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X-ray crystallographic studies of racemic and optically active 4, 4’-dimethyl-1, 1’-binaphthyl Pauptit, Richard A. 1978-03-03

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X-RAYCRySTALIOGRAPHIC STUDIES OF RACEMIC AND .OPTICALLY ACTIVE 4,4'-DIMETHYL-1,1•-BINAPHTMYL by RICHARD A- PAUPTIT E.Sc, University of Cape Town, 1975 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN THE FACULTY OF GRADUATE STUDIES in the department of CHEMISTRY He accept this thesis as conforming to the required standard z The University of British Columbia November 1978 © Richard A. Pauptit, 1978 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of British Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date ii ABSTBACT In contrast to 1, 1 '-binaphthyl, racemic 4,4*-diraethyl-1,1'^binaphthyl does not undergo spontaneous resolution upon heating from room temperature to just below the melting point. Optically active dimethyl binaphthyl may be obtained by seeding the racemic melt site optically active naphthidine. The crystal structures of both the racemic and optically active dimethyl binaphthyls were solved in the hope of understanding the ahove observations. fhe racemate crystallizes in the monoclinic space group C2/c with cell parameters a=13-225, b=1Q.768, c= 1-1.572 A and 114.04 0. There are four molecules per uait-cell; two have the B and two have the S configuration. The structure was solved using direct methods and refined to a=0.074. There is a 3° head in the plane of the naphthalene residues, which are cis-oriented with an angle of 68° between them. The optically active form belongs to one of the tetragonal space groups P4t2\ 2 or P4j2i2 with cell parameters a = b = 8.3031 and c = 23.706 X. Direct methods sere used to solve the structure and the final fi was 0.060. There are four molecules per unit-cell of identical configuration, hut it could not be determined whether this was R or S. The naphthalene residues show a 2-70 bend aad are also cis-oriente-d,hut" Kith an angle of 80» between them. Bond lengths and angles are consistent »ith values iii previously reported for 1,1 "-hinaphthyl and naphthalene- The racemate packs somewhat more efficiently and perhaps for this reason it is slightly more stable thaa the optically active form- It is difficult however to explain the difference in behaviour between the methylated and unmethylated binaphthyls on the basis of these results alone. Further studies would include the crystal structures of optically active 1,1*-binaphthyl and various naphthidines. XV TABLE OF CONTENTS Title Page ......................................... i Abstract ........................... ....r-.»---,-..--- ii Table of Contents .................................. iv List of Tables . ..... .................... vi List of Figures .................................... vii Acknowledgements ...................................viii PART ONE: INTRODUCTION ......... 1. . Preparation of Crystals ............................... 3 PART TWO: CRYSTAL STRUCTURE OF RACEMIC 4, 4 '-DIMETHYL- 1, 1 * -BINAPHTHYL ..... 7 Experimental. ................................ ......... 8 Structure Analysis. ................................... 9 Results and Discussion. .............................. - 11 PAST THREE: CRYSTAL STRUCTURE OF OPTICALLY ACTIVE 4,4»-DIMETHYL-1 ,1»-BINA?HTHYL .......................... ... 19 Experimental ......................«................... 20 Structure Analysis .................................... 20 Results and Discussion ........................... . 23 PART FOUR: CONCLUSION 31 Bond Length and Angle Comparison ...................... 32 Intramolecular Differences 3Cell Parameter Comparison ............................. 32 Packing Comparison ...................... 35 Summary ............................................... 39 V REFERENCES ............. 4 0 APPENDIX Ii Structure Factors for the Racemate ........... 42 APPENDIX II: Structure Factors for the Optically Active Form 51 vi LIST OF TABLES. PART TWO; CRYSTAL STRUCTURE OF RACEMIC 4,4«-DIMETHYL-1,1 BINAPHTHYL ...... .. .... 7 TABLE I : Crystal Data ................................ 8 TABLE II s E Statistics 10 TABLE III : Fractional Atomic Parameters .............. 12 TABLE IV : Thermal Parameters ......................... 13 TABLE V : Mean Planes .................................. 15 TABLE VI : Bond Lengths 17 TABLE VII : Bond Angles ................................ 18 PART THREE; CRYSTAL STRUCTURE OF OPTICALLY ACTIVE 4,4'-DIMETHYL-1,1'-BINAPHTHYL .............................. 19 : Crystal Data ............................. 20 £ S1311stics 21 ?ractio,nal Atomic Parameters .,.«,.,...-.,.,-- 24 TABLE XI : Thermal Parameters ......................... 25 Sean Planes ............................... 26 C X O S € COXl fc CI C t S » » « m •» m m m »•*•<» * «» « o • •* «• 2 "7 Bond Lengths .............................. 28 PART FOUR: CONCLUSION .. ......... ....,.,-..---.--.31 TABLE XVI : Average Bond Length Comparison 34 TABLE VIII TABLE IX : TABLE X : E XI : TABLE XII TABLE XIII TABLE XIV TABLE XV : vii LIST OF FIGURES Figure 1. Enantiomeric Conversion of 1,1 '-Binaphthyl ..... 2 Figure 2. Phase Diagram for 1,1*-Binaphthyl . 4 Figure 3. Preparation of Sacemic 4r4»-Dimethyl-1,1*-cinaphthyl ............................................ 5 Figure 4. Molecular Drawing of Sacemic 4,4*—Dimethyl-1,1 Figure 5. flolecular Drawing of Optically Active 4,4J-Dimethyl-1,l«-hinaphthyl ..,..,.,...,...,.„,.,..,..,..- 30 Figure 6. Bond Length Comparison. ........................ 33 Figure 7. Packing Diagram for the Baceoate. ................. ,36 Figure 8. * Wedge Nesting* in the Bacemate Unit Cell ...... 37 Figure 9- Packing Diagram for the Optically Active Form -. 38 viii ACKNOWLEDGEMENTS I am very grateful to Prof. James Trotter for his valuable assistance and advice during the last two: years, and also Dr. Steve Hettig and the post doctoral fellows in our group for their advice and help with the experimental work-I would like to thank Dr. Hichard Pincock for supplying the crystals and background material. Finally I sould like to thank Prof. C.A.McDowell for interesting me in the University of British Columbia. 1 PART ONE INTRODUCTION 2 This thesis describes the X-ray crystal structure analyses of racemic and optically active k,4'-dimethyl-1,1'-binaphthyl. The background theory involved in x-ray technigues is covered in several standard texts,*-—s and all nomenclature, conventions and crystallographic symbols used are consistent vith those described in International Tables for X-ray Crystallography-6 There has been considerable interest in binaphthyls in relation to the spontaneous resolution of racemic mixtures into optically pure samples.0 1,1'-Binaphthyl is converted into its enantiomer by a simple rotation about the 1,1* bond (see Fig. 1 ), Two crystalline forms of 1,1 *-binaphthyl are known; " R-1,1*-Binaphthyl S-1,1f-Binaphthyl Figure 1. Enantiomeric Conversion of 1,1'-Binaphthyl the low melting form (m-p.