5 . 7 14 I 0 1 5 . 2 2 7 . 8 15 1 0 0 . 0 2 3 . 0 16 0 1 9 . 9 I T . f l IT 0 0 . 0 3 . 7 18 0 1 5 . 2 1 5 . 7 19 0 0 . 0 1 3 . 2 20 o 15 . f t 2 3 . 9 1 1 3 6 . 1 3 8 . 4 2 1 1 4 7 . 2 1 5 7 . 4 1 S&.fl IT .9 4 1 6 1 . 5 7 2 . 4 5 1 2 9 . 3 3 0 . 5 6 1 1 8 . 6 22.2 7 1 1 1 . f t 5 . 6 ft 1 7 2 . 1 6 9 . 8 9 1 U . 9 16.2 10 1 1 3 . 0 5 . 6 11 1 0 . 0 1 2 . 7 12 I 0 . 0 1 5 . 8 13 1 1 7 . 3 1 2 . 0 1 * 1 2 2 . 4 2 T . 5 15 1 0 . 0 9 . 8 16 1 2 0 . 0 1 8 . 1 0 2 6 9 . 2 7 7 . T 1 2 3 7 . 2 4 6 . 7 X 2 2 8 . 0 2 3 . 1 3 5 4 . ) 3 4 . 1 4 2 3 0 . 8 3 1 . 4 5 2 1 9 . 7 2 3 . 4 6 2 4 6 . 3 5 1 . 2 7 2 2 2 . 5 2 2 . 2 ft 2 3 9 . 9 4 1 . 7 9 0 . 0 2 1 . J 10 z 4 5 . 3 4 7 . 3 11 2 2 8 . 6 3 3 . 5 12 2 0 . 0 7 . 9 19 2 0 . 0 1 6 . 4 14 2 2 3 . 6 3 0 . 7 1 } 0 . 0 " B .3 16 2 2 7 . 3 3 0 . 7 17 2 0 . 0 1 2 . 2 18 ] 2 2 1 . 7 1 1 . 3 19 2 0 . 0 5 . 3 20 ' 2 2 2 . 5 1 5 . 8 1 2 1 . 9 2 5 . B 2 3 2 2 . 4 2 3 . 3 9 3 5 6 . 1 6 4 . 3 4 9 5 6 . 1 6 0 . 4 5 3 0 . 0 1 4 . 6 6 3 2 5 . 9 3 5 . 3 T 2 2 . 4 2 2 . 7 • 9 5 1 . 8 4 B . 5 9 3 2 6 . 2 3 0 . 2 10 9 2 7 . 1 2 B . 6 11 3 0 . 0 1 1 . 1 12 3 5 2 . 7 4 6 . 2 19 6 . 0 8 . 8 14 9 1 9 . 3 2 2 . 7 15 3 0 . 0 7 . 6 16 3 1 8 . 6 7 . 3 0 4 0 . 0 2 1 . 6 I 4 1 2 . 6 9 . 3 2 0 . 0 1 5 . 5 3 4 1 3 . 0 1 6 . 8 4 4 4 1 . 5 4 5 . 6 5 4 1 7 . 0 1 9 . 4 6 4 3 2 . 2 3 9 . 5 7 1 4 0 . 0 1 2 . 3 a 2 4 . 7 2 2 . 8 9 4 0 . 0 1 .9 10 4 6 3 . 7 6 6 . 3 L I 4 0 . 0 6 . 4 12 4 1 6 . 5 1 4 . 9 13 4 0 . 0 7 . 2 14 1 7 . 4 2 7 . 0 1 5 1 3 . 7 1 6 . 5 2 5 5 4 . 5 5 4 . 5 3 5 8 . 1 9 . 1 4 5 2 1 . 4 2 4 . 4 5 5 1 5 . 5 2 1 . 0 6 5 0 . 0 1 2 . 9 7 1 4 . 7 2 4 . 4 ft 1 5 6 2 . 5 5 4 . 7 9 1 s 0 . 0 7 . 9 10 5 1 4 . 1 1 5 . 6 11 1 5 0 . 0 1 3 . 3 12 1 5 1 7 . 5 2 0 . 3 13 1 0 . 0 9 . 3 14 1 5 I B . 7 2 2 . 6 0 1 6 7 9 . 2 7 5 . 8 1 1 A 3 9 . 9 3 4 . 1 2 1 6 1 1 . 6 1 7 . 3 3 I 0 . 0 1 0 . 7 4 1 6 5 0 . 6 4 4 . 7 4 1 6 1 7 . 2 1 6 . 7 6 6 3 9 . 3 3 4 . 1 7 1 6 0 . 0 6 . 9 8 1 6 0 . 0 2 . 0 9 6 0 . 0 9 . 9 10 6 3 4 . 0 3 1 . 4 I 1 7 0 . 0 4 . 3 2 1 7 6 0 . 