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Determination and refinement of the structures of some chlorinated carbohydrates Hoge, Reinhold 1968

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THE DETERMINATION AND REFINEMENT OP THE STRUCTURES OF SOME CHLORINATED CARBOHYDRATES by REINHOLD HOGE B.Sc.(Hon.), U n i v e r s i t y of B r i t i s h Columbia, 1965.  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  i n t h e Department of Chemistry  We accept t h i s t h e s i s as conforming t o the r e q u i r e d standard  THE UNIVERSITY OF BRITISH COLUMBIA December, 1968.  In  presenting  an  advanced  the  Library  I further for  this degree shall  agree  scholarly  by  his  of  this  written  thesis  in p a r t i a l  f u l f i l m e n t of  at  University  of  the  make that  i t freely  permission  purposes  may  representatives. thesis  for  be It  financial  available for  of  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada  by  the  is understood gain  Columbia  for  extensive  granted  permission.  Department  British  shall  reference  Head  be  requirements  Columbia,  copying  that  not  the  of  and  of my  I agree  for that  Study.  this  thesis  Department  copying  or  allowed  without  or  publication my  il  ABSTRACT Supervisort Professor James Trotter. The c r y s t a l and molecular structures of three chlorinated carbohydrates whose formal nomenclatures are methyl  2-chloro-2-deoxy-d-D-galactopyranoside  methyl *f,6-dichloro-4,6-dldeoxy- oc-D-glucopyranoside, and methyl 4,6-diohloro-4,6-dideoxy-ct-D-galactopyranoside have been determined by X-ray d i f f r a c t i o n using various methods.  A s c i n t i l l a t i o n counter was used i n each case  to c o l l e c t the datat f o r the f i r s t , CuKot r a d i a t i o n was used; f o r the second and t h i r d , MoK«  radiation was used.  The structure of the 2-chloro-galactoslde was solved by a combination of the Patterson method and t r i a l and error methods.  Two possible positions of the chlorine  atom found from the Patterson function were d i f f e r e n t i a t e d by minimizing R (using h k 0 projection data only) i n r o t a t i o n of a model of the molecule about each chlorine position.  A model was used to go from the solved two  dimensional structure to three dimensions.  Successive  Fourier summations and block diagonal least squares refinement established the c r y s t a l to be composed of a mixture of the oC and /S anomers of methyl 2 - c h l o r o - 2 deoxy-D-galaotopyranoside In the approximate r a t i o of 206:  l / 3 . Both the oC and ^anomers are i n t h e i r expected  C - l (chair) conformations. 0(3),  0(4) and 0(6)  Hydrogen bonding involving  l i n k s molecules  i n f i n i t e sheets, two molecules to the x-axis.  together into  thick and perpendicular  Mean bond distances a r e i C-C = 1.53  A,  C-0 = 1.42 A and C-Cl - 1.75 A. The structure of the 4,6-dlchloro-glucoside was solved by a combination  of the Patterson method (to  locate the two c h l o r i n e s ) , successive Fourier summations (to locate the carbons and oxygens), block diagonal least squares refinement, and a difference synthesis (to locate eight of the hydrogens).  The absolute configuration was  determined by the anomalous dispersion method (CuK« radiation). tion.  The molecule  i s l n the expeoted C - l conforma-  Hydrogen bonding, involving 0(2)  molecules  and 0(3)»  links  together into I n f i n i t e chains p a r a l l e l to the  y-axis; the mean planes of the molecules are approximately perpendicular to the d i r e c t i o n of these chains. bond distances are C-C « 1.52  Mean  A , C-0 - 1.42 A and C-Cl •  1.78 A. The structure of the 4,6-dichloro-galactoside was solved by d i r e c t methods applied to the two dimensional data of two centrosymmetric  projections. A series of  programs, employing the Vand-Peplnsky method of phasing reflexions contained i n Sayre r e l a t i o n s h i p s , was to do t h i s .  written  After refinement using block diagonal least  squares, the two solutions were combined into the three  dimensional  s o l u t i o n , which was  further refined.  A  d l f f e r e n o e F o u r i e r summation r e v e a l e d the p o s i t i o n of s i x hydrogens.  The molecule  C - l conformation. and 0(3)  expected  Hydrogen bonding Involved 0(1),  0(2),  i n a complicated network which i n c l u d e s a  b i f u r c a t e d hydrogen bond. molecules  i s again i n the  As i n the 2 - o h l o r o - g a l a c t o s i d e  are l i n k e d by hydrogen bonds i n t o  s h e e t s , two molecules  infinite  t h i c k and p e r p e n d i c u l a r to the  x - a x i s , but whereas i n t h a t s t r u c t u r e the baslo symmetry elements propagating  the networks of bonding were u n i t  c e l l t r a n s l a t i o n s and t w o - f o l d r o t a t i o n axes, the b a s i c elements propagating  the networks i n 4 , 6 - d l c h l o r o - g a l a o t o  s i d e a r e u n i t c e l l t r a n s l a t i o n s and  two-fold sorew axes.  Mean bond d i s t a n c e s i n t h i s s t r u c t u r e aret C-C C-0  = 1.45  A, and C - C l =1.80  A.  = 1.53  A,  V  TABLE OF CONTENTS Page TITLE PAGE  1  ABSTRACT  1  TABLE OF CONTENTS  1  •  LIST OF TABLES  *H  LIST OF FIGURES ACKNOWLEDGEMENTS  . . .  x  GENERAL INTRODUCTION  1  PART I i THE STRUCTURES OF THREE CHLORINATED CARBOHYDRATES 1. METHYL 2-CHL0RO-2-DEOXY-0d-D-GALACT0PYRANOSIDE Introduction  Ly  Experimental  5  •  Structure Analysis  •  6  a. Two Dimensional (xy) s o l u t i o n and refinement • • • • • • • • b Three Dimensional refinement 0  6 11  Discussion a. M o l e c u l a r S t r u c t u r e and dimensions bo Hydrogen bonding • 2  0  . . . . .  15 18  METHYL 4,6-DICHLORO-4,6-DIDEOXY-0C-D-GLUCOPYRAN0SIDE Introduction Experimental  o . . . . . . . . . .  2  7 29  . . . .  30  Discussion D i r e c t Methods on xz p r o j e c t i o n  5  . . . o . . . . .  Structure Analysis , Absolute C o n f i g u r a t i o n  2  •  ^  2  vi Page PART I i (oont'd.) 3.  METHYL, 4,6-DICHLORO-4,6-DIDEOXY-0t-D-GALACTOPYRANOSIDE Introduction . . . . . .  46  •  46  Experimental Structure  Analysis 48 5 5 5 7  a. D i r e c t methods on xy p r o j e c t i o n . b. D l r e o t methods on xz p r o j e c t i o n c. Three Dimensional Refinement , Discussion a. M o l e c u l a r  61  s t r u c t u r e and dimensions  b. Hydrogen bonding  6 5  PART l i t DESCRIPTIONS OP PROGRAMS D i r e c t Methods Programs Introduction 1.  •  7 4  PREDIR  7 5  2. SAYRE 3.  SIGNS  4.  ESIGND  7 9 83 9 1  R o t a t i o n program f o r c - a x i s p r o j e c t i o n of P 2 2 2 1  1  . . . 9 4  A c o n t o u r i n g program (CONTUR) f o r three dimensional F o u r i e r maps BIBLIOGRAPHY APPENDIX  (Source Deck l i s t i n g s f o r programs i n P a r t I I ) .  **********  9 6 1  0  2  LIST OF TABLES TABLE  Page Methyl 2-chloro-2-deoxy-  I II  tt-D-galaotopyranoslde  Measured and c a l c u l a t e d s t r u c t u r e amplitudes  . . .  F i n a l p o s i t i o n and thermal parameters i n c l u d i n g t h e i r standard d e v i a t i o n s  III IV  VI  22  Bond l e n g t h s and v a l e n c y angles  23  Shorter intermolecular distances  2k  Methyl V  21  4.6-dlchloro-4»6-dldeoxy-o<-D-ftlucopyranoslde  Measured and c a l c u l a t e d s t r u c t u r e amplitudes  • . .  35  F i n a l p o s i t i o n and thermal parameters 36  i n c l u d i n g t h e i r standard d e v i a t i o n s VII  Bond l e n g t h s and v a l e n c y angles  38  VIII  Shorter intermolecular distances . . . .  