= 145°C) has heen shown by X-ray structure analysis42 to be the racemate with two B and two S molecules per unit-cell, and the high melting form (m.p. 158°C) to be the optically active form (i.e. only molecules of one enantiomer per unit-cell). 3 It has been found that in a certain temperature range, the optically active form is the more stable thermodynamically and so upon heating a racemic sample into this temperature range spontaneous resolution could occur-' The phase diagram corresponding to this is shown in Fig- 2 where the dotted line shows the behaviour cf the racemate upon heating- It »as found that one could control the choice of enantiomer to «hich the racemate would resolve by picking an original composition eguivalent to a point (e.g. P) just to the right (or left) of the vertical dotted line and heating it- At all times the mixture would consist of the racemate plus S (or B) impurity, and crystals of the R for S) form would not nucleate. These observations of the behaviour of 1,1'-binaphthyl were not noticed in 4,4*-dimethyl-1,1'.binaphthyl:13 in the dimethyl compound the racemic form seems to be at all times the more stable, and no optical activity develops upon heating (experimentally the a-form of the dimethyl compound has been obtained by seeding the as-melt with B-naphthidine.). It is hoped that this might be better understood by comparing crystal structures of the racemic and optically active forms. Preparation of Crystals (B.E-Pincock) The preparation of the racemate** is illustrated in Fig. 3., 4-Bromo-1-methylnaphthalene (3) was prepared from 1-methylnaphthalene Q) by the sulfonation - bromodesulfonation procedure (developed by Fieser15) via (2) in 35% yield. Bacemic 4,4»-dimethyl-1,1*-binaphthyl (4) was formed (26 - 41$ yield) 158 145 Cb 1 LU I-0 RS 50 %-S-enantiom<2r R + S r i I i i RS+R RS+S P • 100 Figure 2- Phase Diagram for 1,1 *-Binaphthyl 5 6 by the coupling of the Grignard reagent derived from (3), and was crystallized from acetone to give colorless rods. Optically active 4, 4f-dimethyl-1,1 •-.bin apathy! was prepared1* by the induced resolution of the racemic compound using optically active naphthidiae as a seed. Best results sere obtained by weighing out 50mg samples of racemate containing 1% naphthidiae into ampules which were sealed in air. These samples were held in a bath at 150°C for 4 minutes allowing the dimethyl binaphthyl to melt while the naphthidine (m.p. 206 -207°C) remained solid and would seed the subsequent crystallization. Normally crystals formed overnight. 7 PART TWO; CRYSTAL STRUCTURE OP RACEMIC 4.4'—DIBETHYL—1,1'-BINAPHTHYL 8 Experimental-Preliminary x—ray photography shows the well-rformed colorless crystals to be monoclinic ; systematic absences { for general hkl, h+k=2n+1 ; for the hOl zone, l=2n+1 ) indicate that the space group is either C2/c or Cc- Unit-cell and intensity data were measured on a Datex-automated GE XfiD 6 diffractometer with Cu Kx radiation utilizing the €-29 scan technique. Unit-cell parameters were refined by least-sguares methods from manually obtained 2% values of thirty reflections, and the final parameters are listed in Table I .The data were TABLE I Crystal Data C?2 Hl8 f-w. ,= 282.4 amu Monoclinic Z = 4 Space Group = C2/c a = 13.225 (8) 1 b = 10.768(4) A F(000) = 600 c = 11.572(7) A 1-5418 A 13 = 114.04(2) o Dc = 1.246(1) g/cc V = 1505(1) A3 collected at a 20 scan rate of 4 0min_* over a range of (1.80+0.86tan€)o with 10 second background counts at each end of the scan- The 14 strongest reflections were remeasured with aja attenuation of 28.5 . The 7 1 3 reflection was used as a standard and checked every 50 reflections. There were several large deviations in the scan counts of the standard reflection due to electronic difficulties with the diffractometer. The structure was solved with this set of data, but a new set was collected for refinement. In the second set the standard varied more smoothly and was used to scale the data. 611 of the 1497 9 unigue reflections in the 00<28<120° range had intensities less than 3-0q-(I) , where <r2 (I) =S*B* (0. 06S) 2, S is the scan count and B is the background count. Lorentz and polarization corrections were applied to give the structure amplitudes. No absorption correction was applied. Structure Analysis. A lilson plot was used to determine overall temperature IB=3.59 ft2) and scale factors. £ statistics (see Table II ) indicate a centrosymmetric space group (i.e. C2/c) and 204 E*s > 1.4 were obtained. 334 ^^-relationships were found from the largest 50 E*s and used to select origin and symbol reflections. For the space group C2/c two origin determining phases are needed of suggested parities uug and ggu6 (centered cell indices). The largest two E*s (9 5 2 and 2 6 7) sere chosen and three independent symbols selected providing 8 (=23) starting sets to be used in a symbolic addition and tangent refinement procedure. An E-map was calculated from the best set of phased E's (that with the lowest R-Karle of 0.21) and all 11 carbons in the asymmetric unit could be located. 3 isotropic and 2 anisotropic least-sguares refinement cycles were carried out before an electron-density difference map showed all but one (a methyl H) of the hydrogens. The methyl hydrogen positions were calculated geometrically, and three more least-sguares refinement cycles (all reflections unit weight, 11 C's anisotropic, 9 H's isotropic) lowered the R value to 0.089 . TABLE II E Statistics OBSERVED Mean | E] Mean 1E|Z Mean |E2- 1| 0.6732 1.0489 1.2486 SI Reflections with : E > 3.0 1.74 E > 2.0 5.81 I > 1-0 25.25 Centro. 0. 7980 1. 0000 0.9680 THEORETICAL Kon-centro. 0.8860 1.0000 0. 