0 5 8 . 7 3 7 1 8 . 4 2 2 . 0 4 1 Y 3 4 . 9 3 2 . 6 5 1 7 1 8 . 9 1 0 . 5 ft 1 7 2 7 . 3 2 8 . 0 7 1 7 0 . 0 5 . 0 ft 1 7 1 9 . 0 3 . 3 9 I 7 1 4 . 5 8 .1 0 1 ft 2 8 . 2 25.5 I 1 ft 1 9 . 0 1 2 . 4 2 1 6 2 0 . 1 1 2 . 8 1 1 9 1 5 . 2 2 .1 0 I 10 1 9 . 9 9 . 5 2 2 o 1 6 . 3 22.5 9 I 2 2 . J u.y 4 2 0 98.2 4 3 . 1 5 2 0 14. f t 1 6 . 7 6 2 0 6 3 . 4 6 2 . 2 7 2 0 o . a 3 . 0 ft 2 0 3 0 . 8 2 8 . 7 9 2 6 1 9 . ¥ 1 6 . 6 10 2 0 4 0 . 8 3 5 . 0 11 2 0 1 5 . 4 1 3 . 2 11 2 0 9 . 4 1 . 9 11 2 0 C O 2 . 4 14 2 0 1 4 . 7 22 .5 15 7 a 0 . 0 4 . 6 1* 1 o 1 9 . 6 2 1 . 2 1 2 i 1 7 . 3 2 1 . 7 2 2 i 3 3 . 7 3 5 . 5 3 2 i 3 8 . 2 3 3 . 0 4 2 i 4 6 . 8 4 4 . 3 5 2 i 0 . 0 1 B . 0 6 2 i 2 4 . 8 2 B . 5 7 2 i 1 9 . 5 9 2 . 8 8 2 i 3 0 . 7 2 6 . 5 9 2 i 1 4 . 6 2 2 . 7 10 2 0 . 0 1 1 . 9 11 2 i 1 2 ; 7 2 0 . 5 12 2 i 2 2 . 4 2 S . 7 13 2 i 1 2 . 6 I B . 9 14 2 i 2 1 . 0 1 3 . 8 15 2 i 0 . 0 0 . 0 1 4 . 4 1 0 . 1 17 7 L 1 6 . 6 2 5 . 0 18 2 1 1 5 . 2 2 8 . ) 2 4 7 . 7 4 3 . 2 1 2 2 0 . 0 6 . 5 2 2 3 3 . 1 3 3 . 3 2 8 . 7 2ft . 6 4 2 2 5 7 . 4 5 / . 5 5 2 2 1 9 . 6 1 7 . B 6 2 2 3 0 . 6 2 9 . 6 7' 2 2 2 . 4 2 4 . 5 8 2 2 0 . 0 3 . 9 1 9 . 5 2 0 . 7 10 2 2 5 2 . 5 4 9 . 6 11 2 2 2 0 . 6 2 9 . 1 12 2 2 9 . 7 1 3 . 7 13 2 2 0 . 0 1 5 . 2 14 2 2 1 8 . 5 2 4 . 9 2 7 . 6 9 1 . 3 3 2 . 7 9 0 . 4 3 2 3 1 6 . 1 1 7 . 0 4 7 3 1 7 . 3 2 5 . 0 5 2 3 1 6 . 0 1 0 . 2 6 2 9 0 . 0 1 0 . 3 4 . 4 1 5 . 6 ft 2 7 4 . 2 6 4 . 2 9 2 9 0 . 0 1 9 . 2 10 2 9 9 . 2 9 . 3 11 2 3 0 . 0 1 4 . 4 12 2 3 3 5 . 0 3 3 . 5 0 . 0 1 2 . 2 14 2 3 1 1 . 0 2 9 . 9 15 2 3 0 . 0 1 . 7 16 2 J 1 1 . 7 1 7 . 0 0 2 4 7 2 . 4 6 9 . 6 I 2 4 1 5 . 7 2 6 . 2 0 . 0 0 . 4 3 2 4 1 6 . 2 2 0 . 8 4 2 4 2 9 . 1 3 5 . 5 5 2 4 5 . 1 8 . 7 6 2 4 5 B . 6 4 9 . 4 7 2 4 2 3 . 0 2 5 . 3 0 . 0 1 U . 5 9 . 2 4 2 6 . 6 2 5 . 0 10 2 4 2 6 . 0 2 2 . 2 11 2 4 0 . 0 1 5 . 1 12 2 4 2 1 . 2 2 7 . 7 13 2 4 o . o 4 . 6 U . 1 1 2 . 2 1 2 5 0 . 0 7 . 9 2 2 5 5 8 . 7 5 4 . 5 3 2 5 29.7 2 4 . 0 4 2 5 3 0 . 3 3 2 . 2 5 2 0 . 0 1 3 . 2 6 2 9 4 1 . 2 4 0 . 4 7 2 5 2 8 . 