40  XI  D e t e r m i n a t i o n of the a b s o l u t e c o n f i g u r a t i o n w i t h Cu-K Methyl  X XI  radiation  . . . • 41  4«6-dlchloro-4.6-dldeoxy-tt-D-galactopyranoslde  Measured and c a l c u l a t e d s t r u c t u r e amplitudes  . . .  68  F i n a l p o s i t i o n and thermal parameters i n c l u d i n g t h e i r standard d e v i a t i o n s  69  XII  Bond l e n g t h s and v a l e n c y angles  71  XIII  Shorter intermolecular distances . . .  73  vill  LIST OF FIGURES FIGURE 1 2 3  Page Methyl 2-chl6ro-2-deoxy-ar.D-galaotopyranoslde Approximate r e p r e s e n t a t i o n o f model used f o r r o t a t i o n program (ROT) R e s u l t s f o r two p o s s i b l e c h l o r i n e p o s i t i o n s as R v e r s u s ® p l o t s • • . • • •  8 •  9  Superimposed s e c t i o n s of e l e o t r o n d e n s i t y d i s t r i b u t i o n (contours a t 1,2,3...e/A3) and a drawing o f the moleoule . . . . . . . . . . .  16  4  Packing diagram; view a l o n g o  17  5  Hydrogen bonding; view a l o n g c of near o r i g i n r e g i o n (the d o t t e d O's have been o f f s e t f o r clarity)  5  Methyl 4.6-dlohloro-4.6-dldeoxy-q-D-glnoopyranoslde 6  Superimposed s e c t i o n s of e l e o t r o n d e n s i t y d i s t r i b u t i o n (obntours a t l,2.3...e/A3 f o r C and 0; 1,5,10. ..e/A3 f o r CI) and a drawing of the moleoule  .  31  7  Packing diagram; view along b  33  8  Hydrogen bonding; view along o  34  9  B-map o f x z - p r o j e c t i o n (contours on a r b i t r a r y scale) with f i n a l refined solution superimposed  ^5  Methyl 4.6-dlchloro-4«6-dldeoxy-tt-D-galaotopyranoslde 10  11  12  E-map of x y - p r o J e c t i o n (contours on a r b i t r a r y s c a l e ) w i t h the I n i t i a l l y p o s t u l a t e d s t r u c t u r e superimposed . . . . . . .  52  E l e c t r o n d e n s i t y map o f x y - p r o J e c t i o n (contours on a r b i t r a r y s c a l e ) based on phases c a l c u l a t e d u s i n g a l l non-hydrogen atoms except 0(1), C(2) and C(4)  53  F i n a l e l e c t r o n d e n s i t y map o f x y - p r o J e c t i o n (contours on a b s o l u t e s c a l e s e/A x 100) w i t h the r e f i n e d s t r u c t u r e superimposed. . . . . . .  5*  2  1  ix  FIGURE 13  14  Page E-map o f x z - p r o j e e t i o n (contours on a r b i t r a r y s c a l e ) w i t h the i n i t i a l l y p o s t u l a t e d s t r u c t u r e superimposed F i n a l e l e o t r o n d e n s i t y map of x z - p r o j e o t l o n {oontours on a b s o l u t e s c a l e r e/A x 100) w i t h t h e r e f i n e d s t r u o t u r e superimposed . . . .  ->°  2  15  Superimposed s e c t i o n s o f the e l e c t r o n d e n s i t y d i s t r i b u t i o n (oontours a t 1,2,3.,.e/A3) and a drawing o f t h e moleoule  59  6  3  16  Packing diagram; view along c  64  17  Hydrogen bonding; view along b  66  X  ACKNOWLEDGEMENTS  I wish to express my appreciation to Dr. J . Trotter f o r h i s constant Interest and encouragement during the course of this research. I also wish to thank Dr. J.K.N. Jones f o r the c r y s t a l samples used f o r this  thesis.  F i n a l l y , I would l i k e to thank the National Research Council of Canada which, i n the form of a Bursary and three Studentships during 1965-1969, has provided f i n a n c i a l support f o r t h i s work.  1  GENERAL INTRODUCTION Since 1913, when Bragg used i t t o determine the f i r s t c r y s t a l s t r u c t u r e , X-ray d i f f r a c t i o n has been used t o s o l v e many thousands o f s t r u c t u r e s .  The  t h e o r y and standard techniques o f the s c i e n c e of X-ray c r y s t a l l o g r a p h y , o u l m l n a t l n g i n a r e p r e s e n t a t i o n of a c r y s t a l i n terms of i t s e l e c t r o n d e n s i t y ( t h e " F o u r i e r " ) may be found i n any o f many standard r e f e r e n c e books on the  f i e l d , " " - * and w i l l 1  n o t be d e s c r i b e d here.  Standard  techniques now i n c l u d e n o t o n l y " t r i a l and e r r o r " methods and the P a t t e r s o n method but a l s o d i r e c t methods^ Although they have been s u c c e s s f u l l y a p p l i e d t o s t r u c t u r e d e t e r m i n a t i o n s i n non-oentrosymmetJ?rd  space groups,?  d i r e c t methods a r e by f a r e a s i e s t t o apply t o (and have i n the m a j o r i t y o f eases been a p p l i e d t o ) s t r u c t u r e d e t e r m i n a t i o n s i n oentrosymmetrlo space (and plane) groups. The s e r i e s o f t h r e e compounds whioh were s t u d i e d for to  t h i s t h e s i s were chosen because they l e n d themselves a v a r i e t y o f methods o f s o l u t i o n .  The two p e r t i n e n t  f e a t u r e s o f these compounds a r e t h a t 1. although the s t r u c t u r e s of a l l three belong to non-oentrosymmetric consequence  spaoe groups (as a n e c e s s a r y  of the f a c t t h a t they a r e o p t i c a l l y  active  non-raoemates), they each b e l o n g t o space groups having p r o j e c t i o n s as centrosymmetrlc plane groups, and t h a t  2  2. the structure of each has one short axis (of c i r c a 5 A) of projection along which i t can be assumed to have no overlap and to be e a s i l y  recognizable.  This thesis i s thus mainly concerned with the procedures of structure determination (of which the most important part i s that employing d i r e c t methods). Secondary  emphasis i s put on the actual c r y s t a l and  molecular structures of the compounds analysed.  The  most important feature of the o r y s t a l structures of the chlorinated carbohydrates i s the hydrogen bonding they contain.  Replacement of a hydroxy1 group with a chlorine  should not a l t e r the shape of the molecule (because of the s i m i l a r i t y of the s i z e of CI and OH).  Were e f f i c i e n t  packing the only consideration i n determining the c r y s t a l structure, a chlorinated carbohydrate would be expected to have the same structure as a non-chlorinated one. However, because of hydrogen bonding, replacement of a hydroxyl group removes one possible donor to a hydrogen bond with resultant a l t e r a t i o n of the c r y s t a l structure (e.g. methyl  4,6-dichloro-4,6-dideoxy-(X-D-glucopyranoslde  belongs to space C 2 , ^ while methyl belongs to P 2 2 2 1  1  1 1 1  oC-D-glucopyranoside  ).  This thesis i s divided into two parts.  The f i r s t  describes the structure analysis of the three chlorinated carbohydrates studied, which are (respectively)  3  methyl 2-chloro-2-deoxy- ot -D-galaotopyranoslde, methyl 4 , 6 - d l c h l o r o - 4 , 6 - d l d e o x y and,  <X.-D-gluoopyranoside,  methyl 4 , 6 - d i o h l o r o - 4 , 6 - d l d e o x y - oc -D-galactopyranoslde.  The second p a r t d e s o r l b e s the main programs w r i t t e n f o r s p e o l a l purposes  In these a n a l y s e s .  These Include a  c o l l e c t i o n of f o u r programs f o r g e n e r a t i n g s o l u t i o n s by d i r e c t methods, completely g e n e r a l f o r the p r i m i t i v e oentrosymmetrlc systems.  p l a n e groups  of the o b l i q u e and r e c t a n g u l a r  A l s o i n c l u d e d Is the t r i a l and e r r o r program  used f o r the methyl 2 - o h l o r o - g a l a c t o s i d e and a g e n e r a l program f o r c o n t o u r i n g the e l e c t r o n d e n s i t y g r i d s by the F o u r i e r summation program used by the X-ray Crystallography  group.  produced  PART I  THE STRUCTURE OF  THREE CHLORINATED CARBOHYDRATES  4  1. THE STRUCTURE OF METHYL 2-CHL0R0-2DEOXY- OL -D-GALACTOPYRANOS IDE Introduction The  compound analysed below was  prepared by  chloro-  12 m e t h y l a t l o n of a 3,4,6 used was  t r l - 0 - acetyl-hexal.  