7360 0.30 5.00 32.00 0.01 1-80 37.00 ************************* 11 Another four refinement cycles with polynomial weighting schemes*6 (w= V{A+BjFoJ+C|Foj2+D|Fo|, where A,B,C and D are recalculated after each cycle, final values being -0-01153, 0-08308, -0.01806 and 0-001396 respectively) reduced B to 0-078 and Rw to 0-0 74 - The anisotropic thermal parameters used in the refinement are the Bij in f=fo exp {-{Bw h2*B2ik2+B^12+2Brihk + 2B»-ihl*2Ba^fcl)) , where f0 is the tabulated structure factor and f is that corrected for thermal motion. The isotropic thermal parameters are the B»s in f=f0exp (-Bsin2e/<\2) . Final parameters and temperature factors are shown in Tables III and IV , and a comparison of observed and calculated structure factors appears in Appendix I. Results and Discussion. The numbering scheme (see Fig. 4) is that generally used for naphthalene and hydrogens are given the same number as the carbon to which they are attached (H(111), H(112) and H1113) being the methyl hydrogens)- The asymmetric unit is only one half of the dimethyl-binaphthyl molecule; the other half is generated by rotation about a two-fold axis. Equations of and deviations from various planes through the asymmetric unit are shown in Table V - There is a slight bend in the unit, the rings lying at an angle of three degrees to each other. For a similar distortion in 1, 1»-binaphthyl the close contacts between the two halves (e. g. C (8) . ,_C (8*)) have been suggested*2 as possible reasons- The dimethyl-binaphthyl shows close contacts at C (2) .. . C (2') 43. 11.6 (5) &) and C(9)...C(9*) (3.343(4)5) but the C (8) ...C (8') distance is TABLE III Fractional Atomic Parameters (Csl04.HxlQ3) 8ith Their Standard Deviations f | Atom .,_T  J x/a 1 i y/b -f .. i 1 i j T 1 1 C{3) J 4386(2) 1 2978 (2) 1 2296(2) | C(2) | 3898 (2) 1 2039 (2) } 2686(2) i C{3) | 2745(2) 1 1996 (2) 1 2343(2) i cm | 20 56 (2) i 2886 (2) J 1586(2) 1 C (5) i 1834(2) 4747 (2) i 229(2) J C(6) ) 2277(2) ! 5637 (3) 1- 269(2) I C(7) | 3428(2) 568S (3) 1 83(2) i c{8) J 4112(2) ! 4838(2) i 921(2) 1 C|9) J 3681(2) 3892 (2) \ 1492(2) j C(10) | 2513(2) ! 3844 (2) 1 1087(2) I C(11) | 833(2) j 2843 (3) | 1278(3) 1 H (2) J 434(2) ! 136(2) | 322(3) 1 H (3) 1 243(2) ! 133(3) I 270(3) 3 H(5) i 98(3) 1 470(3) I- 43(3) I H(6) I 176(2) ! 626 (3) |- 88(3) J H(7) i 375(3) i 632(3) |- 26(3) 1 H(8) i 494(3) ! 492(2) 1 114(3) 1 H{111) 1 37 (3) ! 266 (3) 1 34(3) 1 H(112) | 52(2) I 367(3) ] 144(3) I H(113) 1 6313) ! 223 (3) 1 178(4) _ -. i _ ._.— j— _ _ j ******************** (6)0* L (Ett) e (Ll t *9 (2U)H (8H "9 (Ul)H (9)8T (8 J H <8>9"9 (£)H (9*6*E f9)H (L) 0-9 (9>h (9>t7"t7 (r)H (5) I "£ (2>H ******************** g mo}? ******************** ******************************************************* (r)9 (2)tr2 (2)61- CE) 16 (£)911 (2) 19 (U>3 (2) oi- (t)ftt (1)6 - C2) E9 (2) 09 (2) ftft (0E) D (2k - (6) El CUs - (2) 99 f2)L9 it) 2t? (6)D (3)9 (2)61 (2)£ - (2) LL (2) £L (2) £tr (8) D (3) 61 (2)92 (2*8 - (2) E8 (2) trX (2) E9 (£)D (27 El (2) El (2)9 (2) 8£ (2) 0£. (2) 69 (9) D (2U - (1)6 (2)2 - (2) 99 (2)9t (2) 2ft (9)D (2 J 6 - (t)9t (t)9t- (2) 69 (2) 08 (2) ftii (ft?3 (2)9 (2) L2 (2)E2- f2) 69 f2) EX (2)E9 (E)D (2)8 (2) ft (2)9 - (2) tr9 (2) fe9 (2) 69 (2) D (2)9 - U) ll (1)2 - (2) LS (2) 09 (2) Etr (1)3 ******************************************************* £Tg ttg t\g tCg XXg ng mo}? ******************************************************* AT 3Tl?I 14 Figure 4. flolecular Drawing of Racemic 4#4»-DiiBethyl-1,1 fcinapbthyl. TABLE V Mean Planes Equations of Planes: Plane 1 1 2 3 0.2380 0-2311 0- 2250 (lX»mY»nZ=p> m -0-5615 -0-6050 -0.5866 n -0.7925 -0.7619 -0.7780 -2-5779 -2-7314 -2.6741 Deviations from Planes: Atom Plane J. Plane Z. Plane 3. cn) -0. 023 (2) * 0.035 (2) -0.034 (2) * C(2) 0.021 (2) * 0.141 (2) 0.052 (2) * C(3) 0.010 (3) * 0. 131 (3) 0.055(3) * C<4) -0. 026(2) * 0.033(2) -0.009 (2) * C(5) 0.06 8(3) -0.007 (3) * 0.009 (3) * C(6) 0. 143 (3) 0.004(3) * 0.041(3) * C(7) 0. 141 (3) 0.002(3)* 0.026(3) * C(8) 0.073(3) -0.003(3) * -0-013 (3) * C(9) 0.008 (2) * -0.007(2)* -0.034 (2) * C(1Q) 0.013(2) * 0.004(2) * -0.015(2) * C(11) -0.093 (3) -0.032(3) -0.061 (3) * H(2) 0.06 (3) 0.22 (3) 0.11 (3) H(3) -0-02 (3) 0. 14(3) 0.05(3) H(5) 0-09(3) 0-01 (3) 0.04(3) H(6) 0. 18(3) 0.00(3) 0.06(3) H<7) 0- 19(3) 0.00(3) 0.04(3) H{8) 0.07 (3) -0.01 (3) -0.02(3) *Atoms included in mean plane calculations. Angles Between Normals to the Planes; (degrees) Planes (1) and (2) 3.1 Planes (1) and (3) 1.8 Planes (2) and (3) 1.4 *********************** 16 slightly too large (3-447(5)1) to be used for such an argument. However the close approaches at C(2) and C(9) might still be the reason for distortion. There are no intermolecular steric repulsions of importance. The two methyl-naphthalene residues are cis-oriented with an angle of 68.4(2)° between them. This is in agreement with the reported valueof 68° for 1,1'-binaphthyl (which also crystallizes in space group C2/c) . Bond lengths and bond angles are listed in Tables VI and VII, with standard deviations calculated from errors in positional parameters. They are not significantly different from those in 1,1 a-binaphthyl or naphthalene. The C(1)-C(1») bond connecting the two asymmetric units has a length of 1.495(4)a and is bisected by the two-fold axis. TABLE VI Bond Lengths J&l Carbon-Carbon Bonds cm -C(2) 1.371 (3 C (1) -C{9) 1. 433 (3 C(1) -co *) 1.495(4 C (2) -C(3) 1.411(3 C (3) -c (4) 1.367(3 C (4} -C(10) 1.432 (3 C(4) -C(31) 1.509(3 C 15) -C (6) 1.367 (4 C(5) -C(10) 1.4181(3 C (6) -C(7) 1.408 (4 C(7) -C(8) 1.369 (4 C (8) -C(9) 1.4 22 (3 C (9) -C(10) 3-426(3 Carbon-Hydrogen Bonds C (2) -H(2) 0. 98(3) C(3)- a (3) 1. 00(3) C(5|- H(5) 1. 05(3) C(6)- H(6) 1. 02(3) C (7) - H(7) 0. 97(3) C (8) " H(8) 1. 02(3) C (11) -H(l 11) 1. 02 (3) C (11) -H(112) 1- 03(3) C{11) -H(113) 0. 95(4) ********* MM-M vxi Bond Angles j°) Involving Carlsons Only Involving Hydrogens C (9) -C(1)- C(2) 118. 0(2) C(l)-C(2)-H(2) 321 41 C {1 •« )-c (1| -C(2) 119. 5(2) C (3)-C (2)-H{2) 11741 C (1 • )-C(1) -C(9) 122. <H2) C(2)-C(3)-H(3) 319 42 C(1) -C(2)- C(3) 122. 1(2) C(4)-C(3)-H(3) 119 (2 C{2) -C(3)- C(4) 121. 3(2) C (10)-C (5)-H (5) 118 42 C(6)-C|5i-H45) 120 (2 C(3) -C(4)- C(11) 120. 0(2) C |3) -C (4)- C(10) 118. 9(2) C (5)-C(6)-H(6) 118 (2 C (10)-C (4) -C 411) 121. 0(2) C (7)-C(6)-H(6) 122 (2 C(10)-C(5) -C (6) 121. 2(2) C(6)-C(7)-H(7). 119 (2 C (8)-C(7)-H(7) 121 (2 C{5) -C (6)- C(7) 120- 1 (2) C47)-C|8)-H(8) 117(2 C (6) -C(7)- C(8) 120. 4 (2) C (9)-C48)-H(8) 122 (2 CO) -C(8)- C(9) 321. H2) C44)-C (11)-H (111) 112 (2 C(4)-C(11)-B (112) 113 42 C(8) ~C(9)- C(10) 118. 3 <2) C (4)-C|11)-H (113) 110 (2 C<8) -C{9)- C{1) 121. 5(2) H(133)-C(11)-H(112) 105 (3 C(1) -C(9)- 120. 1(2) H f 3 11).-C (11)-H (113) 110 (3 H (112-C (11)-H(113) 107 (3 C (9) -C (10) -c m 119. 5 42) C(9) -C (10) -C (5) 118. 9(2) C(4) -C(10) -C (5) 121. 7*2) *************************** 19 PART THREE; THE CRYSTAL STRUCTPRE OF OPTICALLY ACTIVE 4 ,4* —DIMETHYL-1.1 *-BINAPHTHYL 20 Experimental. From x-ray photography the crystal was found to be tetragonal and of one of the enantiomeric space groups B1\2\2 or P4j2i 2 (systematic abscesses: 001 for l#4n, hOO for h#2n). Unit-cell parameters were refined by least-sguares methods from the observed 2B values of 2 8 planes (see Taisle VIII for final cell parameters). TABLE VIII Crystal Data C*^Hi6 f. w. = 282.4 amu Tetragonal Z =4 Space Group = ?4(.2\2 or P4s2i2 a = b = 8,3031 (8) A c = 23. 