5 2 4 . 3 S Z 5 27. ft 2 B . 0 9 2 5 1 7 . 6 2 2 . 3 10 2 5 1 0 . 5 1 0 . 6 11 2 5 1 0 . B 1 1 . 1 1? I 9 3 1 . 6 2 4 . 6 0 Z 6 7 6 . 4 6 1 . 7 1 I 6 1 8 . 8 1 6 . 1 2 I 6 1 2 . 0 1 0 . 9 B I 6 0 . 0 3 . 4 4 1 6 3 0 . 8 3 0 . 8 5 1 b 2 2 . 2 1 5 . 4 ft 1 6 3 0 . 4 2 9 . 9 I 6 O.O 2 . 7 I 6 0 . 0 6 . 1 9 ! 6 0 . 0 i I 19.4 u.i 1 l T 1 0 . 4 1 7 . 6 t ( T 3 7 . f t I B . 6 1 0 1 1 . 1 1 8 . 9 t » 0 1 9 . 1 1 8 . 6 2 I 0 1 4 . 7 2 7 . 8 B 1 0 6 . 0 7 . 2 4 3 0 9 6 . 7 3 9 . 2 9 1 0 1 5 . 9 1 7 . 8 6 1 0 0 . 0 9 . 3 T k 0 1 8 . 5 4 . 7 ft 1 0 0 . 0 7 . 8 9 1 6 U . 9 V.S 10 0 2 2 . 0 1 5 . 3 11 1 0 0 . 0 7 . 5 12 I 0 1 0 . 0 7 . 6 1 1 1 9 . 8 1 6 . 0 2 1 3 6 . 7 3 8 . 7 3 1 3 4 . 8 3 1 . 1 4 i L 2 9 . 8 3 7 . 1 1 i 1 0 . 0 1 0 . 1 6 1 3 5 . 2 3 2 . 3 7 1 2 4 . 1 2 5 . 5 ft 1 3 9 . 5 3 3 . 0 9 t 1 1 0 . 1 1 0 . 9 10 1 0 . 0 5 . 0 11 i 1 1 3 . 6 1 5 . 6 12 t 2 6 . 7 2 5 . 4 13 I 0 . 0 1 1 . 5 14 I 1 1 9 . t 1 3 . 8 IS 1 l 0 . 0 1 3 . 4 16 1 1 6 . 5 1 7 . 3 2 4 . 2 3 7 . 6 1 i 2 2 4 . 6 2 5 . 9 2 i 2 8 . 9 1 4 . 7 1 2 8 . 6 3 0 . 4 4 i 2 1 B . B 1 5 . 2 5 2 2 4 . 7 2 6 . 8 6 4 7 . 7 4 3 . 6 7 2 1 3 . 7 1 6 . 0 ft 2 8 . 4 1 2 . 1 9 2 0 . 0 1 2 . 3 10 i z * 2 . 3 2 6 . 3 1 3 3 1 7 . 9 2 7 . 1 2 ' 3 3 1 . 5 3 5 . 1 3 1 3 2 9 . 8 2 3 . 0 4 3 3 1 9 . 7 l e . o 0 . 0 e . i 6 1 9 L B . 2 1 7 . 9 • 7 I 3 2 1 . 0 1 7 . 2 s 1 3 2 5 . 4 2 4 . B 9 3 9 9 . 4 1 5 . 1 10 * 3 2 3 . 3 1 2 . 9 0 . 0 9 . 4 12 1 3 2 7 . C 2 7 . 3 13 1 3 O.U 1 3 . 4 14 i 3 1 1 . 4 7 . 9 I 4 2 3 . 7 2 3 . 4 1 3 4 1 0 . 6 1 1 . 0 0 . 0 1 0 . 5 1 4 0 . 0 1 3 . 8 4 1 4 1 3 . 0 2 1 . 7 5 1 4 1 2 . 3 1 0 . 9 6 1 4 > 0 . 9 2 0 . 5 7 I 4 0 . 0 1 2 . 7 0 . 0 2 1 . 4 9 1 4 0 . 0 6 . 0 to 3 4 2 6 . 7 2 7 . 8 11 3 4 1 5 . 2 1 5 . 1 I 1 s 9 . 0 1 5 . 8 1 3 5 2 6 . 4 3 1 . 4 1 4 . 3 1 2 . 5 4 1 5 1 3 . 3 1 1 . 5 5 I 5 0 . 0 5 . 9 6 i 5 0 . 0 1 3 . 5 7 1 4 . 3 1 8 . 0 9 2 0 . 8 2 4 . 1 2 6 . 5 2 2 . 2 1 1 6 1 5 . 6 1 1 . 5 3 6 0 . 0 5 . 8 9 1 6 1 4 . 4 1 0 . 4 4 1 6 2 5 . 3 2 7 . 1 5 6 0 . 0 1 5 . 9 0 . 0 1 0 . 