The  a sample of D - g l u c a l which can y i e l d  p o s s i b l e p r o d u c t s ! the oc and deoxy-D-gluoopyranoslde and  hexal  four  j8 anomers of methyl 2-chloro-2the  ot and ft anomers of methyl  2-chloro-2-deoxy-D-mannopyranoside.  A c r y s t a l of the pro-  duct i s below, however, shown to be composed predominantly of methyl 2-chloro-2-deoxy-«-D-galactopyranoslde (although the /$ anomer i s a l s o p r e s e n t ) .  The  r e a c t i o n performed  the hexal should not i n v e r t the c o n f i g u r a t i o n at C(4) only d i f f e r e n c e between a g l u c o s i d e Only i f the s t a r t i n g m a t e r i a l  and  i n the D - g l u c a l  r e s u l t s be e x p l a i n e d .  The  (the  a galactoside).  i s D-galactal  p r e s e n t as an i m p u r i t y  on  (possibly  sample) can  the  proposed r e a c t i o n i s RATIO  O-fcOAc  I.CHUDROMETHYlr ATfON 2.DEACETYLATI0N  H  Experimental Crystals are o d o u r l e s s plates elongated along b. The c r y s t a l ohosen had dimensions 1.0 x 0.5 x 0.1  mm.  Unit c e l l and space group data were determined from r o t a t i o n and Weissenberg photographs  (CuK«).  CRYSTAL DATA ( \ , CuK«= 1.5418 A) Methyl 2-chloro-2-deoxy- oc-D-galaotopyranoslde C  7 13°5 » H  C 1  M  Orthorhombio U =» 959.7 A3  "  2 1 2  •  7  t a « 29.57 * 0.05, b - 6.92 ± 0.03, c • 4.69 * 0.02 A.  Dm = 1.45 gm/oc ( f l o t a t i o n i n carbon tetrachloridebenzene). Z m 4, D - 1.470 gm/co. 0  Absorption c o e f f i c i e n t f o r X-rays, ^(CuK*) » 35.1 cm P(000) - 448 Absent spectra  h 0 0 when h = 2n + 1 0 k 0 when k = 2n • 1  Space group i s 22^ 2  1  2 (D^)  The i n t e n s i t i e s of the reflexions were measured on a General E l e c t r i c XRD - 5 manually operated spectrogonlometer with a s c i n t i l l a t i o n counter.  CuK r a d i a t i o n was used a  together with a N l - f l i t e r and pulse-height analyser. Of 662 reflexions with 2<9(CuK«. ) - 119.48 (minimum interplanar spacing O.89 A), 278 whose net i n t e n s i t i e s (corrected f o r background) were less than 50 counts, (maximum counts 56470 f o r (1 0 1)) were c l a s s i f i e d as "unobserved" and were included i n the analysis with  F  Q  = 0.6 F (threshold).  The c r y s t a l was mounted with b p a r a l l e l to the ^ - a x i s of the goniostat.  A general background correction was made  6  f o r eaoh r e f l e x i o n (scanned f o r h(2 6) * 2°) w i t h s p e c i a l treatment g i v e n  t o r e f l e x i o n s o c c u r r i n g on s t r e a k s of  lower order r e f l e x i o n s .  L o r e n t z and p o l a r i z a t i o n f a c t o r s  were a p p l i e d , and the s t r u c t u r e amplitudes Structure  derived.  Analysis  a. Two Dimensional (xy) s o l u t i o n and refinement The  three-dimensional  Patterson  function  presents  two  p o s s i b l e c h l o r i n e atom p o s i t i o n s , one a t (0.05,0,0),  and  the other a t (0.167,0,0.10), each appearing t o be  equally l i k e l y positions.  Due t o the shortness  of the  z - a x i s , the mean plane o f the molecule can be expected t o l i e approximately p e r p e n d l o u l a r  t o z.  A model o f methyl  2-ohloro-2-deoxy-or-D-mannopyranoslde, t h e proposed c o n s t i t u e n t of the c r y s t a l i n v e s t i g a t e d , was used t o o a l c u l a t e approximate r e l a t i v e p o s i t i o n s i n p r o j e c t i o n , of a t l e a s t 11 o f the 13 atoms.  Radial coordinates  (r, d)  of the 6 carbons and 4 oxygens i n the model used ( a rough diagram o f which f o l l o w s ) were c a l c u l a t e d u s i n g  chlorine  as the o r i g i n , a s s i g n i n g C(2) a l v a l u e c l o s e t o 0.0, and  a s s i g n i n g the c l o c k w i s e  values  of 6 . atom  0(1) 0(3) 0(4) 0(5) 0(1) C(2)  S?! !l! C(6) C  C(4) c  d i r e c t i o n to increasing  The r a d i a l c o o r d i n a t e s r(A)  3.0 2.7 4.9 3.94  2.64  1.70 2.66 4.10 4.5 5.8  o f the eleven atoms a r e i  ^(radians)  +1.005 -0.930 -0.459 +0.302 +0.482 -0.026 -0.457 -0.300 +0.017 -0.026  7  A program (ROT;  see Appendix) was written which  would rotate the non-chlorine atoms about a given fixed p o s i t i o n f o r a chlorine, s t a r t i n g with ®  at 0 with the  C l ( 2 ) - C(2) bond p a r a l l e l to the y-axis.  This program  uses the p r o j e c t i o n data, F(h k 0), to calculate the discrepancy value, R, f o r d i f f e r e n t values of 9 , as the model Is rotated clockwise about the chlorine by small increments  through 2JI radians.  The meaning of the  various parameters referred to above i s best i l l u s t r a t e d by a diagram (Figure 1) which follows. The r e s u l t s , on 76 reflexions of highest i n t e n s i t y , f o r the two possible chlorine atom positions are shown l n Figure 2, as plotted by the program. The minimum value of R, 0.480, with C l at (0.05,  0.0)  occurred f o r & equal to 0.855 (angles between J C and 3TC/2 need not be considered as f o r those values, the molecule l i e s on a two-fold a x i s ) .  Seven cycles of refinement by  the method of l e a s t squares on a l l two dimensional data resulted l n the following reductions i n the R-value: 0.594 ( i n i t i a l ) , 0.526, 0.483, 0.461, 0.446, 0.433. 0.412, and 0.391.  As 0(3), 0(4), C(3) and C(5)  s t i l l had large  p o s i t i v e s h i f t s (~ 5«0) Indicated to already large values of thermal parameters ( B » 7 . 0 ) , these atoms were deleted from a Fourier summation.  The peaks on the Fourier  apart from those corresponding  map,  to the atoms used i n the  phasing, bore no recognizable r e l a t i o n to a carbohydrate molecule.  8  t  X F i g u r e 1.  Approximate r e p r e s e n t a t i o n of model used f o r r o t a t i o n program (ROT).  Cl at (0.167, 0.00)  Figure  2.  Results  f o r two  p o s s i b l e c h l o r i n e p o s i t i o n s as R versue Q p l o t s .  10  The minimum v a l u e o f H, 0.499, w i t h the c h l o r i n e atom a t (O.I67, 0.0) occurred  f o r <& equal t o 4.175.  Seven c y c l e s o f refinement by l e a s t squares, a g a i n on a l l two d i m e n s i o n a l d a t a , r e s u l t e d i n the f o l l o w i n g reductions  0.590 ( i n i t i a l ) ,  In the R- v a l u e i  0.492, 0.467, 0.449, 0.430, 0.415, and 0.402.  0.532,  Now  however, only 0(4) and 0(1) s t i l l had l a r g e p o s i t i v e shifts  (~ 7,0)  Indicated  parameters ( B « 6 . 0 ) .  to l a r g e values of thermal  A F o u r i e r summation based on t h e  c a l c u l a t e d phases o f t h e remaining nine atoms c l e a r l y i n d i c a t e d the a c t u a l p o s i t i o n s of the excluded atoms. The p o s i t i o n , i n p r o j e c t i o n , of 0(4) needed t o be s h i f t e d by 0.7 A, and t h a t of 0(1), by 1.3 A. summations p l a c e d  Further  Fourier  a l l t h i r t e e n atoms.(The atom which had  p r e v i o u s l y been l a b e l l e d 0(1) became C(7).  Five  cycles  of l e a s t squares refinement ( a p p l y i n g a f t e r each c y c l e only 50% o f the i n d i c a t e d s h i f t s ) r e s u l t e d i n the following reductions  0.283 ( i n i t i a l ) , 0.226, 0.203,  i n Rt  0.189, 0.182, O.I76 As the C(4)  to C(5)  distance  i n p r o j e c t i o n was  1„64 A, an attempt was made t o r e d e f i n e the p o s i t i o n s of the two atoms i n v o l v e d by a F o u r i e r summation from which they were excluded.  The f i n a l f o u r c y c l e s o f l e a s t  squares refinement (each atom was g i v e n an i n i t i a l  tem-  p e r a t u r e f a c t o r B, of 4.0 A ; 50# of the c a l c u l a t e d 2  a p p l i e d a f t e r each c y c l e ) gave a f t e r each c y c l e , the  shifts  11  f o l l o w i n g B- v a l u e s i 0.337 ( i n i t i a l ) , 0.262, 0.202, and 0.189.  