706 47) A F(000) = 600 Dc = 1. 1478(4) g/cc \ = 1.5418 A V = 1634.3 (5) A3 Intensity data were collected as before for 0-°<29<160.°# the crystal mounted with (0,2,3) perpendicular to the goniostat axis and using 4 2 2 as the check reflection. The check reflection scan count showed only slight random variations and no data scaling was used. 395 out of 1117 unique reflections had intensities less than 3.0 cr (I) » and structure amplitudes were calculated as before. Structure Analysis. A Wilson plot yielded an overall temperature factor of 6.11 A2 and an overall scale factor. E statistics (which are not conclusive fcr either a centrosymmetric or a non-centrosymmetric structure) are shown in Table IX and 17 2 E*s are greater than 1.4 . From the largest 50 E*s 559 21 .TABLE IX E Statistics Mean |Ej Mean JEJ* Mean |E2-1J OBSERVED 0.8193 0.9873 0.9031 THEORETICAL Centro. 0.7980 1.0000 0.9680 Npn-centro. 0.8860 1.0000 0.7360 SI Reflections aith : E > 3.0 0.18 E > 2.0 3.38 E > 1-0 31-58 0.30 5.00 32-00 0.01 1-80 37.00 t********* *************** 22 relations were obtained and used to aid in origin and symbol choice. The spacegroups P4(2(2 and P432\2 belong to type 2P22 for which suggested origins6 are 0(OOu)=O or TT and $ (hkO)=0 or (h+.k=odd) or other sets of indices for which the structure factor amplitude expressions result in a choice of two phases differing by ft. The (OOu) reflections are systematically absent in these space groups and could not be used. The 6 7 0 reflection was assigned phase 0 (the amplitude expressions simplify to B=0, i.e. only phases 0 and Tf allowed), the 5 5 10 reflection (a structure invariant hence not origin determining, but must have phase 0 or tt ) was assigned phase 0, and the 3 3 17 reflection (for which amplitude expressions result in A=G and hence only ± TT/2 are allowed) was given phase +fV2-With two symbols, expressions may be derived for the phases of the 50 largest E*s, so only two symbols, (0 7 7) and {2 4 15), with eight starting values each, were used to give 64 starting sets in a symbolic addition and tangent refinement procedure. The best starting set (3rT/2,3YT/2) refined to an R— Karle of 0.17 1 and determined 169 out of the 172 phases. Using these 169 phased E's an E-map was calculated in which all 11 carbons in the asymmetric unit could be located. After 3 isotropic and 3 anisotropic least-sguares refinement cycles, when the R value had dropped to 0.12, a difference map was calculated to locate one methyl hydrogen enabling all other hydrogen positions to be determined geometrically. 3 more least-sguares cycles including the hydrogens reduced R to 0.063. A weighting scheme where w= 1/ {1+J. {| FoJ-F*) /G* j2j was 23 introduced (first with F*=5 and G*=20 and then a further cycle with F*=6 and G*=15) and lowered fi to its final value of 0,060. Structure factor tables appear in Appendix II, and final atomic parameters and temperature factors are listed in Tables X and XI -Determination of the absolute configuration was attempted using anomalous dispersion technigues, but differences in B values between the two enantiomers were insignificantly small (perhaps understandably so as we are dealing with a hydrocarbon) yet all differences lean in the same direction; the slightly smaller residual factors suggest P4| 2<2 (in which the structure was solved). Results and Discussion. Table XII shows the results of mean plane calculations. The molecule exhibits the same bending found in the racemic compound, the angle between the rings now being 2.7°. The two methyl-naphthalene residues are linked by bond C(1)-C(1*) of length 1.510 (8)& and the angle between them is now 80.6(3)°-T'he slightly lesser bending might agree with the slightly greater dihedral angle than in the racemic dimethyl—binaphthyl, but it is hard to see why this bending should be three times that in binaphthyl. Comparing close contacts for the two structures under study and binaphthyl12 (see Table XIII ), we see no obvious trend. It would seem that the C(8)...C(8«) close approach should play a greater role in this bending than the other close approaches, but this is not evident from the results. More TABLE X Fractional Atomic Parameters (CxlO».Hxl03) With Their Standard Deyiations * • — '• -] Atom - i— -I x/a 1 y/b ~ 1— 1 z/c i I H I C(1) 1 951(5) J 271 (5) ( 2401(2) i C{2) ) 2489(6) J 276(7) J 2618(2) I C(3) | 3641 (6) | 1444 (9) i 2431(2) 1 C(4) | 3269(6) 1 2563(7) } 2035(2) 1 C(5) i 1250(8) i 3696(7) 1 1371(2) 1 C(6) j- 243(8) I 3636(9) 1 1130(3) 1 C(7) 1-1377(7) | 2577(8) 1 1325(2) 1 C{8) 1-1014 (6) 1 1493 (6) I 1742(2) ] C(9) J 525(5) J 1450 (6) I 1988(2) 1 C(10) j 1690 (5) | 2604(6) 1 1795(2) i C(11) I 454 (1) 1 374(1} | 1836(4) I H<2) I 271(5) J- 57(5) I 291(2) 1 H<3) i 485(6) 3 118(5) J 262(2) J B(5) I 206 (7) 1 434(7) I 121 (2) i H(6) J- 42 (7) I 435(7) } 81(2) i H(7) 1-254(8) I 259(7) I 121 (2) 1 H(8) 1-177(7) i 86(6) 1 185 J2) J H (111) I 482(8) J 339(8) | 139(3) 1 H(112) 1 562(8) | 341(8) j 201(3) j H(113) I 408(9) | 470(7) | 192(3) i_ j .. .... - JL_ _ a - . j TABLE XI Anisotropic Thermal Parameters Of The Carbon Atoms Jith Their Standard Deviations fx 10 4) ******************************************** Atom Bt i B2.2. B33 Bvi Biz Br* ******************************************************* C(l) 190 (8) 229 (8) 21 m 25(6) 3 42) - 9(2) C(2) 216 (9) 333(12) 21 (1) 49 49) -10<2) - 6 43) CJ3) 173(8) 425(15) 24 (1J -16 (10) 2(3) -22 43) C(4) 213|9) 320(12) 25 (1) -36(8) 14 43) -21(3) C(5) 264 (11) 273(11) 35 (1) - 8(10) 30(3) 24(3) C<6) 260 (12) 385 (16) 43 (2) 34(12) 15 44) 65 (5) C(7) 205 (10) 372(14) 35 (D 67(10) - 143) 35 44) C(8) 172 (8) 239 (9) 28 (1) 15(8) - 2 42) 12 43) C(9) 175 47) 230 (8) 22 03 15 46) 5 42) - 4 42) C(1Q) 172 (8) 247 (9) 26 (D - 6 47) 22 42) - 8 43) C(11) 2 38(14) 513 425) 47 (2) -122(16) 3145) -16 46) ******************************************************* Hydrogen Isotropic Thermal Parameters jkx) ******************** Atom B ******************** H(2) 5|1) H43) 8(1) H (5) 9 42) H(6) 11(2) H(7) 11(2) H48) 8(1) H(11 1) 12(2) H(112) 12(2) H(113) 12 42) ******************** TABLE XII Mean Planes Equations of Planes: Plane 1 1 2 3 0- 29 33 0.3105 0. 3001 (lX+mY>nZ=p) m -0.6267 -0.6556 -0.64 12 n -0.7220 -0.6883 -0.7063 -4.0213 -3.9098 -3-9401 Deviations from Planes: Atom Plane 1. Plane 2. Plane 3. C(1) 0.000 (5) * 0.037(5) 0.013*4) * Cil2) -0.005 (6)* 0.096(6) 0.030|5) * C<3) 0.003 (5) * 0. 130(5) 0.008(6) * C(4) 0. 