4 T 3 6 0 . 0 1 4 . 7 8 3 6 1 5 . 7 2 3 . 6 1 3 7 0 . 0 5 . 1 2 1 T 2 2 . 0 2 0 . 0 1 3 7 1 3 . 1 8 . 9 0 1 8 1 6 . 5 1 8 . 2 Table IX. 54 4-Biphenylylferrocene measured and structure factors. calculated •14 0 ) 19.3 11.0 -10 0 T 4.4 1.2 0 1 0.0 11 0 14 .9 11 . 1 0 1 1.7 a.4 - I t 0 O.o 1.1 a 1 0.0 2 .3 12 0 10.0 19.9 0 1 0.0 1.4 -11 0 0.0 4.6 h k 1 Fc :|j 0 0 0 0 1 IS.l 1 0.0 1 0.0 1 6.1 4 10. 1 11.» 1.4 4 .1 . 24.4 11 0 -11 0 14 0 -14 0 0 0 1 1.9 1.0 0.0 a.6 13.4 1 .1 6.1 1.4 6.1 21.0 0 0 u.l 17.4 a 4 16.9 19.9 ' 1 0 0.0 0 .1 0 0 19.0 4.T a * 61 . 1 49 .0 -1 0 10.1 6.7 0 0 111.? 111.4 0 * 9.7 2 0 6.7 9.1 0 0 11*.i U l . l 0 4 16.9 19.4 - 1 0 19.6 20 . 1 0 0 61. 9 64.0 0 4 80.1 73.3 1 0 19 .1 1B.4 0 0 II. T 19. T 0 4 11.9 19 . 1 - 1 0 13 . 1 16 .0 0 0 16.6 ) ) . 9 0 * 36.4 57 . 1 4 0 16.7 U . 3 0 0 48.7 46. 1 29 . 1 0 4 41 .8 90.4 - 4 0 11.1 10. 1 0 0 16. 1 4 i t . r 24. 1 1 0 r.4 9 .2 ill 0 0 l i . 1 4. 1 4 72.3 71.4 - 9 0 14 .0 i a . 4 0 0 24 . * 27.4 0 4 42 .2 40 .0 4 0 10 .0 11.5 0 26.9 IT.9 0 4 11.9 10.6 -4 0 10.0 11.9 0 0 I.T 12.» a 4 59.4 93. B 7 0 l a . s i a . 4 0 0 11.6 0 4 64. T 63 .2 - 7 0 9.1 10 .1 29.9 IT.3 * 90.4 46.4 a o 14.6 11.4 0 0 21.0 19.1 0 4 67 .0 61.1 - a o 11.4 11.4 0 0 9 . 1 0 4 12.9 14.7 9 0 4 .1 0 0 1 0 . \ ~ 1.4 ' 11.1 0 4 19.7 26 . 1 -4 0 10 .1 9.9 o U.l 0 * 21.2 i a . 0 10 0 4.4 11.1 0 21.6 21 . • 0 4 14 .1 14.9 •10 0 0 . 0 1.7 0 32 .9 19.1 0 4 19.7 i a . i 11 0 17.7 19 . 1 0 10.0 0 4 41 . 1 3S.0 -11 0 10 .8 11.4 0 1 1 . * 10.4 0 4 14 .4 10 . 1 11 0 2 .1 1.2 0 46.0 49.9 4 18.4 13. B -11 0 7 .6 3.1 0 2) .2 11.9 0 4 18 .9 17.4 -11 0 11.4 10 .0 0 l o . a 10.4 0 II. 1 0 0 0.0 l.T 0 29. 1 29.4 0 4 14.7 11.7 I 0 1 .6 0.6 0 4.7 9.4 0 4 11.7 14.6 - i a 1.7 4 .1 c 14.4 19.9 0 4 14 .1 14.4 J 0 0.0 0.1 0 0.0 1.6 0 4 9 .0 6.6 -1 0 9 .2 9.9 a 22.6 11.9 0 4 4 . 0 4.4 1 0 0.0 0 .3 a 0.0 1.1 a 4 6.4 1.2 - 1 0 9.1 4.0 0 i . a It.9 0 4 4 .1 0.7 0.0 i . a 0 6 .4 0.0 0 4 4.T -4 0 1.0 1.4 -• D 11.0 11.6 0 9 4.2 1.6 9 0 9 _ 0.0 I.) 0 0.7 0 1 11.7 12.0 - 9 0 6.0 i . i D 14.2 19. 