The C(4) to C(5)  and no o t h e r bond was  d i s t a n c e was  now  1.52  A,  l a r g e r l n p r o j e c t i o n than I t s  expeoted v a l u e l n t h r e e  dimensions.  b. Three Dimensional Refinement The only model which c o u l d s u c c e s s f u l l y be onto the two d i m e n s i o n a l r e f i n e d s t r u c t u r e was  fitted  one i n  which C l ( 2 ) and 0(4) were i n v e r t e d w i t h r e s p e c t to mannoslde proposed  as the c o n s t i t u e n t of the o r y s t a l .  the z - c o o r d i n a t e of C l ( 2 ) i s known, only two  possible  s o l u t i o n s e x i s t , which are r e l a t e d by r e f l e x i o n the plane z = z ^ .  Least-squares  the two p o s s i b i l i t i e s .  P.4-57  0.419, and 0.412; the second y i e l d e d * 0.290  to  c a r r i e d out  The f i r s t y i e l d e d f o r two  c y c l e s , the f o l l o w i n g v a l u e s of R i  0.243, and 0.222.  through  refinement o f the tem-  p e r a t u r e f a c t o r s , s c a l e , and z-ooordinates was for  (initial), (initial),  When a l l the c o o r d i n a t e s were allowed  s h i f t , the R- v a l u e f o r the second p o s s i b i l i t y  reduced to 0.192  As  was  i n two f u r t h e r o y c l e s of refinement.  The d a t a had o r i g i n a l l y been mounted w i t h "minimum o b s e r v a b l e " i n t e n s i t y as 50 counts 56470 f o r 1 0  1).  (maximum recorded  Any r e f l e x i o n which has a net  was  intensity  of  l e s s than 50 would be excluded from the c a l c u l a t i o n  of  R.  As l t was  felt  that t h i s value excluded too many  r e f l e x i o n s , the counter d a t a was  again processed reducing  12  t h i s value to 9, and at the same time adjusting  the  readings of nine reflexions which on the basis of Weissenberg f i l m s appeared to have values very d i f f e r e n t from those o r i g i n a l l y estimated from the counter. the 662 r e f l e x i o n s recorded, 578  {&7%) were now  Of  classi-  f i e d as observed with the remaining 84 c l a s s i f i e d as unobserved.  As the solution proposed above (except f o r  the inversion at the two centres) i s the enantlomorph of the correct configuration, subsequent work was c a r r i e d out on the above structure mirrored  through y • 0.  After  three cycles of refinement by l e a s t squares, the R- value was  0.26.  A Fourier summation with phases based on a l l  13 non-hydrogen atoms, was C(7)  carried out to t r y to relocate  and 0(1) which had temperature factors (7.7  respectively) higher than was 0(1)  bond length of 1.16  very short).  expected.  and  (Also the C(l) -  f o r the refined structure  In t h i s Fourier map  C(7)  and 0(1)  was  appeared  i n the refined positions with maximum density of 4.2 and 7.0  e/A^,  respectively.  However, 0(1) was  extended i n the z-direotion, enough so that two maxima occurred OMe  and a  ^-OMe  6.8  e/A^  greatly distinct  i n that d i r e c t i o n and that both an ocgroup could be postulated as  to the r e s t of the pyranose r i n g . temperature factors B • 7.0  Two  0-Me  attached  groups (with  f o r each atom) were introduced  into the structure factor c a l c u l a t i o n , the oxygens separated i n the z-directlon by approximately 2/5  c» the carbons by  approximately 1/4 c (the oxygens were also s l i g h t l y  13  displaced  In y - d l r e c t i o n ) .  A f t e r one  c y c l e of refinement,  the H- v a l u e was  reduced to 0.218.  f a c t o r s on  group were, however, l a r g e r than, those  on the for  one  the  o i - group.  When each group was  (100%  cycle  The  of the  temperature  tried  separately  i n d i c a t e d s h i f t s to the  thermal  parameters were a p p l i e d ) , the r e s u l t s were  The  OC-groups  R- v a l u e s 0 . 2 5 5 ( i n i t i a l ) , 0.244 ( f i n a l ) f i n a l temperature f a c t o r s f o r C and 0, 8.9 and 9.4 r e s p e c t i v e l y .  ^-groups  R-  tf-group  values 0.294 ( I n i t i a l ) , 0 . 2 8 5 ( f i n a l ) f i n a l temperature f a c t o r s f o r C and 0, 11«4 and 9 . 9 r e s p e c t i v e l y .  gave b e t t e r agreement but  the problem p e r s i s t e d ,  e s p e c i a l l y a f t e r a F o u r i e r summation w i t h the phases of only the  ten atoms ( d e l e t i n g C ( l ) , 0(1) oC-group  weaker.  The  t i o n o f the 20C i lf3  and ^ - g r o u p  .  and  C ( 7 ) revealed  a l t h o u g h the l a t t e r was  somewhat  b e s t f i t to the data appeared to be a combinatwo  structures  i n the approximate r a t i o  Subsequent r e f i n e m e n t s were c a r r i e d out  postulated  s t r u c t u r e c o n s i s t i n g of 2/3  the o p p o s i t i o n  and 1/3  0(1)  - C(7)  0(1)  following reductions  In the R-  0.211, 0.201, 0.189, 0.185, and  i n t o two  0(1)  and  positions  C ( 7 ) » and  on  a in  i n the /-> p o s i t i o n .  valuer 0.183.  thermal parameters were i n t r o d u c e d  of  - C(7)  F i v e c y c l e s of l e a s t squares refinement produced  excluding  both  0.232  (initial),  When a n i s o t r o p i c  f o r the  C ( l ) which was  separated by 0.5 A,  the  and  ten -atoms separated the  scale  changed s l i g h t l y , f i v e c y c l e s of b l o c k - d i a g o n a l l e a s t squares refinement on a l l parameters, except those of  C ( l ) , resulted i n theae reductions i n the R- valuet 0.189 ( i n i t i a l ) , 0.176, Q.I68, 0.1#*> 0.14*, and 0.147. The weighting scheme which was  f o r the refinement of  t h i s structure and others i n %Hl8 thesis assigns Vw = 1 when ]P | £ P«, end TSF » P»/J^ when |p | > P«. For the 0  0  f i n a l stages of the ref lne»#jit P* was here given a value of 6.0. A f i n a l difference Fourier synthealB showed only random f l u c t u a t i o n s , gen«r*lif botween 0.3 e/A3 and -0.3 e/A^  9  the maximum value att&lAedV being 0.6 e/A-V  One  very encouraging sign f o r the eprreotness of the above refinement was that r e f l e x i o n 0 0:1, a f t e r the refinement of the structure whiohineittde^ only an of- OMe group, had |Po| / (Pol as 52.4/9.7• w h i l i *f.tijp feflneoient of the f i n a l mixed structure, had |Pol / |Po| as 43.7/41.2. P r i o r to the f i n a l computation  of structure f a c t o r s ,  the i n t e n s i t i e s of the reflexions with the worst agreement between observed and calculated Values of the structure factors were reestlmated using f i l m s .  The following  seven reflexions were then included with a revised value of i n t e n s i t y  f o r the r e c a l c u l a t i o n of observed structure  f a c t o r magnitudes which appear i n Table I i 0 2 2, 3 3 4, 1 2 0, 0 1 1 , 2 1 1, 2 3 1, and 10 1 2.  As these changes  are small and few l n numbers, they do not a l t e r the previous r e s u l t s or the f i n a l H- value.  The f i n a l posi-  t i o n a l and thermal parameter* jare given i n Table I I , the bond lengths and valency angles i n Table I I I , aad the shorter intermolecular distance* In Table IV.  15  Discussion a. M o l e o u l a r S t r u c t u r e and Dimensions The c r y s t a l s t r u c t u r e i n v e s t i g a t e d has been shown to be a mixture of an Of-galactoside and a ^ - g a l a c t o s i d e i n the approximate  r a t i o of 2 t l .  0(1)  and C(7) were  shown i n the refinement to occupy two d i s t i n c t (oC and ft ).  positions  In the a c t u a l c r y s t a l which c o n t a i n s a  mixture of the two  s t r u c t u r e s , i n s t e a d of the r e s t of  the atoms occupying the mean p o s i t i o n s i n d i c a t e d by the r e f i n e m e n t , they oocupy s l i g h t l y d i f f e r e n t depending  positions  upon whether the t e r m i n a l group i s OC or j3  •  T h i s group would a f f e c t the p o s i t i o n of C ( l ) most (and f o r t h i s reason,, C ( l ) was and 0(3), 0(4), and 0(6)  separated i n t o C ( l ) and least  0(1*)  ( e s p e c i a l l y as these are  hydrogen bonded among themselves). The c o n f o r m a t i o n of the moleoule F i g u r e 3 In p r o j e c t i o n along c.  