003 (4) * 0.090(4) -0.018 (6) * CC5) 0.016(5) -0.007 45) * -0.012(6) * C{6) 0.077 (6) -0.011 (6)* 0.051 (7) * C(7) 0. 135 (7) 0.023{7)* 0.006 (6) * C(8) 0.056 j6) -0.017(6)* -0.024 (5) * C(9) 0.006 (4) * -0.001 (4) * -0.029(4) * C{10) -0. 007 (4) * 0.013(4)* -0.030 (4) * C<11) 0.04 (1) 0.05(1) -0.00(1) * H(2) 0.11 (4) 0.24 (4) 0.04(4) H (3) -0.01 (4) 0.17 (4) 0. 13(4) H(5) -0.03(5) -0.04(5) 0. 12(5) H{6) -0.01 (6) -0. 13(6) 0.16|6) H(7) 0.27(6) 0.11 (6) -0.09(6) H<8) 0.20 45) 0.11(5) -0.06 (5) *Atoms included in mean plane calculations. Angles Between Normals to the Planes: (degrees) Planes (1) and (2) 2.7 Planes (1) and (3) — 1.3 Planes (2) and 43) — 1.5 *********************** 27 TABLE XIII CloseContacts Eacemic dimet hyl-binaphthyl Optically active dimethyl-binaphthyl 1, 1 •-Binaphthyl C (2)...C(2») C (9) C 19*) C (8) C (8*) 3.11 A 3.34 A 3.4 5 A 3.31 A 3.36 A 3.63 A 3.107 A 3.277 A 3.321 A Bending angle; Angle between asymmetric units; 3 o 68.4 o 2.7 0 80 o 68 o 1 o results from other structures Mould be necessary for a more conclusive argument. Bond distances and angles are listed in Tables XIV and XV. The numbering scheme is the same as before (see molecular drawing Fig. 5) , and standard deviations were obtained from errors in positional parameters only as unit-cell errors were negligible. The bond lengths and angles have normal values. TABLE XIV Bond Lengths (&) Carbon-Carbon Bonds C (1) -C(2) 1. 377(6) C (1) -C(9) 1. 429(5) C (1) -C(l') 1. 510 (8) C (2) -C(3) 1. 432 (8) C(3) -C(4) 1. 357(7) C(4) -C(10) 1. 429 (6) C(4) -C(11) 1. 512 (8) C(5] -C(6) 1. 366 (8) C(5) -C<10) 1. 402(7) C (6] -C(7) 1. 369 (8) C(7j -C<8) 1. 371 (7) C(8] -C (9) 1. 405 (6) C (9] -C{10) 1. 436 (6) Carbon-Hydrogen Bonds C(2)-H(2) 1- 01 (4) C (3)-H(3) 1. 11(4) C(5)-H(5) 0- 94(6) C(6)-H(6) 0. 98(6) C(7)-H(7) 1- 02(6) C(8)-H(8) 0. 86 (6) C(11)-H(111) 1. 12(7) C(31)-H(112) 1- 02(6) C (1 1)-H(113) 0- 91 (6) ********* TABLE XV Bond Angles J°l Involving Carbons Cnly Involving Hydrogens C(9)- C{1)- C(2) 1 38. 9(4) C(1)-C(2)-H(2) 115(2 C(1») -C{1) -C (2) 120. 6 (4) C(3)-C(2)-H(2) 125(2 C(1f) -C<1) -C(9) 120. 5(3) C(2)-C(3)-H(3) 110 (2 C(1)- C(2)- C(3) 120, 4 (5) C(4)-C(3)-H (3) 128 (2 C 12) -C{3)- C(4) 121- 8(5) C(10)-C(5)-fl(5) 119(3 C(6)-C (5)-H(5) 119 (3 C(3)- C(4)- C(11) 120. 0(6) C (3) - C(4)- CJ10) 120. 0 (5) C(5)-C(6)-fl{6) 116 (4 C(10) -C(4) -C(11) 120. P (6) C (7)-C (6)-B (6) 123(4 C(1Q) -C(5) -C(6) 120. 8(5) C(6)-C(7)-H(7) 124 (3 C(8)-C(7)-H(7) 115 (3 C(5)- C(6)- C{7) 120. 5(6) C(7)-C(8)-H(8) 117 (3 C(6)- C(7)- C(8) 120. 9(5) C (9)-C(8)-H (8) 122 (3 C(7)- C(8)~ C(9) 121. ? (5) C(4)-C(11)-H (11 1) 106 (4 C (4)-C (11)-H (112) 109 (4 C(8)- C(9)~ C {1-0) 117- 7(4) C(4)-C(11)-iI (113) 102 (5 C(8)- •C (9)- C{1) 121. 6(3) H(111)-C(11)-H(112) 97(5 C(1)- C{9)- C(10) 120- 6 (4) H(111)-C(1l)-H(113) 120 (6 H(112)—C(11)-H (113) 122 (6 C(9)- C(10) -C (4) 118- 4(4) C(9)- C(10) -C<5) 119. 0 (4) C (4)-•c ( 1 0) -C(5) 122. 6 (5) *************************** 30 Figure 5- Molecular Drawing of Optically Active 4,H'-Dimethyl-1,1•-binaphthyl. PART FOUR: CONCLUSION 32 Bond Length and Angle Comparison As shown in Fig- 6, the naphthalene residue consists of four types of bonds, here called types a, b, c and d. This figure also schematically shows the bond lengths and bond angles of hoth the racemic and optically active 4,4*-dimethyl-1,l*-binaphthyl to facilitate visual comparison. For each compound, the bond lengths have been averaged within each type, and the results compared to those of 1, 10-binaphthyl and naphthalene in Table XVI . These average bond lengths are very similar in all cases, and one may say that the structure of the naphthalene residue is reasonably invariant in these four compounds. Reasons for differences of stability will have to be sought in overall molecular geometry and intermolecular interactions, i-e. packing differences. Intramolecular Differences. These new reduce to differences in the angle between the residues and the differences in bending of the naphthalene unit. As mentioned before, it seems there is no correlation between the amount of bending and the dihedral angle (or the close contacts involved). The dihedral angle in each case is probably that with which the molecule packs most easily into its space group. Cell Parameter Comparison. The total mass content of the unit cells of the racemic and optically active forms is the same, but the cell volume of the racemate is smaller {1505 &3 as compared to 1634 A3) and Figure 6. Bond Length Comparison. 34 TABJLE XVI Average Bond Length Comparison Bond Lengths {%) Compound a b c d Bacemic 4,4*-dimethyl-1,1 '-binaphthyl; 1.410(3) 1-369 (2) 1.426(3) 1.426 (3) Optically active 4,4*-di-methyl-l,1»-binaphthyl: 1.401 (22) 1.368(4) 1.416(6) 1.436(6) Average 4,4,-dimethyl-1,1«-fcinaphthyl: 1.405(12) 1.368(2) 1-421(4) 1-431 (4) 1,l'-Einapbthyl; 1.404(3) 1.357(4) 1.418(4) 1.416(3) Naphthalene:'1 1-416(6) 1.357(4) 1-420(3) 1.405(6) (errors are the maximum of the rms deviation from the mean and the rms standard deviation of the bond lengths) 35 hence the density is greater (1.246 g/cm3 as compared to 1.118 g/cm3). In other words, the racemate is packed slightly •tighter' and for this reason its lattice will be of slightly higher lattice energy, hence somewhat more stable than that of the optically active form. Packing Comparison. The mode of packing is quite different for the two structures solved. By inspection of the packing diagram for the racemate ( Fig. 7 ), we see that the structure essentially consists of layers parallel to the (001) planes, each layer containing molecules of one enantiomeric form, and so we have alternating layers of H and S molecules. The unit cell is a cross-section of two such layers, as is necessary for it to contain the entire repeating unit. Furthermore, within each layer all molecules have the same orientation with respect to the crystal axes, so there are only two orientations with which a molecule may add to the lattice during crystallization, and these two orientatons are enantiomeric. If we picture the molecule as two planes forming a wedge, the molecules are oriented such that the wedges are 'nested* along the shortest axis (c=10.8%), an axial length apart (see Fig. 8 )-In optically active 4,4»-dimethyl-1, 1*-binaphthyl (Fig- 9) the molecules spiral around a 4-fold screw axis so there are four unique orientations- The shape of the unit-cell is (unlike the racemate) quite an elongated square prism. The square edge is only 8-3 S long, which means that four identically oriented molecules surround each molecule at this distance- This at Figure 7- Packing Diagram for the Sacemate. Figure 8. 