1 0 9 0.0 0 .1 6 0 4.6 4.1 0 0.0 1.1 a 9 11.7 14.1 -4 0 1.1 7.4 0 9. t 1.0 0 9 9 .2 1.7 7 0 1.1 1.6 0 0.0 6.9 0 9 19.« 1.1 - 7 0 4.3 1.1 0 7.9 10.9 0 3 1.0 1.4 a o 0.0 a . i 0 0.0 1.2 0 5 11 .6 12.4 - a o 1.0 1.4 0 14.3 12.1 0 9 14 .0 19.2 e . i 6.0 11.8 IT.9 0 9 1.9 9.7 -4 0 0 . 0 0.0 0 4.9 0 9 22.1 70.4 -10 0 0.0 1.6 0 • .6 11.1 0 1 14 .0 i a . 6 0 0 11.2 11.2 0 B.4 0 » »t* 50-> 1 0 10 . ) 11.6 0 11,6 0 1 0.0 11.0 - 1 0 0.0 e . i 0 17,7 14.7 0 9 19.9 10.1 1 0 11.0 a.4 0 0 9 0.0 1.4 - 1 0 11.9 10.0 0 9.7 0 9 1.7 1.2 1 0 0.1 0 17.1 16.6 0 9 6.9 9.9 -1 0 . 12^4 17 .2 0 S.l 9.6 0 9 9.4 4 0 7 .6 11.7 0 3 14.4 14 .9 -4 0 7.0 8 .6 0 1.4 0 » T.T 1.1 4 0 11.9 15.2 0 1 1 . 0 11.0 0 9 10.2 11 .0 -9 0 12.4 19.4 0 94 .9 100.4 0 9 1.9 0 .1 6 0 3 . 1 3.1 0 T6.1 T8.4 0 9 14.6 14.6 -4 0 4.0 9.9 0 102.2 101.9 9 10 . 1 9 T . l -I 0 110. T 116.4 i s 0 7.4 1 1 0 9.9 ll'.l 0 64.0 TO.9 0 9 9.4 1 . 1 0 9 . 2 9.4 0 94.0 94.7 0 3 6.8 a . i 0 9.6 7.9 0 21.3 22.7 0 9 0.0 0 .1 0 19.4 21.9 0 4.3 11.4 0 9 6.0 6.1 0 9. a 7.6 0 61.1 61.0 0 9 12.1 21.9 0 9 . 1 4.1 0 14.0 31.1 0 9 0.0 7.9 0 9.4 10.7 30.7 91.0 0 9 11.0 11.1 0 19.1 10.a a 37.3 9>.l 0 9 1.9 4.9 0 13.1 19.1 0 13.4 17.2 a 6 17.6 17.4 ' 0 21.0 17.1 0 16.6 16 . • a 6 14.9 41 . 1 0 11.7 19 . 1 0 42.9 41.7 a 6 14.9 14 .0 0 14.8 16.8 0 14.2 17 . 1 0 6 74.9 73.1 0 6.6 4 . 1 0 1.1 9.B 0 6 61 . 1 61 .0 0 4.3 11 .0 0 11.4 12.1 0 6 11.1 20.4 0 11.1 14 . 1 0 10.1 14. T 0 6 41 .0 91.2 0 6.2 10 .1 0 » - J _ 91 .0 0 6 44.1 47.2 0 4.6 ' 4 . 1 0 9.1 1.0 0 6 T.l 6.6 4 .1 0 It.4 ' 24.4 0 4 35.1 94.6 toa .6 U l . l 0 14.9 i e . i 0 4 19 . 1 24 .2 40 . 1 41.6 0 11.4 1.9 0 6 IB.4 i s . a 140.0 199.8 0 11.1 17 . 1 0 6 94 . 1 41 .0 104 .1 113.4 0 18.0 40.1 0 6 0.0 1.0 79.6 M .7 0 " 1 1 .0 " 21.4 a 6 41 .0 17.1 91.4 VT . l 0 9.6 0.9 0 6 19.7 29 . 1 14 .1 14.9 0 4.2 T . l 0 6 1.9 0 .6 69.9 79.0 0 21.1 (9.1 a « 14 . 1 16.6 « . 7 78.8 a 27.4 11.4 0 6 19 .9 14.0 u . i 12.8 a 10.7 T . l 0 4. 11.0 10.1 92 .a 39.4 o™ t~ J i . i 11.9 ' 0 6 10.1 14.4 99.a 60.1 a 7.1 6.4 0 4 0.0 14 . 