The  group appears w i t h s o l i d l i n e s , the group appears w i t h broken l i n e s .  i s shown i n c*(C(l)-0(lHC(7))  y5(C(l«)-0(l*)-C(7*))  Both the OC-anomer and  the ^-anomer have a c h a i r form pyrahose r i n g on which the s u b s t l t u e n t s have conformations ft Ile2e3e4a5e).  The packing of the molecule  u n i t c e l l i s shown In F i g u r e 4.  i n the  The bond l e n g t h and  the v a l e n c y angles In the moleoule Table I I I .  (ottla2e3e4a5e;  are given i n  The v a l u e s f o r the C(l)-0(1)-C(7)  and  C.(l* ) - 0 ( l * )-C(7 ) group have been i n c l u d e d but w i l l l  l e s s a c c u r a t e than the r e s t .  be  The range of the carbon-  carbon d i s t a n c e s (not i n c l u d i n g those i n the t e r m i n a l  18  group) i s 1.48 - 1.60 A (o-= 0.02), w i t h a mean v a l u e of 1.52 (0-= 0.01) w h i l e t h e range f o r the C-0 d i s t a n c e s ( a g a i n e x c l u d i n g those i n the t e r m i n a l group) i s 1.40 1.45 A ( cr= 0.02), w i t h a mean v a l u e of 1.42 A (0" = 0.01). The v a r i a t i o n In v a l e n c y angles  (not i n c l u d i n g  those  i n v o l v i n g atoms of the " t e r m i n a l " group) i s from 104° to 114°  (0"= 2°) w i t h a mean v a l u e of 110.5°. The  standard d e v i a t i o n s quoted  above are those  e s t i m a t e d from the i n v e r s e s o f t h e d i a g o n a l elements of the m a t r i x o f the normal equations used t o c a l c u l a t e to parameters i n the l e a s t squares refinement.  A block  d i a g o n a l m a t r i x i s used t o approximate the c o r r e c t matrix.  shifts  full  Estimates o f t h e standard d e v i a t i o n s tend to be  too low i n such an approximation beoause of the n e g l e c t of the I n t e r a t o m i c i n t e r a c t i o n s . which Is a m i x t u r e ,  Also, f o ra structure  the parameters r e f i n e d f o r each atom  (except 0(1) and C(7) which a r e separated i n t o d i s t i n c t p o s i t i o n s ) g i v e the "average"  p o s i t i o n of each atom w i t h  the p o s s i b i l i t y t h a t the bond l e n g t h s and angles may not correspond  t o e i t h e r molecule  In p a r t i c u l a r .  b. I n t e r m o l e c u l a r d i s t a n c e s and hydrogen All  bonding  i n t e r m o l e c u l a r d i s t a n c e s l e s s than 4.0 A were  c a l c u l a t e d and those l e s s than 3.6 A a r e i n c l u d e d i n T a b l e IV.  The t h r e e s h o r t e s t approaches t h a t occur  correspond  t o p o s s i b l e H-bonds between the t h r e e atoms  0 ( 3 ) , 0(4) and 0 ( 6 ) ,  F i g u r e 5 shows the arrangement of  20  atoms around the o r i g i n and shows these close approaches. Two hydrogen bonding schemes are possible, both of which correspond to a hydrogen bonding network which s p i r a l s along the z-direction.  The two aret  1. 0(4)-H (lower l e v e l ) . . . 0 ( 3 ) - H ( l e v e l of moleoule represented)...0(6)-H...0(4)-H... 0(3)-H (higher l e v e l ) . . . e t c 2. 0(4)...H-0(3)...H-0(6)...H-0(4)...H-0(3). If the bonding hydrogens are located between oxygens then the successive H-O-C  angles f o r the two schemes  would be 1. 141° - 122° - 119° - 1 M ° - 122° etc. 2.  -  87° - 115° - 111'  0  -  87° etc.  Assuming that these angles tend toward the tetrahedral angle  (H-O-H i n water i s 105°, i n ordinary i c e 0*-0-0"  i s tetrahedral), the second scheme i s the most probable one. Only two other short approaches oocur, C ( 7 ' ) - 0 ( l * ) ? a distance of 3.09 A and 0(4)-C(3)» a distance of 3.15  A.  The former separation involves the j8-group whose p o s i t i o n i s poorly defined; the l a t t e r arises as a consequence of the hydrogen bond of 0(4) to the oxygen attached to C(3) ( i . e . 0(3))  and corresponds to a van der Waals separation.  21 TABLE I Measured and c a l c u l a t e d s t r u c t u r e amplitudes (x 10). Unobserved r e f l e x i o n s have P » -0.6 F ( t h r e s h o l d ) . 0  B47 590 10?  612 17J 243 350 167 230 467 230 595 140 <»U 2H  475 120 1T7 1 73 1b2 1 tt9  133 19B 776 159  313 645  30 352 552 LIS 147  425 904 290 518 215  [A 7 10* 155  2?? . 1S7  459 251 366  551 15*. 176 354 15* 2J9 429 265 614  146 104 100  22  TABLE I I FINAL POSITIONAL PARAMETERS ( f r a c t i o n a l ) . ISOTROPIC THERMAL PARAMETERS ( A ) . AND ANISOTROPIC THERMAL PARAMETERS 2  (exp - { b h  2  n  + b  1 2  hk + b-^kl + b  2 2  k  2  + b^kl+  \>^l ]) Z  f  t o g e t h e r w i t h estimated standard d e v i a t i o n s i n p a r e n t h e s i s , r e f e r r i n g t o t h e l a s t decimal p o s i t i o n s o f r e s p e c t i v e v a l u e s . Atom Cl(2) C(2) C(3)  C(4)  0(5) C(6) 0(3)  0(4)  0(5) 0(6)  C(7) 0(1)  C(7?)  0(1«) C(l) c(i«)  y  z  0.1665(2)  -0.0036(7)  0.0952(13) 0.267(4) 0.082(3) 0.253(4) 0.343(4) 0.523(3) -0.001(2)  0.1329(4)  0.0948(5)  0.169(2) 0.233(2)  0.0665(3) 0.0448(3)  0.700(2) 0.077(1) 0.299(1)  0.0661(5) 0.0969(5) 0.0739(5) 0.1330(4)  0.0388(3) 0.2192(8)  0.1858(4)  0.2315(12) 0.1944(8)  0.1650 0.1564  0.39K2) 0.548(2)  0.481(2)  0.797(2) 0.526(5) 0.401(2) 0.501(6) 0.314(4)  0.317 0.336  11  Cl(2) C(2) C(3) C(4) C(5) C(6) 0(3) 0(4) 0(5) 0(6)  B  X  P  0.007(2 •0.004(2 0.002(2 0.006(1 -0.0014(9) 0*002(2 -0.0011(11) -0.003(2 0.004(2 •0.0009(15) -0.0003(13) .0.0005(17) -0.0013(9)  -0.0014(9)  0.282(6)  0.185(4) 0.415(8) 0.530(6)  0.436  0.343  13 "12 0,00218(6) 0,0018(5) 0;006(1 0.0013(1) -0.0010(12) 0.006(2 0.0024(2) •0.0013(14) •0.002(2  0.0019(2) 0.0017(2) 0.0024(2) 0.0019(1) 0»0018(1) 0.0022(1) 0.0017(1)  0.497(2) 0.516(2) 0.385(3)  p  22  Oi032(1 0.019(3 0.021(3 0.019(3 0.017(3 0.029(4 0.020(2 0.024(2 0.025(2 0.025(3  7.83(15)> 4.6(4) 6.1(5) i 5.7(4) 4.6(4) 6.0(4) 5.3(3) 5.K2) 5.9(3) 6.3(3) 7.4(6) 5.9(3) 4.6(8) 5.4(6) 5.0 5.0  33 •2? .126(4) •0.013(5) 0 -0.007(11)0 .074(8) •0.042(9) 0 .069(8) •0.009(11)0 .068(9) 0.025(10)0 .086(9) •0.001(13)0 .049(7) 0.011(7) 0 .069(5) •0.021(8) 0 .063(5) •0.006(10)0 .070(5) •0.005(10)0 .103(7)  23 TABLE I I I BOND LENGTHS AND VALENCY ANGLES D(1J)  1 Cl(2) 0(1) 0(1M 0(1) O(l') 0(3) 0(4) 0(5) 0(5) 0(5) 0(6) C(l) C(l«) C(2) c(3) C(4) c(5)  C(2) C(l) 0(1") C(7) C(7») C(3) C(4) C(l) C(l») C(5) C(6) C(2) C(2) C(3) C(4) C(5) C(6)  1.75 A 1.45 1.43 1.39 1.78 1.42 1.45 1.52 1.46 1.42 1.40 1.61 1.40 1.49 1.60 1.48 1.51  (distances not Involving 0(l«),C(lM,or C(7M  1  k  C(l) C(l«) C(2) C(2) 0(5) 0(5) 0(5) 0(5) C(l) C(3) C(2) C(4) C(3) C(5) C(4) 0(5) C(5) C(l) c(i«) c(l) C(l») C(2) C(3) C(4)  0(1) 0(1' ) C(l) C(l« ) C(l) C(l« ) C(l) C(l» ) C(2) C(2) c(3) c(3) C(4) C(4) C(5) C(5) C(6) 0(5) 0(5! C(2) C(2) c(3) C(4) c(5)  C(7) C(7M 0(1) 0(1») 0(1) 0(1») C(2) C(2) Cl(2) Cl(2) 0(3) 0(3) 0(4) C(4) C(6) 0(6) C(6) c(5) c(5) C(3) C(3) C(4) C(5) 0(5)  Angle (1.1k) 106.5° 102.9 96.1 117.4 99.5 96.1 103.2 118.3 109.2 111.4 112.2 110.2 109.1 111.2 113.2 104.5 114.4 125.0 105.5 122.8 106.2 108.3 108.6 112.6  0* = .02-0.03 (angles not Involving 0(1»),C(1«), or C(7») C » 2°  TABLE IV SHORTER INTERMOLECULAR DISTANCES  0(5) C(7') 0(1M 0(4) 0(5)  Yl  i  0(1)  II VI II II II V IV III V II III IV III V  O(l')  Cl(2) C(3) C(3) 0(6) 0(3) 0(3) 0(4) 0(3) 0(3) 0(3) 0(4) 0(6)  C(4)  C(6) C(6) C(6)  0(4)  0(6) 0(6) 0(6) 0(4)  ( 3.6A) D(X*-Y*)  3.55 A 3.09 3.54 3.15 3.36 3.42  3.44 3.59 3.51 2.89 2.78 3.56 3.52 2.61  Symmetry Code I  x  y  z  II  x  y  z + 1  III  x  y + 1  z  IV  x  y + 1  z + 1  25  2.  