'Hedge Nesting' in the Racemate Unit Cell Figure 9. Packing Diagram for the Optically Active Form. 39 first might seem to be very dense packing, but in fact the 1-1' bond is oriented closer to the sguare diagonal than to the axes, which means that the direction of •wedge-nesting * is along the diagonal, and the repeat distance here is approximately 11.7 A*, i.e. , not as close as for the racemate. Perhaps the complications of packing four molecular orientations account for the long c-axis and the slightly lower density of the optically active form. Summary. Any difference in stability in crystalline racemic and optically active 4,4*-dimethyl-1,1•-binaphthyl is reflected in the lattice energies of the two structures - a higher lattice energy is associated »ith greater stability of the lattice. The racemate is likely to have the greater lattice energy, as it is packed slightly tighter and with a little more strain in the molecules (lower dihedral angle between naphthalene residues). This would agree with the observation that the dimethyl-binaphthyl dees not resolve spontaneously upon heating to the optically active lattice (as it is less stable) in contrast to 1,1•-binaphthyl, but this does not explain the difference in behaviour between these two species. It would be of interest to study the crystal structures of optically active 1,T'-binaphthyl and other related compounds for comparison, but even then the effect of increased temperature on the lattice is not always predictable. 40 BEFEBENCES G. H. Stcut and L.H.Jensen. X-ray Structure Determination! A Practical Guide. The MacMillan Company, London- 1968. H. Lipson and W.Cochran. The Crystalline State, Vol. Ill : The Determination of Crystal Structures, 3rd edn. G.Bell and Sons, Ltd, London. 1960. H.J.Buerger. Crystal Structure Analysis. J.Hiley and Sons, Inc., New York. 1959. M.J.Buerger. Vector Space. J.Hiley and Sons, Inc., New York. 1959. M.M.Woclfson. X-ray Crystallography- Cambridge University Press. 1970. International Tables for X-ray Crystallography, Vols- I-IV. Kynoch Press, Birmingham. Vol. I, 1952; Vol. II, 1959; Vol. Ill, 1962; Vol. IV; 1974. B.E.Pincock and K. B.Hilson. , J.Chem. Ed. 50, 455 (1973). 41 8- R. E. Pincock, R.P. Bradshaw, and R. R. Perkins. J.Mol. Evol. 4, 67 (1974). 9. R.E.Pincock and K.R.Wilson. J. Am.Chem. Soc. 97, 1474 (1975) -10. R.E.Pincock and K.R-Wilson. Can.J.Chera. 55, 889 (1977). 11. Y.Badar, C.C.K.Ling, A.S.Cooke and M.M.Harris-J.Chem-Soc., 1543 (1965). 1.2. K.A.Kerr and J.H.Robertson. J.Cbem.Soc. (B) , 1146 (1969). 13- J.Sanders, B. Sc. Thesis, University of British Columbia, 1971. 14. F.H.Fung and R.E.Pincock, unpublished work, 1975. 15- L-F-Fieser. J. Am.Chem. Soc. 6J, 136 (1939). 16. D. K-J. Cruickshank in J.S.Rollett, ed. Computing Methods in Crystallography, p. 14. Pergamon Press. (1965). 17. D.H.J.Cruickshank. Acta Cryst. JO, 504 (1957). APPENDIX I. STRUCTURE FACTOR TABLES FOR HACEHIC 1.1«-DIMEIHYL-a,4'-BINAPHTHYL fa k 1 Fo Fc -6 0 12 4-61 4.56 -8 0 12 2- 12 2.44 -5 -1 12 2-14 2.25 -2 -2 12 5-4 0 5.34 -4 -2 12 9-50 8-84 -6 -2 12 4-31 4-79 -3 -3 12 11-59 11.52 -5 -3 12 4-71 5.01 -7 -3 12 4-26 4.48 -9 -3 12 6-53 6.64 -6 -4 12 3- 26 3.20 -8 -4 12 2-58 2-71 -1 -1 11 6.96 6.95 -7 -1 11 4-24 4-24 -11 -1 11 5.03 4-96 -2 -2 11 9-98 9-54 -4 -2 11 6-90 6.49 -10 -2 11 3-25 3-19 -3 -3 11 3-86 3-67 -5 -3 11 5-35 5-22 -9 -3 11 4-82 4.63 -2 -4 11 4-31 4-33 -4 -4 11 12-76 11.90 -8 -4 1 1 2.93 3.17 -3 -5 11 2.46 2-65 -4 -6 11 5-59 5-70 -2 0 10 2.27 2-27 -4 0 10 6-22 5.96 -6 0 10 1 1-78 10.59 -10 0 10 12. 11 11-70 -12 0 10 24.23 22.68 -3 -1 10 4. 17 3.81 -5 -1 10 5.37 5.31 -7 -1 10 9.19 8.40 -11 -1 10 6-09 5.77 -4 -2 10 4.61 4.44 -6 -2 10 5-62 5.38 -8 -2 10 2. 19 2.25 -1 -3 10 3-66 3.23 -3 -3 10 10-84 10.40 -7 -3 10 3.73 3.52 -11 -3 10 2.66 2.96 -2 -4 10 12.05 11.46 -4 -4 10 10.46 9-38 -1 -5 10 5- 10 5- 19 -3 -5 10 14.71 13.76 -5 -5 10 2. 86 2-85 -7 -5 10 4.21 4.31 -9 -5 10 11.67 11.65 -2 -6 10 5,48 5.65 -4 . -6 10 5.82 5.73 -10 -6 10 2. 13 2.4 0 -1 -7 10 3- 12 3.21 -3 -7 10 1 7. 55 17.41 -5 -7 10 6.06 5.99 -5 -1 9 10.53 10.25 -9 -1 9 3.15 3.39 -11 -1 9 15.60 14.85 b k 1 Fo Fc -4 -2 9 2-39 2.33 -6 -2 9 2.41 2. 29 -8 -2 9 3.29 3.26 -3 -3 9 5.21 5.01 -11 -3 9 4. 81 5.04 -2 -4 9 16. 12 15. 85 -4 -4 9 3.80 3.93 -8 -4 9 2. 17 2. 59 -12 -4 9 3-65 3.78 -1 -5 9 8.51 8.27 -3 -5 9 10. 48 10. 09 -9 -5 9 4. 58 4. 68 -4 -6 9 10. 18 9.57 -8 -6 9 9.35 9.74 -1 -7 9 3-03 3.39 -3 -7 9 7.45 7.51 -9 -7 9 2- 03 2-67 -2 -8 9 6.06 6. 36 -4 -8 9 3.38 3.59 -4 0 8 2.78 2. 30 -6 0 8 13. 10 12.89 -8 0 8 3. 16 3.42 -10 0 8 15- 51 15. 59 -12 0 8 6.85 6-72 -1 -1 8 2-51 2.49 -5 -1 8 16. 50 15. 42 -7 -1 8 6.34 5.93 -9 -1 8 3.59 3-42 -11 -1 8 6. 83 6.88 -13 -1 8 5.61 5.67 -2 -2 8 3. 25 3.27 -4 -2 8 5.81 5. 20 -10 -2 8 9. 15 9.49 -12 -2 8 9. 95 9.74 -1 -3 8 4-07 4. 08 -3 -3 8 2.59 2-68 -7 -3 8 5. 12 4.79 -11 -3 8 4.24 4-46 -2 -4 8 16.50 16-16 -4 -4 8 5.09 5. 12 -6 -4 8 2- 15 2- 15 -8 -4 8 9.34 8.98 -10 -4 8 3.28 3- 12 -1 -5 8 9.86 10. 35 -3 -5 8 32.44 31.42 -5 -5 8 3. 08 3.61 -7 -5 8 2.91 3.03 -9 -5 8 3.47 3. 18 -2 -6 8 9.99 9.78 -8 -6 8 4.52 4.89 -10 -6 8 2. 25 2.54 -12 -6 8 3. 84 3.42 -3 -7 8 2.91 2-86 -5 -7 8 2.65 3.02 -6 -8 8 2-24 2. 05 -1 -9 8 2-55 2. 70 -3 -9 8 4.76 4.43 -5 -9 8 2-54 2.80 h k 1 Fo Fc -3 -1 7 19.03 14.51 -5 -1 7 18.62 15.54 -7 -1 7 2.68 2.69 -9 -1 7 9.27 9. 15 -11 -1 7 14.04 13. 37 -2 -2 7 1 1.58 11.63 -4 -2 7 5. 39 5.27 -10 -2 7 18.21 18.27 -12 -2 7 10.33 10. 09 -1 -3 7 2.69 3. 12 -3 -3 7 2.23 2.64 -9 -3 7 7.40 7.70 -11 -3 7 3.78 4. 0 3 -13 -3 7 7.57 7.26 -2 -4 7 9.29 9.59 -4 -4 7 1 1. 11 11.48 -8 -4 7 12-74 13. 13 -1 -5 7 8.31 8. 16 -3 -5 7 5- 18 5-43 -5 -5 7 3.08 2.93 -7 -5 7 4.03 4.31 -9 -5 7 5. 64 5.85 -11 -5 7 4.85 4-69 -2 -6 7 42.27 34.98 -4 -6 7 6.90 6.83 -8 -6 7 6.61 7.64 -10 -6 7 3. 99 3.87 -1 -7 7 9.83 9.6 9 -7 -7 7 7.61 8-16 -9 -7 7 4.67 5. 16 -6 -8 7 4- 38 4-66 -8 -8 7 5.05 5-16 -10 -8 7 4-43 5-00 -1 -9 7 ii. 63 5-02 -3 -9 7 4-72 4.74 -4 -10 7 3-35 3.76 -2 0 6 11.64 9.73 -4 0 6 12-39 13.34 -6 0 6 9-40 8.83 -8 0 6 3.51 3-58 -12 0 6 3. 18 3.39 -1 -1 6 5. 89 5-85 -3 -1 6 11.26 12-05 -5 -1 6 10.28 11- 10 -9 -1 6 5-44 5-53 -11 -1 6 8.27 8-63 -2 -2 6 5.33 5-01 -6 -2 6 12.69 13-51 -10 -2 6 18.04 17.20 -9 -3 6 9.54 9.24 -2 -4 6 15.72 15.20 -4 -4 6 8.78 9.24 -6 -4 6 8.06 8-44 -10 -4 6 3. 15 3.12 -12 -4 6 4.75 5.04 -1 -5 6 15.96 17.59 -3 -5 6 4.95 5.70 -7 -5 6 4.26 4.16 h k 1 Fo Fc -11 -5 6 2.65 3- 10 -2 -6 6 3. 04 3.38 -4 -6 6 2. 27 2- 53 -6 -6 6 3.47 3-70 -8 -6 6 3.56 3.93 -1 -7 6 6. 01 5-92 -3 -7 6 12-46 12. 14 -7 -7 6 4.77 5-20 -9 -7 6 2-55 2.83 -11 -7 6 3.66 3.85 -2 -8 6 10. 