1 40.0 41.1 0 1.6 0.1 0 • 19.8 10.7 96 . 1 94.7 0 11.9 11.4 0 6 6.2 7.1 9.4 9.0 0 10.1 11.4 0 4 0.0 1 .1 41.1 11.1 0 14 . t 14.1 0 4 19.2 14.4 14.9 l a . 4 0 l . l " 4.4 0 4 14.6 i i . a tl.O 14.1 a 4.0 4.4 0 t 9.4 4.6 47.4 48.4 0 14.0 14.1 a 6 1.2 1.4 »».(__ 0 1.1 10.1 0 • 4.1 1.4 19.a 24.0 0 7.3 4.1 0 6 I T . ! 16.4 11.9 23.1 0 _ J 0 - * _ 10.9 0 6 4.0 i . a a.o 3.9 0 11.7 id". > 0 7 4.9 1.0 4.1 10.9 0 12.7 10, 7 0 7 S . l 6.1 28.1 23.7 0 11.4 17 .9 0 7 0.0 0.1 10.0 14.2 0 1.1 9.1 0 T 10.1 14.9 14,1 24.6 0 11. 7 1.0 0 T 0.0 2.4 I T . l 26.7 0 14.1 14.4 0 7 . _ H L J L _ 24.8 19.1 0 14.1 11.7 0 7 0.0 4.1 14.1 16.4 0 14.4 22.1 0 7 11.1 14.1 11.1 11.8 0 14.4 14 .1 0 7 1.6 0.0 _. 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A 17.) 10.a 9.0 7.8 12.1 7.8 fr 1.6 10.4 21 0 I I . 1 4 4 7 0.0 a.9 10.4 16. 1 12.0 a. 1 0.0 6 2 .a 1 .1 11 f 4.9 - 4 4 7 3.0 9,1 fr.9 T . a 20.2 19.0 10.T T.T IB.6 6 1.1 4 .1 8 a a . i 3 4 7 0.0 4.1 T . l 12.6 17.2 i 6 . r IT . ) 7 24.1 24.9 9 4 9.4 -9 4 7 7.8 9,4 4.4 6 . 9 a.9 4.T 11.9 7 27.2 17 .9 2) 4 i o . a 6 4 7 4 . 7 10.) 10.9 9.7 14.7 16.8 6 .4 16.) 7 8.A a.e 6 4 6.6 -fr 4 T 8^1 i i . ) 9.9 0.0 A.4 2.4 1.4 7 4.4 9.4 1 4 4.9 7 4 T 0.0 9 ,a IT.A 24.1 1.7 3 .7 T.T 10.a 9.9 7 11.9 11.9 10 4 11.0 -7 4 7 4 . 6 8 .6 13.4 12.7 8 . 9 a.9 2.9 7 1 1 . a 11.6 7 9 12.6 a 4 T 2.9 a.6 6. T 3.6 a.9 A.T 3.5 1.9 4.7 7 19.1 19.3 11 - 8 4 7 4 . ) 6.7 0.0 3 . ) 19.8 19. 7 4 . 9 T 10 .a • 21.4 0 4 4 7 3.7 1.9 9.4 12.a 1 1 . a 1.4 2.1 T 26 . ) 16.1 0 0 t.T - 9 4 7 2 . 8 l . I . 6.8 10.1 9.9 T . 9 1.4 3.0 T T . 9 T . 8 2a 4 i». a 10 4 7 0.0 a.4 6.6 a . 7 11.4 11.6 4.0 B.B _ 3 i T 1 1 . a 14.1 . 1 * 1 14 fr 19.) -10 4 7 9.0 1.9 1 5 4 0.0 ) - i a fr 2 1.2 1.6 ) . ) BIBLIOGRAPHY 57 1. H. Lipson and W. Cochjran, "The Determination of Crystal Structures", G. Bell and Sons Ltd., 3rd edn. (1966). 2. M.J. Buerger, "Crystal Structure Analysis", Wiley, New York (1960). 3. "International Tables for X-ray Crystallography", Kynoch Press, Birmingham, Vol.11 (1959). 