THE CRYSTAL AND MOLECULAR STBUCTUBE OF METHYL 4.6-DICHL0R0-4.6-DIDEOXY- oc - D ~ ~ GLUCOPYRANOSIDE !  Introduction Methyl 4 , 6 - d l o h l o r o - 4 6 - d l d e o x y - o > D - g l u c o p y r a n o s l d e t  Is prepared by r e a c t i o n of methyl ot-D-galactopyranoside w i t h s u l p h u r y l c h l o r i d e , f o l l o w e d by d e s u l p h a t l o n . ^ 1  The r e a c t i o n goes as f o l l o w s t  ChfeOH  CH^CL  26  The present c r y s t a l s t r u c t u r e i n v e s t i g a t i o n of the compound was  undertaken w i t h three o b j e c t s i n v i e w i to examine the  use of d i r e c t methods of c r y s t a l s t r u c t u r e a n a l y s i s f o r non-centrosymmetrioal  s t r u c t u r e s ; to attempt  to measure  the a b s o l u t e c o n f i g u r a t i o n u s i n g the anomalous s c a t t e r i n g of the c h l o r i n e atoms ( f " = 0.7  f o r CuK  radiation);  a  t o o b t a i n f u r t h e r d e t a i l s of the geometry and of carbohydrate molecules. r e a d i l y determined  and  dimensions  S i n c e the s t r u c t u r e  was  from the P a t t e r s o n f u n c t i o n the  first  o b j e c t has not been pursued, but the s t r u c t u r e and a b s o l u t e c o n f i g u r a t i o n have been  determined.  Experimental C r y s t a l s of the compound (from  chloroform/petroleum  e t h e r ) a r e c o l o u r l e s s p l a t e s , elongated along b, w i t h developed.  U n i t c e l l and space group d a t a were  from r o t a t i o n and Weissenberg  photographs  (001)  determined  and on the  G.E.  spectrogoniometer. C r y s t a l data  (A, C u K  a  1.5^18  =  A; >, MoK = 0.7107 A) a  Methyl 4 , 6 - d i c h l o r o - 4 , 6 - d l d e o x y -  °7 12°4 2» H  C1  M  -  w  « =  231.1  m. 119-121°; fc^D = +122°(c,  1.9)  M o n o o l i n i o , a = 16.51 ± 0.03, b = 5.06 i 0.01 c = 13.16 ± 0.03 A, U = 991 A3 DJU = 1.5^  oc-D=glucopyranoside  ( f l o t a t i o n i n carbon aoetone)  n  0=  115.6  ~ o.l.  tetrachloride-  27  Z = 4, D = 1.55e.cm."3 c  A b s o r p t i o n c o e f f i c i e n t s f o r X-rays, «(CuK 58 cm." 1  p(MoK  a  P(000)  a  )=  r  ) = 6.4 cm."  1  =480  Absent s p e c t r a l h k l when h + k = 2n + 1 Space group i s C  Cm and C2/m being  Z ( C ^ )  excluded s i n c e the compound i s o p t i c a l l y a c t i v e . The  i n t e n s i t i e s o f t h e r e f l e x i o n s were measured on a  G e n e r a l E l e c t r i c XHD 5 Spectrogoniometer, using a s c i n t i l l a t i o n c o u n t e r , MoK* r a d i a t i o n ( Z r f i l t e r and p u l s e a n a l y s e r ) , and a 6-2& soan.  Of 810 r e f l e x i o n s w i t h  2#(MoK ) 6 4 7 ° (minimum i n t e r p l a n a r s p a c i n g , a  had  i n t e n s i t i e s greater  height  0.89 A ) , 544  than 1.5 times the background.  The  266 r e f l e x i o n s w i t h i n t e n s i t i e s l e s s than 1.5 times the background were c l a s s i f i e d as unobserved, and were i n the a n a l y s i s w i t h |P I 0  = 0.6 P ( t h r e s h o l d ) .  included  The c r y s t a l  was mounted w i t h b p a r a l l e l t o t h e j> a x i s of the g o n i o s t a t , and  had o r o s s - s e c t i o n 0.2 x 0.05 mm.;  t i o n s were a p p l i e d .  no a b s o r p t i o n  correc-  The i n t e n s i t i e s were c o r r e c t e d f o r  background (which was approximately a f u n c t i o n o f 8 o n l y ) , L o r e n t z and p o l a r i z a t i o n f a c t o r s were a p p l i e d , and the s t r u c t u r e amplitudes were d e r i v e d . Structure The  Analysis  c h l o r i n e atom p o s i t i o n s were determined from  the t h r e e - d i m e n s i o n a l P a t t e r s o n and  (0.125, 0.5, 0).  f u n c t i o n as (0.067, 0, 0.192)  A three-dimensional  electron-density  28  d i s t r i b u t i o n , computed w i t h phases based on the c h l o r i n e atoms (R = 0.48) had f a l s e m i r r o r planes a t y = 0 and but  t h e whole molecule was n e v e r t h e l e s s  and  coordinates  c l e a r l y indicated,  were o b t a i n e d f o r a l l non-hydrogen atoms,  except C ( l ) and C ( 6 ) , which were p o o r l y r e s o l v e d . second F o u r i e r summation r e v e a l e d two  atoms.  A  the p o s i t i o n s of these  The s t r u c t u r e was then r e f i n e d by l e a s t - s q u a r e s  methods, w i t h m i n i m i z a t i o n o f Sw(|F I D  Vw - 1 when J F | 6 0  - |F | ) , with 0  F», and *fw = F*/ | F | Q  A n a l y s i s o f t h e v a l u e s o f w( | F | 0  when |F | > F*. 0  |F I )* d u r i n g t h e O  course o f the refinement i n d i c a t e d F* = 25 as being appropriate. Tables  The s c a t t e r i n g f a c t o r s o f t h e I n t e r n a t i o n a l were used, without c o r r e c t i o n f o r anomalous d i s -  p e r s i o n , s i n c e the c o r r e c t i o n s radiation.  R, i n i t i a l l y 0.33, was reduced by f i v e i s o t r o p i c  c y c l e s t o 0.13 0.11.  a r e n e g l i g i b l e f o r MoK*  9  and by f i v e f u r t h e r a n i s o t r o p i c c y c l e s t o  At t h i s s t a g e , an ( F - F ) s y n t h e s i s 0  c  revealed the  p o s i t i o n s o f a l l t h e hydrogen atoms, except the three methyl hydrogens and the hydrogen bonded t o 0(2) [ i n f a c t the measured 0(3) - H(8) d i s t a n c e intermolecular  i s about 1.3 A i n an  0(3)...0(2) hydrogen bond o f l e n g t h 2.70 A,  so t h a t H(8) appears only s l i g h t l y c l o s e r t o 0(3) than to 0(2), and i t s exact l o c a t i o n i s doubtful] . c y c l e s of least-squares,  Two f u r t h e r  i n which the hydrogens were  i n c l u d e d but not r e f i n e d , completed the r e f i n e m e n t , the f i n a l R being 0.09 f o r the 544 observed r e f l e x i o n s .  29  The measured and f i n a l c a l c u l a t e d s t r u c t u r e f a c t o r s are l i s t e d  i n T a b l e V.'  S e o t i o n s of the f i n a l t h r e e -  d i m e n s i o n a l e l e o t r o n - d e n s i t y d i s t r i b u t i o n are shown i n F i g u r e 6, t o g e t h e r w i t h a drawing of the s t r u c t u r e . f i n a l d i f f e r e n c e map -0.6  e.A~^  A  showed maximum f l u c t u a t i o n s of  near the t w o - f o l d axes and the c h l o r i n e atoms.  The f i n a l p o s i t i o n a l and  thermal parameters are g i v e n  i n T a b l e V I , the bond l e n g t h s and v a l e n c y angles i n Table V I I , and the s h o r t e r i n t e r m o l e c u l a r d i s t a n c e s i n Table V I I I . Absolute C o n f i g u r a t i o n As a f i n a l step i n the a n a l y s i s the a b s o l u t e c o n f i g u r a t i o n of the molecule was  determined  by the anomalous d i s -  14 p e r s i o n method*, ^  S t r u c t u r e f a c t o r s were c a l c u l a t e d f o r  all  the h k l and h k l r e f l e x i o n s , u s i n g s c a t t e r i n g  for  the c h l o r i n e s of the forms f  - oi (f  F o r GxxKvradiation,  +  f  'ci»  f  0  +  1  - 0.3,  factors  o"i  f  f " « 0.7.^  Thirty-two p a i r s  of r e f l e x i o n s w i t h the l a r g e s t d i f f e r e n c e s between and  F (hkl) c  were chosen,  and  measured w i t h a s c i n t i l l a t i o n The c r y s t a l was circle perform hkl  c  the i n t e n s i t i e s were c o u n t e r and CuK  tt  radiation.  mounted about b, so t h a t w i t h a q u a r t e r -  o r i e n t e r i t was  n e c e s s a r y t o use two mountings t o  the measurements.  The  i n t e n s i t i e s of the h k l and  r e f l e x i o n s were r e c o r d e d , the c r y s t a l was  upside down, and  F (hkl)  remounted  the h k l and "hkl i n t e n s i t i e s were measured.  30  I ( h k l ) was taken as the average of the f i r s t two r e a d i n g s , 0  and I ( h k l ) t h e average o f the second s e t . 