92 10.90 -4 -8 6 4.30 4.63 -6 -8 6 3.74 3.89 -9 -9 6 4.60 5.01 -1 -1 5 8-76 8.91 -3 -1 5 7.72 8-31 -7 -1 5 10.47 10.31 -11 -1 5 4. 71 4-98 -2 -2 5 3-41 2-92 -4 -2 5 27. 45 25. 20 -6 -2 5 4.05 4-38 -8 -2 5 17.99 16. 53 -1 -3 5 55. 32 42.93 -3 -3 5 42.76 35.39 -5 -3 5 12.93 12.39 -7 -3 5 13.32 13.71 -9 -3 5 17.77 17-45 -11 -3 5 13.73 13. 39 -2 -4 5 49.20 39.69 -8 -4 5 4. 11 4-69 -10 -4 5 22-67 22. 10 -12 -4 5 2.85 3.00 -3 -5 5 3.78 3.98 -5 -5 5 4. 19 4. 35 -9 -5 5 3-15 2.91 -2 -6 5 3.60 3.64 -4 -6 5 9. 18 8.59 -10 -6 5 7.25 7.06 -1 -7 5 13.80 14. 18 -3 -7 5 10.47 10.78 -9 -7 5 4.80 5-21 -11 -7 5 6.76 6-38 -2 -8 5 15.56 14-97 -4 -8 5 9. 75 9. 15 -8 -8 5 5.32 5-89 -10 -8 5 7.82 8-39 -1 -9 5 3.98 4. 15 -5 -9 5 8.51 8.75 -7 -9 5 8.96 9-20 -1 -11 5 5.75 5.37 -2 0 4 30.70 28-67 -6 0 4 11.26 10. 64 -8 0 4 6.84 7. 15 -10 0 4 5. 54 5.28 12 0 -4 5.97 5-88 14 0 -4 6.54 6. 44 - 1 -1 4 14.57 12.79 -3 -1 4 8-55 9.00 ll k 1 Fo Fc -7 -1 4 5-77 5.45 -9 -1 4 8-52 7.58 13 1 -4 4.30 4.58 -2 -2 4 20.82 19.77 -4 -2 4 20-79 16-74 -6 -2 4 15.56 15-80 -8 -2 4 7.81 8- 14 -10 -2 4 3.32 3.49 12 2 -4 8. 19 8-34 14 2 -4 3.38 4.24 -1 -3 4 34-88 30.25 -3 -3 4 30-94 24-56 -5 -3 4 1-83 1.94 -7 -3 4 14.41 13.90 -9 -3 4 23.26 18.85 -11 -3 4 12-66 11-92 -6 -4 4 9-38 8.95 -8 -4 4 14.52 15.01 -10 -4 4 13.09 13.60 12 4 -4 2.90 2.92 -3 -5 4 4. 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5 1 10 2.76 2-85 5 3 10 6.82 7. 16 h k 1 Fo Fc 4 4 10 5. 84 6.02 3 5 10 2- 88 2-51 0 8 10 3. 20 3.01 4 2 11 5.32 5. 45 3 3 11 6.43 6.58 2 4 11 4-01 4.47 0 0 12 2. 85 2-74 1 1 12 3.91 3. 75 2 2 12 2-56 2.57 1 3 12 4-25 4. 41 0 4 12 2-34 2.55 -7 -7 8 3-90 4. 13 -9 -7 8 4. 33 4.85 -13 -1 5 4- 27 5.22 -2 -4 4 24.57 21-64 -9 -7 4 16.30 14. 74 -7 -1 3 28.41 24-30 10 6 -3 21. 55 19. 57 6 0 -2 60. 59 44.24 7 1 0 23.95 17-97 11 1 1 7.24 7.45 0 0 6 2. 19 1-87 -11 -3 13 3- 98 4.28 -1 -1 1 46. 54 48.09 -2 -2 2 67.27 67.06 -1 -1 2 42.78 37. 02 -2 0 2 30. 20 31-99 -2 -2 3 59. 85 56.99 -1 -1 3 90.49 84.73 6 0 0 28. 77 35.39 2 0 0 58.06 54. 91 0 2 1 33-80 32.26 5 1 1 21- 14 26-01 1 1 2 33- 37 41.58 0 2 2 94.63 96.27 0 2 3 40-36 47-52 0 4 0 18. 15 21. 15 51 APPENDIX XI-STBOCTURE FACTOR TABLES FOB OPTICALLY ACTIVE 1,1"—DIMETHYL-4.4*—BINAPHTHYL h k 1 Fo Fc 1 1 0 42-94 80.47 0 2 0 17-65 29.09 3 2 0 37. 15 65.46 2 2 0 6.52 10.89 1 3 0 35. 11 24. 18 2 3 0 8.69 14. 11 3 3 0 29-68 50-56 0 4 0 33.08 57-09 1 4 G 6-26 8-99 2 4 0 13.99 23.20 3 4 0 4. 13 7.56 4 4 0 3.65 5- 84 1 5 0 6.25 8-82 2 5 0 10.28 16.83 3 5 0 3-99 6-31 4 5 0 2. 79 3. 03 0 6 0 3.66 5-72 1 6 G 9.21 15.66 2 6 0 9.39 16.37 4 6 0 4- 85 8.39 1 7 0 5.92 8-96 2 7 0 5.33 7.95 3 7 0 6.60 31-19 0 8 G 9-81 17.29 2 8 0 3-24 5-17 0 1 1 11.64 11-51 0 2 1 3,58 2.58 1 2 1 17.06 27-40 1 3 1 25.87 40.22 2 3 1 12.49 13.37 0 4 1 5-84 6- 34 1 4 1 26.80 4.88 2 4 1 19.06 15- 85 3 4 1 9.02 7.71 1 5 1 15.57 2. 19 2 5 1 16.45 10-77 3 5 1 10.74 10.75 1 6 1 12.02 17.95 2 6 3 8-03 13. 11 3 6 1 13.35 21.87 4 6 1 4.35 4. 17 5 6 1 3.04 4.41 0 7 1 5. 36 5.82 1 7 1 4.22 5.08 2 7 3 3 1.34 15-69 3 7 1 5.32 8.88 0 8 1 7.71 8- 86 1 8 1 2-96 4.73 1 2 2 4-51 3. 10 2 2 2 19.86 35.26 0 3 2 2-94 5.09 1 3 2 11.29 15.31 2 3 2 23.05 29.50 3 3 2 20.53 • 34.22 1 4 2 7.47 4.24 2 4 2 38-43 34.42 3 4 2 7. 18 10-74 4 4 2 2.58 4-82 fa k 1 Fo Fc 0 5 2 6-74 12.68 1 5 2 8. 06 9.35 2 5 2 9.42 4.60 3 5 2 5. 94 11-.143 4 5 2 4.76 1.45 5 5 2 4.48 8.80 1 6 2 5-22 8.68 2 6 2 19.23 23.95 3 6 2 8-33 4.41 4 6 2 5. 95 7. 32 5 6 2 6. 93 10-17 1 7 2 9. 92 12.96 2 7 2 4.87 2.32 3 7 2 5. 09 6-44 1 8 2 5-20 7.44 0 2 3 77-60 85- 59 1 2 3 33.26 46-43 0 3 3 2-61 4.06 1 3 3 14-58 22-61 2 3 3 35-63 13.35 0 4 3 6.97 8.29 1 4 3 28.39 33.31 2 4 3 9. 11 7.63 3 4 3 10. 43 14. 29 0 5 3 5. 06 6.23 1 5 3 6.96 4.92 2 5 3 18.97 18.32 3 5 3 4. 12 5.47 4 5 3 3-77 1.34 0 6 3 6. 26 6. 32 1 6 3 4.75 1.55 2 6 3 3. 52 2.54 3 6 3 13. 02 4. 67 4 6 3 6-24 11. 97 5 6 3 3.88 6.62 0 7 3 7. 06 7.99 1 7 3 10.50 17.97 2 7 3 8.81 14.38 4 7 3 3.63 2.45 1 8 3 8. 29 12. 12 0 0 4 5.37 12.79 1 1 4 56. 02 97. 28 0 2 4 23.60 38.38 1 2 4 ' 37. 81 52.83 2 2 4 14.76 23. 38 1 3 4 23-04 11. 24 2 3 4 13. 64 17.61 3 3 4 15.76 26.,98 0 4 4 23-53 33.39 1 4 4 18. 43 29.02 2 4 4 6. 12 0.71 3 4 4 2-90 5.60 4 4 4 8.25 12.54 1 5 4 8.36 3. 11 2 5 4 2. 41 1.33 3 5 4 13. 49 12.41 4 5 4 5. 00 4.25 5 5 4 4.73 8. 24 a k 1 Fo Fc 0 6 4 3- 27 5. 12 1 6 4 6.40 6.81 2 6 4 11. 17 12.29 3 6 4 4.42 3.27 * 6 4 6.50 10.85 5 6 4 1.01 5.39 1 7 4 15.66 0. 18 2 7 4 3.61 4-26 4 7 4 3.51 2-04 1 8 4 3.49 3. 16 0 2 5 56-76 65.52 1 2 5 66.29 96. 92 0 3 5 9.36 13.37 1 3 5 26.63 35.84 2 3 5 24.95 3.37 0 4 5 8.79 11.74 1 4 5 5. 44 5.70 2 4 5 10.62 7.00 3 4 5 2.50 5. 10 0 5 5 4.41 6.49 1 5 5 2-94 2.79 2 5 5 3.45 6.26 3 5 5 6.53 9.29 a 5 5 8.85 14.61 0 6 5 2. 10 1.84 1 6 5 8.08 10.76 2 6 5 5.23 0.41 3 6 5 5.75 0-51 5 6 5 10.62 9-97 0 7 5 3.46 2-62 1 7 5 14.62 23.98 2 7 5 3.45 2.31 7 5 3.46 5.94 0 8 5 9.82 11.42 1 . 8 5 3.60 3.45 0 1 6 34.45 54.62 1. 1. 6 2.30 1-85 1 2 6 16.49 25.26 2 2 6 6.26 10.75 0 3 6 51.02 7S-98 3 6 37.78 35.02 2 3 6 19.81 18-52 3 3 6 6.30 9.54 1 4 6 11.28 8-53 2 4 6 6. 13 5.61 3 4 6 3.70 2-10 0 5 6 9.92 14.64 1 5 6 6.42 11.29 2 5 6 12-80 16.57 3 5 6 6.34 9.77 4 5 6 8.15 14.66 5 5 6 12.06 21.23 1 6 6 8.08 5-00 2 6 6 8.37 3.71 3 6 6 12- 15 17.49 4 6 6 4.98 0.35 5 6 6 6-85 2-84 0 7 6 9.57 16-41 fa k 1 Fo Fc 1 7 6 7.75 8- 16 2 7 6 2- 88 1-09 0 1 7 5. 14 8.63 0 2 7 19- 98 25- 15 1 2 7 45.89 40. 75 2 2 7 45-75 0-01 0 3 7 21.59 25.26 1 3 7 26-80 39.76 2 3 7 11.26 19.84 0 4 7 10.30 11-62 1 4 7 24-97 10. 19 2 4 7 6. 15 3.78 3 4 7 3. 88 3. 58 0 5 7 3. 93 3. 25 1 5 7 4.75 4.37 2 5 7 6.55 10.38 3 5 7 6. 53 6. 81 4 5 7 18.99 16. 41 0 6 7 10.25 10.86 1 6 7 11. 02 17. 82 2 6 7 2.88 3-90 3 6 7 3.77 6. 14 4 6 7 6.42 10.65 0 7 7 23.05 25.67 2 7 7 3- 25 4-25 3 7 7 5-68 7. 47 0 0 8 31.97 38-98 1 1 8 63.25 104.86 0 2 8 18.98 31-91 1 2 8 9.07 10-51 2 2 8 17.22 21.50 1 3 8 39-21 59.37 2 3 8 32-82 36. 02 1 4 8 10.81 9.89 2 4 8 11-31 14.30 4 4 8 5- 10 5. 98 1 5 8 8.03 11-92 2 5 8 3. 74 4- 79 3 5 8 7.50 12-76 4 5 8 8.69 13. 17 5 5 8 2.67 3- 18 1 6 8 4.64 7.49 2 6 8 7. 30 9. 13 3 6 8 3.91 5.68 4 6 8 10.51 15-91 1 7 8 7.60 11.56 2 7 8 3. 06 2.36 3 7 8 3. 52 0.63 0 1 9 11. 11 7.28 0 2 9 8.91 12.82 1 2 9 33. 28 16.94 1 3 9 21-44 28.80 2 3 9 16.77 13.39 0 4 9 17-59 18.63 1 4 9 5. 09 8. 26 2 4 9 7. 48 9-48 3 4 9 4- 87 1.48 0 5 9 8.72 11.83 fa k 1 Fo Fc 1 5 9 5-66 9-45 2 5 9 9.89 1 7. 53 3 5 9 10.00 12.99 4 5 9 8.20 2.96 0 6 9 9.48 10-82 1 6 9 10.65 16. 17 2 6 9 4.34 2. 03 3 6 9 3.77 5.38 4 6 9 5-80 1-60 0 7 9 14. 18 16.70 1 . 7 9 3-42 1.69 2 7 9 4. 43 5.85 0 1 10 19.54 27.54 1 1 10 10-06 19.70 1 2 10 14.58 13. 16 2 2 10 34-65 59.72 0 3 10 4. 12 11.46 t 3 10 29.03 31.56 2 3 10 9-93 1 1.76 3 3 10 2-35 0.29 1 4 10 22. 