4. R.H; Vernon, J . Chem. Soc., 86 (1920). 5. H.D.K. Drew, J. Chem. Soc, 560 (1929). 6. C.E. Brion and F.W.B. Einstein, Private Communication. 7. R.J. Gillespie and R.S. Nyholm; Quart. Rev. £, 339 (1957); R.J. Gillespie, J . Chem. Soc., 4672 (1963). 8. R.H. Vernon, J . Chem. Soc, 105 (1921). 9. E.E. Galloni and J. Pugliese, Acta Cryst. _3> 3 1 9 (1950). 10. A. Zalkin, J.D.Forrester and D.H. Templeton, Inorg. Chem. 3_, 639 (1964) 11. "International Tables -for X-ray.Crystallography", Kynoch Press, Birmingham, Vol.Ill (1962). 12. M;Ci Day and J. Selbin, "Theoreticl Inorganic Chemistry", Reinhold Publishing Corporation, New York (1962). 13. G.D. Christofferson, R.A. Sparks and J.D., McCullough, Acta^ryst. 1J_, 782 (1958). 14. G.Y. Chao and J.D. McCullough, Acta Cryst. 1_5, 887 (1962) . 15. L. Pauling, "The Nature of the Chemical Bond", Cornell University Press, Ithaca, -3rd edn. (1960). 16. 0. Bastiansen, Acta Chem. Seand. 3_, 408 (1949). 17. J . Trotter, Acta Cryst. 14_, 1135 (1961); A. Hargreaves and S. Hasan Rizvi, Acta Cryst. 15_, 365 (1962); G.B. Robertson, Nature 191, 593 (1961); 192, 1026 (1961). 18. T.J. Kealy and P.L. Pauson, Nature 168, 1039 (1951). 19. J.D. Dunitz, L.E. Orgel and A. Rich, Acta Cryst. 9, 373 (1956). 20. E.A. Seibold and L.E. Sutton, J . Chem. Phys. 23, 1967 (1955) . 21. G. Wilkinson, P.L. Pauson and F.A. Cotton, J . Am. Chem. Soc. 76, 1970 (1954). 22. Von E. Weiss and E.O. Fischer, Z. Anorg. Chem. 278, 219 (1955). 58 23. G.L. Hardgrove and D.H. Templeton, Acta Cryst. 12_, 28 (1959). 24. Z. Jellineck, Z. Naturforsch. 14b, 737 (1959). 25. A.C. Macdonald and J. Trotter, Acta,Cryst. 1_7, 872 (1964). 26. J. Trotter and A.C. Macdonald, Acta Cryst. 21_, 359 (1966). 27. M.-B. Laing and K.N. Trueblood, Acta Cryst. 19_, 373 (1965). 28. M.D. Rausch, Inorg. Chem. 1_, 414 (1962). 29. P.R. Pinnock, C.A. Taylor and.H. Lipson, Acta Cryst. 9_, 173 (1956). 

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