0  The r e s u l t s  (Table IX) i n d i c a t e (unambiguously, a p a r t from one r e f l e x i o n of those measured) t h a t the parameters used t o c a l c u l a t e the s t r u c t u r e f a c t o r s (those of Table VI r e f e r r e d t o a right-handed s e t o f axes) r e p r e s e n t the t r u e a b s o l u t e configuration.  A l l the diagrams d e p i c t t h e c o r r e c t a b s o l u t e  c o n f i g u r a t i o n o f D-gluoose. Discussion The a n a l y s i s has e s t a b l i s h e d the s t r u c t u r e and a b s o l u t e c o n f i g u r a t i o n o f methyl 4,6-dichloro-4,6-dldeoxy-  ot-D-  g l u c o p y r a n o s i d e , the molecule having the u s u a l c h a i r c o n f o r mation ( F i g u r e 6 ) .  The C-C bond d i s t a n c e s (Table VII) a r e  i n the range 1.50-1.55 A (0" * 0.04 A ) , mean 1.52^ A ((T« 0.02 A ) , and the range of C-0 d i s t a n c e s i s 1.39-1.44 A (0*= 0.04 A ) , mean 1.422 A ( <X « 0.02 A ) . The C - C l d i s t a n c e s a r e 1.75 and 1.81 A, mean 1.78 A (cr - 0.03 A ) .  None of  the i n d i v i d u a l bond d i s t a n c e s d i f f e r s s i g n i f i o a n t l y the mean l e n g t h s .  from  The mean d i s t a n c e s a r e s i m i l a r t o those  i n other p y r a n o i d s u g a r s . T h e  carbon v a l e n c y angles  w i t h i n t h e r i n g vary from 107° to 110° (0-* 2 ° ) , mean 108.6° (cr= 1 ° ) , and the angle a t 0(5)  i s 113°, perhaps s l i g h t l y  l a r g e r than the t e t r a h e d r a l a n g l e , as i s commonly found i n o t h e r sugars.X6 to 114° (cr= 2 ° ) .  <re e x t e r n a l angles a r e i n the range 106° n  31  0  1  Figure 6.  •  1  i  •  2  I  '  i_  3 I  i  4 L  5A  1  1  Superimposed s e c t i o n s o f e l e o t r o n d e n s i t y d i s t r i b u t i o n (contours a t 1 , 2 , 3 . ..e/A.I f o r C and 0 ; 1 , 5 , 1 0 . . . e / A ^ f o r CI) and a drawing of the m o l e c u l e .  32  The bond l e n g t h s and Valenoy angles i n v o l v i n g hydrogen (Table V I I ) have been determined l e s s p r e c i s e l y , and the methyl hydrogens and the hydrogen bonded to 0(2) have not been l o c a t e d *  The range f o r C-H bonds i s 0.9-l«3 A  ( 0 - « 0.3 A ) , and f o r H-C-X ( C * 17°).  angles (X * C, 0, or C l ) 9 2 ° - 128°  The average v a l u e s a r e 1.1  A and 109°, and the  d i f f e r e n c e s between i n d i v i d u a l v a l u e s a r e not s i g n i f i c a n t . The packing of the molecules i n the u n i t c e l l  (Fig.7)  and the s h o r t e r i n t e r m o l e c u l a r d i s t a n c e s (Table IV) i n d i c a t e the presence of one d e f i n i t e hydrogen bond, 0 ( 3 ) . . . 0 ( 2 ) = 1V  2.70  A, and a second p o s s i b l e bond, 0 ( 2 ) . . . 0 ( 3 ) IV  » 3.08  A.  T h i s l a t t e r d i s t a n c e l e however a t the extreme of hydrogen bond d i s t a n c e s u s u a l l y found ® (2.68-3.04 A ) . 1  a t 0(2) and 0(3) H(8) t o 0(3),  The angles  ( F i g u r e 8) support the assignment of  and the hydrogen bonding schemet ...OU  H...0(3) -H...0(2-^) -H...  The other i n t e r m o l e c u l a r  d i s t a n c e s correspond t o van d e r WasIs i n t e r a c t i o n s .  111  ) -  0  1  1 i  2 i  3  J  4  I  5A  1  KJ)  F i g u r e 7.  Packing diagram; view along b.  F i g u r e 8.  Hydrogen bonding; view along  35 TABLE V Measured and c a l c u l a t e d s t r u c t u r e amplitudes. Unobserved r e f l e x i o n s have * -0.6 F ( t h r e s h o l d ) .  h k I IEI E l 0 0 Q__ 0 0 0 D 0  o  0 0 0 0 2 2_  0 1 0 2 0 . 0 4 0 3 0 6 0 7 8 0 0 9 0 10 0 11 p |2 0 13 0 0 0. - 1 _ 0 0 2 0 -2 0 1 0 - J 0 « 0 -4 0 5 0 -5 0 0 -A 0 7 0 -7 0" B p -B 9 0 0 -9 ,0. 0 -10 0 11 0 -11 0 li 0 -12 0 -11 0 0 0 1 0 -1 2 6 0 -2 0 3 0 -3 0 0 -4 0 5 0 -5 0 0 -A 0 T 6 -T 0 e 0 -8 0 9 0 -9 0 10 0 -10 0 It 0 -11 0 0 -11 0 0 I 0 0 -1 0 2 0 -2 0 1 0 6 0 0 5 o" '-S~ A 0 -6 7 0 0 -7 0 a ' 0 -8' 9 0 -9  z -I 2  i i2  2 2 ' 2 2 2 2 .2 2 ' 2 2 2 2 • 2 ' 2 2 2 2 2 2 4  * 4~ .4  *  4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 6 o 6 6 . 6 6 6 6 6 6 6 6 6 6 6 6 6 6 &  _l$  -«  -i  15" fi  io.a  10.2 -4. a  -i.i  69.4 ...T.* A1.4 91.3 A9.9 -2.7 13.3 98.5 68.2 49.3 20.4 21.7 29.6 12.2 -3.3 16.4 -3.6 24.2 -3.9 9.6 -4.1 -5.0 -4.4  -5.6  -4.7 11.0 113.5 34.6 a.o 110.4 36.1 130.2 11.0 115.T -1.6 24.0 44.0 12.5 20.4 -1.3 -4.4 56.6 -4.7 52.4 -5.0 32.8 10.7 31.2 9.3 12.4 16.0 A2.4 16.4 30.9 54.2 10.1 26.2 -3.T 7.1 -4.0 60.2 15.0 1T.6 12.9 40.7 10.6 10.4 -5.0 -J.B 9.6 -4.1  a.a  IB.9 ..«»*. 12.0 106.4 BB.2 32.6 0.4 13.7 29.2 6.7 2.7 3.5 BO. 3 9.6 55.2 76.3 60.6  -u b o  A e" e  12 i  ; j > | :  ll12  ' •  12 12 12 12 12  U_. 12 12  12  U  12 12 12 12 14 14  *.l •  IT.4 90.6 55.9 40.6 20.6 23.3 25.7 12.4 6.3 17.7 4.8 21.1 4.4 .7.0 4.3 1.7 0.8 6.6 1.2 7.A 103.3 35.9 10.2 95. B 35.5 9.2 119.6 14.1 121.7 2.2 20.2 18.3 7.4 19.0 2.4 2.2 49. B S.t 90.1 2.5 29.0 9.1 12.1 7.2 12.1 16.0  U  14 14 14 14 14 14 14  • :  . ' . 1  . 14 14  , ; ' '.  H 14 14 16 16 16 16 16 16 16 16 16 16 16 16 14 16  .  ,  ii ia  .  18  ia ia  •  IB  IS l  • '  l  l I l l l i  ' . •  55.3  1 i i i" l i  '  j" 3 3 1 3 3 3" 3 3 3 1 3 3 } 3 3 1 3 3 1 3 1 3 3 1 5 5 3 5 5 5 5  '  5  11.T f  -  *b~  _.(L  -a  -9  6-io  0 -11 0 -12 6 - l l 0 0 0 1  ' '  -t  42.7  1 -11  1  -1  4  113.1 15. B 29.0 33.6 14.6 43.6 IB.9 51.7 16.1 22.5 21.5 21.6 10.4 9.1 11.1 -4.T 9.3 20.4 -4.8 -3.1 21.6 40.9 135.3 6.1 14.5 38. A 20. B 18.9 27.4 53.4 43.0 40.6 48.6 7.3 47.1 10.3 6.7 22.3 13. B -4.9 25.5 -5.2 29.1 20.0 -4.9 51.0 23.4 7B.7 . HW 31.9 55.0 31.9 11.0 51.9  21.3 8.3  tilt ,  11.5 10.6 7.0 29.8 . 4.3 ia.4 0.2 ' 60.7 9.0 12.3 6.1 4.B 32.6 11.2 4.4 24.5 4.8 0.6 0.9 29.4 15.1 ' 3.9 9.1 14.0 21.4  i n  3.9 9.a 16.1 1.1  :  e.i ,  4.9 0.6 3.5 7.1 2.1 3.7 4.5 2.8 6.4 6.3 4.7 8.6 6.a 6.3 3.1 3.0 , 6.2 8.2 3.6 2.1 8.1 8.5 16.2 89.4 119.2 80.6 27.2 #4,4 114.0 13.5 28.3 30.0 13.3 43.4 18.5 30.4 18.1 20.8 26.2 20.8 10.5 • 7.7 . 11.1 3.7 6.1  17.3  _i  a  ..  1 2  1  13.6 40.9 -4.4 24.0 19.0 22.6 21.9 19.6 -5.2 28.7  14.2 16.1 2.+ 22.6 ..(9,t 22.7 18.7 21.0  19.2 12.3  19.2 11.8 39.0 24.4 42.1 4.7  A2.B  24.6 43.3 -3.6  1  13 13  1 1  13  1-  to.o  16.6 36.1 '21.1 16.4 25.6 34.5 40.7 • 41.5 49.0 3.0 . 46.B • 12.5 . . U.6 20.0 11.6" 5.4 23.5 2.9 26.1 19.6 4.8 , 51.5 23.6 , 70.2 12.0 32.B 32.6 33.6 , 29.2 49.4  i.a  30.2  49.1 2 46.9 IB.A 1 19.8 21.7 3 21.6 IS.A 4 16.1 4 9.1 4.9 ' 5 41.4 41.7 92.7 5 99.3 6 22.1 21.8 36.0 6 40.2 1.2 7 -4.7 17.4 -7 17.1 7.4 0 . 10.2 3.5 : -a - 3 . 8 3.9 9 -3.2 21.3 9 22.6 10 26.4 24.2 22.8 11 21.1 12 16.9 15.6 11 -4.9 ' 1.2 . 0 29. B 2B.B IT.2 1 16.7 26.4 -1 23.3 10.7 2 15.1 -2 24.4 24.4 9.3 1 10.2 -3 16.5 13.0 4 26.3 27.4 12.3 -4 9.0 19.5 3 20.3 -3 32.1 12.1 6 • 16.6 1A.1 •6 24.9 2A.0 7 11.4 7.7 6.0 -7 -3.a 2.1 a -5.3 7.0 -a -3.9 4.2 -9 -4.1 10 9.6 10.0 11 19.3 16.4 12 -4.7 ?.b 13 9.0 7.8 0 -4.2 1.9 ' 15.8 1 17.3 -1 *.9 9.3 12.9 2 14.8 11.7 -2 13.2 7.0 1 0.5 43.9 -3 44.3 4 14.0 13.0 14.7 -4 11.2 A.9 4 11.3 -5 23.0 22.B 6 -3.3 9.3 -A 11.9 12.0 -7 -4.0 4.6 -B 20.0 20.1 -9 31.0 24.1 10 -4.4 6.2 ]1 9.4 10.9 12.3 12 12.4 14.5 11 17.6 0 15.9 17.9 1 22.6 14.6 -I 13.4 12.7 3.2 2 -4.9 3.1 -2 -4.3 3 9.3 2.7 9.1 -3 -4.3 4 -5.3 3.7 19.B -4 18.6 -5 26.9 27.5 -A ' 2 1 . 4 ' 23.3 20.7 -7 21.1 13.1 -a. 1 2 . T IB.7 -9 18.0 5.1 10 -4.6 11 8.7 7.2 9.6 12 10.1 7.1 13 -5.1 0 13.1 9. 1 1 9.S 8.5 -1 13.2 14.6 2 -5.4 7.7 -2 -4.7 5.1 -1 16.A 15.0 -4 -4.6 3.1 18.9 -5 20.7 -* 13.2, 1*.7 -7 11.3 13.a A. 6 -4.7 -9 - 4 . 8 5.3 10 11.0 7.a 4.8 11 -5.0 8.0 12 -3.2 -2 -3.2 7.0 -3 10.4 10.1 4.4 -4 -5.0 -3 -5.0 2.2 -A -5.0 3.T -7 -3.0 2.5 12.5 -B 11.3 -9 -5.1 5.2 10 -5.2 5.2 65.4 1 51.3 59.3 ; 2- 20.6 22.0 A5.5 20.4 3 19.0 20.9 4 19.a 5 29.7 32.3 A 33.3 36.2 7 7.1 a.o 7.9 9 10.5 10.6 22.2 10 23.A 8 11 19.7 16.5 3.3 12 -3.1 0 71.0 63.4 . 