52 19-09 2 4 10 7.21 1.61 3 4 10 4.68 7.09 4 4 10 4.24 8.54 1 5 10 6.03 9.75 2 5 10 10-93 8-96 3 5 10 10.02 9.33 5 5 10 13.26 22.76 1 6 10 6.87 9-27 2 6 10 4. 48 6.81 3 6 10 7.28 8.58 4 6 10 5.47 7.04 1 7 10 3.57 4.73 2 7 10 5. 13 4.37 0 1 11 27.52 31.71 0 2 11 12.67 15.68 1 2 11 17.69 6.34 0 3 11 20.53 21.00 1 3 11 18.68 14.48 2 3 11 4.40 4.52 0 4 11 3-43 3.65 1 4 11 23. 70 34-70 2 4 11 10.66 1.71 3 4 11 9.60 4.41 1 5 11 7.44 1 1-46 2 5 11 4.32 0.95 3 5 11 9.56 2.57 4 5 11 5.43 8.71 0 6 11 3.44 3.85 1 6 11 4. 72 4.35 2 6 11 2.88 2-79 3 6 11 6.23 7.87 4 6 11 3.79 2-72 1 7 11 5.01 2.38 2 7 11 2-74 4-00 1 1 12 13.47 22.41 0 2 12 12-84 23-77 1 2 12 3.90 3.52 fa k . 1 Fo Fc 2 2 12 7-98 3-22 1 3 12 7- 27 5- 88 2 3 12 22-81 35.99 3 3 12 3-49 4-80 0 4 12 4-13 14.46 1 4 12 11. 14 15- 25 2 4 12 7.34 4. 19 3 4 12 12. 04 12.59 4 4 12 11-57 15-99 1 5 12 8. 13 9.22 2 5 12 8.41 12.81 3 5 12 9.27 1.03 4 5 12 4.34 4. 80 5 5 12 3.77 6.56 0 6 12 2.68 1.77 1 6 12 6- 04 2.36 2 6 12 9-21 3. 18 3 6 12 3. 87 6.82 1 7 12 7.40 0.05 0 1 33 17. 69 24.57 0 2 13 18. 53 20. 77 1 2 13 7.95 4.60 1 3 13 9.37 10.40 2 3 13 16.79 12-98 0 4 13 12- 85 12.95 1 4 13 3. 76 7. 11 2 4 13 19.94 22-42 3 4 13 7.52 5- 12 0 5 13 6. 05 8.97 1 5 13 6.80 1.41 2 5 13 11.68 2. 17 3 5 13 3-61 0-97 2 6 13 3. 75 4. 16 3 6 13 2.36 2.98 0 1 14 18-38 22-31 1 1 14 7.79 10.47 1 2 14 6-20 5.50 2 2 14 7.36 12.29 0 3 14 2-36 6.46 1 3 14 8. 45 8.40 2 3 14 . 7-62 13.96 3 3 14 3.60 2. 38 1 4 14 5-35 8.00 2 4 14 19-31 12.20 3 4 14 2. 45 0.80 0 5 14 3.25 3.55 1 5 14 4. 18 2-35 2 5 14 15.35 3.88 3 5 14 6.51 11-29 2 6 14 4.54 5. 17 0 1 15 6.22 5. 15 0 2 15 3. 06 3. 46 0 3 15 5.78 3.95 1 3 15 6.23 7.95 0 4 15 10- 56 32.31 1 4 15 3. 70 4, 42 2 4 15 21.65 3-49 3 4 15 5. 53 0-74 h k 1 Fo Fc 0 5 15 8-57 3 0.03 2 5 15 5-33 7.03 3 5 15 4-58 3.29 1 6 15 2-82 0-48 2 6 15 3-77 4.51 0 0 16 60-59 80-80 1 1 16 5.99 9.32 2 2 16 3-68 15.63 1 3 16 2.36 3.52 2 3 16 4.49 1. 12 3 3 16 5-99 9.31 0 4 16 5.45 13.56 1 4 16 16.42 1-91 2 4 16 9-45 5.35 3 4 16 7.36 5-36 1 5 16 6- 67 2-92 2 5 16 6.67 0-24 3 5 16 7-63 4.72 0 1 17 4-09 6-53 1 2 17 2-70 0.78 0 3 17 6-94 11-21 1 3 17 6-50 2.97 2 3 17 6.32 6-53 0 4 17 10- 16 13-49 1 4 17 7.41 9-99 2 4 17 6-86 2-42 3 4 17 3.06 2-07 0 5 17 3.59 3.96 2 5 17 4.90 5-50 0 1 18 4.36 2.56 1 1 18 1 1.62 17.86 1 2 18 3. 66 S.94 1 3 18 8.84 11.58 2 3 18 3.92 2.91 3 3 18 10. 18 19.33 1 4 18 7.44 1.45 3 4 18 3.70 6.87 0 5 18 2.60 5.48 1 5 18 4.76 2-37 0 1 19 2. 17 5.25 0 3 19 2-44 1.96 1 3 19 10. 11 18-54 2 3 19 13.33 8. 14 0 4 19 4.05 4.54 1 4 19 4.45 3.04 2 4 19 4.79 6.02 0 0 2 0 6.00 0.22 0 2 20 2-88 4.27 1 2 20 5.31 4-91 1 3 20 3-76 5.70 2 3 20 9.66 17.26 3 3 20 4.24 5.91 1 4 20 8.91 5.95 0 1 21 6.69 8.20 0 2 21 6.33 7.09 1 2 21 5.09 9-08 0 3 21 6.97 10.03 1 3 21 6.77 8.07 b k l Fo Fc 2 3 21 5.09 3-47 1 1 22 3.89 4.90 1 2 22 4.00 9.48 2 2 22 3. 50 5.90 6 6 0 11.56 19.47 5 7 0 2. 20 3. 26 6 7 0 5.39 8.73 1 9 0 3- 17 3.64 2 9 0 4.07 6.46 5 7 1 2.83 3.02 6 7 1 3.74 2-99 3 8 1 4.40 4.52 4 8 3 2- 26 2^00 0 9 1 2-50 2. 59 6 6 2 7.02 11.71 5 7 2 2-62 0.88 6 7 2 4.50 6. 14 1 9 2 4. 17 7. 08 5 7 3 2.94 3- 57 6 7 3 3. 57 5.64 3 8 3 2.63 3.85 4 8 3 2.95 3. 48 2 9 3 2.69 3. 14 5 7 4 3-28 1-52 2 8 4 4. 15 5. 17 2 9 4 2. 94 2-69 2 8 5 3. 55 3-53 3 8 5 2-38 1.49 0 9 5 3.36 4.40 6 6 6 2. 14 2. 43 1 8 6 2.53 1.71 2 8 6 3.69 2-55 3 8 6 2- 49 2.73 4 8 6 2.50 3. 29 4 7 7 3. 08 4.72 0 8 7 5. 86 6.47 1 3 7 3- 20 0.79 2 8 7 2.38 3. 67 5 6 8 3- 76 4.87 6 6 8 2. 27 5-35 5 7 8 2-34 0.71 0 8 8 10.75 17.39 1 8 8 4.32 7. 13 3 8 8 3. 11 0.58 0 8 9 3. 21 3-91 1 8 9 6.65 1.96 2 8 9 2-48 4.30 3 8 9 2.66 2.81 5 6 10 4. 45 2.40 6 6 10 2. 13 3. 24 4 7 10 2. 12 1. 18 1 8 10 5.96 3. 65 2 8 10 5. 13 5.91 3 8 10 2. 88 3.83 5 6 11 5. 04 2.51 4 7 11 3. 54 0.98 0 8 11 5.06 5.74 1 a 11 4.74 5.27 h k 1 Fo Fc 2 8 11 3-90 4-90 4 6 12 4.29 6- 12 2 7 12 3-88 5.93 3 7 12 2.96 2-31 1 8 12 4-41 6.59 2 8 12 3.93 0.86 4 6 13 2-83 3.91 0 7 13 4.00 4.49 1 7 13 4.36 6.83 3 7 13 4.24 4.89 4 7 13 2.86 0-75 1 8 13 3.27 5-07 5 6 14 4.56 6.79 0 7 14 2.22 1.21 1 7 14 2.97 3. 14 2 7 14 3.09 2.56 3 7 14 2-40 0.65 a 5 15 2.31 2.04 3 6 15 4.20 7.61 4 6 15 3.68 5.33 2 7 15 4.66 6.58 2 6 16 3.24 1.02 4. 6 16 3.28 0.55 1 6 17 2-80 3.49 2 6 17 4.29 8.69 2 5 18 8-87 0.53 3 5 18 6.03 8.58 4 5 18 2.80 4.08 1 6 18 2-89 1-38 2 6 18 3. 81 7.51 3 6 18 4-45 0.53 2 5 19 2-77 0.07 2 6 19 2-54 2.46 2 4 20 3 c» .2 5 5.96 3 4 20 3. 11 4.69 1 5 20 3-58 1.49 2 5 2 0 4-76 2-57 3 5 20 3.76 7- 10 0 4 21 2.66 3.66 1 4 21 6.52 11.05 2 4 21 4.85 5. 18 3 4 21 3.24 2.04 1 5 21 3. 10 2-77 2 5 21 3.68 4.91 0 3 22 7.95 9.69 2 3 22 5.17 5.79 1 4 22 5.28 9.06 2 4 22 5.95 0.67 3 4 22 2.25 0-37 0 2 23 2.92 1-05 0 3 23 5.62 4.02 1 3 23 6.81 12.09 2 3 23 3.58 3-30 0 4 23 6.91 9. 17 0 0 24 3-97 1.54 1 2 24 3-44 4.39 1 3 24 3-32 0-54 2 3 24 4.24 1-62 h k 1 Fo Fc 0 2 25 4.76 5-90 0 3 25 5. 10 7.63 1 3 25 5.90 1- 19 7 7 0 3. 32 6. 19 0 10 0 4.92 8.93 5 8 1 2.40 0-82 4 9 1 2.56 3-01 7 7 2 4. 04 6-88 6 8 2 2. 29 1- 90 2 10 2 2-44 0.90 5 8 3 2.42 0.76 3 9 3 2.85 4.95 4 9 3 2. 22 2.84 6 8 4 2.57 0.20 3 9 5 2-45 2.23 1 10 5 2.43 0.24 7 7 6 2-24 2-68 4 9 6 2.90 3.34 6 7 8 2.47 3. 17 3 9 8 2.62 1.27 4 9 8 2-81 0.54 0 9 11 3.26 4.48 2 9 11 2-35 0.63 3 8 12 2. 93 3.06 1 9 12 3- 23 3.38 2 8 13 3.24 1.73 4 8 13 3-05 3.91 1 8 14 4. 12 4.74 3 8 14 2-79 4.20 5 6 15 2.34 1.88 4 7 15 2-83 1.65 5 7 15 2.70 4. 30 0 8 15 2- 40 0.46 2 8 15 2.82 4.39 6 6 16 2-93 4.03 3 7 16 2-46 3-30 4 7 16 3-00 1.72 0 8 16 2-72 2-79 3 8 16 4.06 1.69 3 7 17 2. 65 3.00 0 8 17 3.42 3.00 2 8 17 2. 13 1. 59 5 5 18 2.37 1.71 5 6 18 2. 27 1-63 2 7 18 2. 28 2.96 3 6 19 3.08 2. 31 1 7 19 3. 10 4.05 2 7 19 3. 42 3.98 5 5 20 2- 16 2.85 4 6 20 2. 13 1.58 4 5 21 2.52 0.99 0 7 21 2- 29 0.98 1 7 21 2.74 4.05 3 5 22 2.39 0.47 4 5 22 2. 62 4.94 1 6 22 2. 20 3. 11 0 5 23 2.50 0. 97 3 5 23 2. 52 1.83 h k 1 Fo Fc 1 4 24 4.53 3.05 2 4 24 3.36 1.15 3 4 24 2.22 0. 16 2 5 24 2.96 2.77 2 3 25 3. 18 0. 16 0 4 25 2.43 2. 18 0 5 25 2.30 1.62 2 2 26 5.16 8.96 1 4 26 3-67 1-25 2 4 26 2.21 0.43 0 1 27 3-26 6. 16 1 2 27 2.13 C.95 0 3 27 2-43 0.92 1 3 27 3.49 0.84 1 1 28 2-07 3.59 0 2 28 2. 19 2.39 1 2 28 2- 13 1.77 2 2 28 1.90 3.75 5 9 0 2- 19 3-57 5 9 4 1.99 0.76 2 10 5 2-02 2-72 1 10 8 2.00 0.76 6 8 9 1.69 0. 16 6 7 13 1.97 3-01 h k 1 Fo Fc 2 9 14 1. 99 2-96 4 8 15 2- 15 2-96 3 6 17 2.70 3.73 3 8 17 2. 17 2- 10 6 6 18 2. 53 4.41 2 8 19 2.28 2. 51 5 6 20 2. 48 4-06 3 7 20 2. 43 3.62 5 5 22 1.85 3.64 4 6 22 2.29 2. 41 0 7 22 2-35 3. 19 4 5 24 1. 83 0.63 0 5 26 2- 62 3.67 1 5 26 2.67 3. 34 1 4 27 3-58 5-/12 2 3 28 2- 70 3.71 0 1 30 2-82 5.07 0 1 2 82. 13 138.03 1 1 2 96.26 165.71 0 1 3 83. 49 94.62 1 1 3 104.62 0. 01 0 1 5 127-71 144. 25 1 1 5 133.33 0.01 

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