32.7 1 35.B 9.2 . 7.08 66.6 ' 2 AO. 14.3 -2 12.9 3 14.T 15.1 41.9 -1 38.1 4 26.3 10.0 -4 21.9 26.0 5 25.7 24.5 -5 22.4 26.3 6 17.1 20.2 -6 7.9 11.6 7 25.0 _. " - - 2 _ -7 12.1 11.0 11.1 -a IA.A IB.l 26.7 9 26.8 9.1 11.0 -9 19.9  13  3.4 6.5 19. 8 35.0 119.T  . 13.1 M.I-..il' 13.54.  V  7 .7  e.a  b  L . J .  : .9 : 5 5 5 5 9 5 9 9 5 5 : 5 5 5 ' 7  18.4 -4.6 10*4 10.7 . ->.Q... 9.1 31.2 -5.2 17.0 -3.4 61.0 9.9 10.1 -4.3 -4.3 33.7  -3.0 24.5 -4.9 -4.6 6 - l 10.4 0 -2 28.8 19.1 0 3 0 -3 -4.4 0 -4 11.1 0 -5 13.2 0 -6 21.0 0 - 7 . 23. 5 -4.5 0 -9 11.1 15.3 0 -to 0 - 1 1 - -a - 4 . B 0 -12 12.0 0 -13 -5.2 0 0 -5.3 0 I -3.4 9.1 6 - i 0 -2 -4.9 0 -3 -4.B 0 -4 -4.B 0 -5 -4.8 0 -6 -4.8 -4.a 0 -4.8 o -a 0 -9 12.6 9.1 o -to 0 -11 -5.1 D -12 -3.2 0 -3 -1.1 0 -4 -9.2 0 -5 -9.2 0 -6 -3.1 0 —T -5.2 -9.2 o -a 9.5" 19.1 92.0 111.1 T8.0 23.9 1 -2  1 l l  1  t°  -1 2 -2 3 -3 4 -4 3 -5 6 -6 -7  1 l l l l  o.i  T  0 0 0 0 0 0 0 0 0 0 0 0 D 0  J  12.9 28.1 - 43.1 9.7 • 23.1 ' 3.6 12.2 0.2 57.4 13.5 1B.1 10.4 38.5 9.2 10.8 6.5 3.1  6.1 .' 33.4 19.6 22.2 9.7 10.7 • ' 9.6 9.9 1" - l 6 1.3 ' 0 -1 11.4 14.6 a 0 2 18.4 37.0 a 0 -2 " 65.0 61.5 0 1 28.6 2B.2 a 0 -1 59.9 59.7 a * u 22.1 26.3 o -4 -3.2 4.4 8 0 3 10.9 2B.1 0 -5 15.8 14". 6 a 0 6 9.4 6.2 B 0 -6 51.B 51.9 " B 6 17.t 17.3 0 -7 -3.6 2.3 a B 0 B 17.4 14.0 ' 55.0 51. A B~ 0 9 -5.3 6.3 a B 0 -9 B.O 9.2 0 -10 8 -4.1 0.7 B 0 -11 19.9 IB.7 B -12 17.3 16. 8 0 -11 6.1 a 10. a 0 0 24.1 23.7 IP 0 1 35.1 33.7 to 10 0 -1 15.9 la.t _JLP__ - P 2 8.6 7 9 10 0 -2 -3.6 2.3 10 0 1 8.0 6.9 0 3 10.3 13.0 10 10 0 28.0 24.4 10 3 . 6 2.9 0 -JO. .0 5 -4.6 7.2 10 0 -3 . 6.6 5.6 10 0 6 14.4 11.7 10 Q 3B.4 16.9 10 0 7 12.6 B.9 10 0 -T -3.B 1.3 20. A. _ 2 * . 9 J 9 . . . J>. 10 0 -4.1 6.T 10 0 -10 t8.7 19.1 0 -4.5 7.9 lo 0 -12 14. 1 14. 7 10 0 -13 -4.9 3.1 12__ _o_ __1*_..7_ 12 12.9 9.3 a l 6 6 b 8  0 -10 0 -12 0 -11 0 0  -I.) 23.A 94.6 16.2 12S.2 104.9 36.1 -l.T 14.7  -fl  r  17  0 0 . ,P_  a-  0 0 0 0 0 0 0 . 0 • 0 2 . 2 2 2 2  "  2 2 ' 2 2 2 2 2 , :  2 2 2 2  r 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2  i2  2 2 2 2 2 2 2 2 2  p2 i2 2  2  0  2  2  10  2  2  11  14.9 a.5 3.2  10.0 40.6 32.9 35.3 41.1 14.1 26.9 35.1 15.6 41.2 21.0  6.B IB.4 4B.7 34.4 42.4 13.6 25.6 14.6 13.7 46.7 21.3  4.5  23.2  44.0 11.7 12.9 -3.a -4.7  2T.1  A  8 3  a e  6  12 12 12 12 12 12 12 12 12 12 12 12 12 12 12  1  a.4  -f  a  13.7 9.9 -3.0  -5.0 19.9 -5.2 1T.B 17.7 -4.a 49.0 32.0 58.9 -3.8 49.7 13.0 10.2 16.9 42.7 24.7 22.5 19.9 28.5 -4.8 1B.4 9.1 11.5  2 - 8  -5.2  12.1 la.B 15.7 14.6 -3.9 10.i 17.B 34.2 ""' 17^9 2 1 26.6 47.5 2 - 3 2 4 10.1 25.0 2 - * Z 5 -4.7 21.a 10.0 14.0 10.4 19.7 11.9 31.5 18.2 9.9 -4.A 15.3 7.a 17.9 1A.1 -4.5 15.9 12.1 15.8 -4.9 1A.2 11.3 12.1 . r5-2 2B.0 -4.1 21.3 9.8 -4.A 12.2 IA.2 2 0 11.2 2 1 9.7 2 -1 9.0 2 2 -4.9 2 -2 -4.4 2 3 IS. 3 2 - 3 10.4 2 4 10.7 2 -4 7.8 2 - 3 -4.3 2 -6 1 A. 8 2 - 7 22.7 2 -B 9.2 2 -9 -4.6 2 -10 -4.7 -4.9 14.6 -5. 1 9. 5 -4.a -5.3 15.0 -4.7 16.4" -4.6 9.3 11.4 B.7 -4.8 11.1 -5.1 -3.2 -5.2 -5.1  "  "-s.r -5.0 15.2  12.1  10.3 -3.1  1  1  (  1 3 1 l i - l  10. 1  25.2  45.8 9.2 10.5 3.7 4.9 26.7 6.2 19.1 O.B 16.4 17.6 7.9 41.2 30.0 54.5 4.B 43.3  Si.4  11.2  1  11.0 ' 14.6 40.4 24.3 22.7 is.7 30.0  3  5  10.s  5  • 11 .  i i i  i  1.3 7.4 2.9" 3.9 ' 13.9 10.7 7.0 ».7 3.9 a.A 13.7  w.o 16.9  11.7 3B.1 " 13.4 ia.7 '  2.5  21.8  ti.a  A.l 23.1 4.1 16.1 .7 -7 .7.0 8 13.4 -8 19.2 9 4.2 16.6 -9 11.9 8.6 -10 8.8 6.5 3.0 1 -11 11 . _- 3 U..06 1 0 34.6 45.7 1 I . 14.7 13.8 3 -1 47.9 45.3 4.* 3 2 -3.4 1 -2 6,6 6.4 1 1 -4.0 7.9 1 -1 -3.7 2.9 21.2 » ' 4 2o.a 1 -4 11.4 13.5 » * 16.8 17.4 1-5 7.1 B.3 1 6 13.0 12.4 40.9 21.0 6 37.2 7 19.7 -7 12.0 14.7 11.5 i 8 13.6 i -a - 4 . i 1 •> -5.7 r.B '4.7 -10 9 4 .. 4 5 -- 5 1.9 -10 8.6 7.4 1 -11 -4.9 a.5 1 0 -3.9 1.5 3 1 9.0 11.0 1 -1 14.6 11.6 3 2 9.9 10.7 3 -2 57.3 52.3 3 1 37.4 35.7 1 -1 . 22.3 21.9 3 4 19.3 ia.9 1 -4 -1.9 8.3 1 3 10.2 9.4 3 -3 -1.9 7.2 1 6 6.7 a.8 1 -6 13.7 lA.a 1 7 -5.0 4.3 1 -7 26.6 27.1 1 fl 16.4 IA.0 1.-8 8.9 9.6 3 9 -5.4 9.1 3 -9 -4.5 2.4 3 -10 -4.7 6.7 1 -11 11.fl 9.4 1 0 22.6 20.5 1 t 14.1 13.5 3 -1 -4,0 7.6 1 2 -4.4 2.6 3 -2 -4.0 6.8 3 1 -4.5 6.2 3 -3 20.9 20.4 3 4 9.6 7.5 1 -4 35.9 15.0 4.1 8.5 3 -5 : - 4 . i 1 6 9.2 B.O 1 -A 1A.2 20.B 3 7 -5.3 A.l 3 -7 -4.3 1.9 3 -fl -4.4 8.2 3 -922.5 23.3 3 -10 9.7 9.4 3 -11 10.1 7.2 3 0 23.9 25.6 3 1 9.4 9.4 3 -1 11.7 11.7 3 2 11.4 11.2 3 -2 r4.2 6.1 3 1 -4.8 9.2 3 -3 20.4 20.6 3 4 U.2 10. A 3 -4 15.0 16.8 3 5 10.6 12.6 3 -5 40.540.7 3 6 -5.4 2.3 3 -614.3 17.1 3 -T -4.4 7.4 4.9 3_..r" -*.3 1 -9 -4.7 3.1 3 -10 12.5 12.6 1 -11 20.4 19.4 1 0 ,9.6 9.T 3 1 14;2 12.9 1 -1 11.9 11.0 3 2 -5.0 6.4 3 -2 -4.5 2.1 3.7 - 39.2 .2 3 - 33 9.1 3 4 -5.4 5.9 3 -4 14.2 15.0 1 -5 9.2 8.2 3 -6 8.3 7.B 3 -7 -4.A 4.B 1 -8 -4.T 6.3 1 -9 19.2 16.6 3 -10 9.1 4.5 3 -11 -5.1 1.4 1 0 9.5 a.4 3 1 -5.3 7.3 3 -1 9.0 6.1 1 -2 -4.9 4.3 3 -3 11.2 11.7 4.6 3 -5 11,2 12.7 -4 -4.8 5.4 -7 8.9 8.2 -8 14.1 1 t.O 3 -9 -5.0 9.5 -10 -15.1 4.6 -2 -5.2 6.6 -3 -5.2 6.7 -4 -S.'l 4.8 -5 -5.1 3.1 -A -5.1 4.9 -7 -J.2 6.8 -8 -5,2 8.5 0 23.9 22.3  i  3.3  It.2 33.3 19.6 23.4 45. B 19.1 24.8 7.5 21.0 9.5 15.4 a.3 18,7 9.9 30.5 20.2 13.2 2.7 14.2 7.0 20.1 17.0 A. 2 17.5 10.6 16.3 8.2 17.A 11.1 14.2 3.1 29.2 1.0 21.1 9.7 2.4 11.6 14,9 12.0 7.2 10.3 3.B 17.1 14.6 12.0 9.9 8.3 1.2 14.0 23.1 9.a 5.3 6.B 6.4 14.3 2.9 A.8 2.5 3.2 12.7 4.4 16. l " 7.2 11,0 12.1 ' 6.6 4.3 7.3 1.4  12.3 34.4 32.1 12.4 -4.0 19.1 10.0 -1.9 24.3 -4.0 lb.3 8.6 lb.6 1B.0 -4.8  -4.5 17.0 11.2 10.5 11.5 8.0  '1'3  U.l  i  19.6 10.2 11.2 14.3 17.6 17.1 13.6 5.5  2 -2 3 -3 4 -4 3 -3 6 -6  i  i2.7  " -sr. -3.2 17.9  1  1 3 3 3 1 1 1 1 1 1 1 1 3 3 1  0  h.  1  14.2 12.5 9.9 -4.9 ~=4.4 -5.0 10.4 —5.2 -S.2  11.0 9.S 6.0  36 TABLE V I FINAL POSITIONAL PARAMETERS ( f r a c t i o n a l ) . ISOTROPIC THERMAL PARAMETERS ( A ) . AND ANISOTROPIC THERMAL PARAMETERS 2  (exp - ( b h  + b  2  n  hk + b ^ k l + b  1 2  t o g e t h e r w i t h estimated  2 2  k  + b^kl + b^l )),  2  '33  2  J  standard d e v i a t i o n s i n p a r e n t h e s i s ,  r e f e r r i n g t o the l a s t decimal p o s i t i o n s o f r e s p e c t i v e values, X  Atom  Cl(4) Cl(6) 0(1) 0(2) 0(3) 0(5) cd) C(2) C(3) C(4) C(5) C(6) C(7)  C(l  C(2 c(3 C(4 C(5 C(6 C(7  ll  0.0052(3) 0.0090(4) 0.0044(7) 0.0052(9) 0.0053(7) 0.0053(7) 0.0047(10) 0.0048(10) 0.0040(9) 0.0035(9) 0.0043(11) 0.0068(14) 0.0061(12)  12  D  •0.006(3) 0.003(4) •0.001(6) •0.002(6) 0.004(6) •0.003(6) •0.001(8) •0.003(7) 0.008(6) 0.002(7) 0.005(8) -0.004(10) 0.010(9)  b  B  0.1968(6) •-0.0064(7) 0.3496(14) 0.4963(16) 0.4098(14) 0.1989(14) 0.3131(19) 0.3790(19) 0.3563(18) 0.2269(20) 0.1648(22) 0.0381(26) 0.3236(25)  0 o.o64i(5) 0.1209(6) 0.494(3) 0.3742(10) 0.032(6) 0.35*3 d l )> 0.387(6) 0.1633(12) 0.344(5) 0.2866(12)1 0.313(5) 0.3441(16] 0.293(7) 0.295*(17) 0.401(7) 0.2145(15) 0.235(6) 0.1548(15) 0.233(7) 0.2093(18) 0.141(8) 0.1583(22) 0.172(9) 0.4457(19) -0.052(10)  D  Cl(4 Cl(6 0(1 0(2 0(3 0(5  z  y  n  0.0053(5) 0.0073(7) 0.0056(12) 0.0038(17) 0.0066(13) 0.0062(12) 0.0047(17) 0.0052(17) 0.0050(15) 0.0038(18) 0.0032(21) 0.0065(25) 0.0101(22)  *  22  0.057(4) 0.061(4) 0.054(11 0.059(12 0.052(12 0.057(11 0.050(15 0.039(13 0.037(12 0.045(15 0.050(15 0.060(20 0.072(23  5.05(17) 6.59(23) 4.3(4) 5.0(5) *.7(5) *.*(5) 3.8(6) 3.9(6) 3.3(6) 3.7(6) 3.9(6) 5.*(8) 6.1(10)  b  2 3  *o. 002(3; o.oo3(4; .0.007(7; •0.008(8; 0.001(7; 0.005(7; 0.008(9 •0.005(8; 0.004(8; 0.003(9 •0.002(10) •0.007(12) •0.008(13)  b  33  0.0087(5) 0.0092(6) 0.0073(H) 0.0080(14) 0.0077(12) 0.0060(10) 0.0049(14) 0.0053(15) 0.0050(14) 0.0059(16) 0.0066(18) 0.0079(20) 0.0123(22)  37  Hydrogen p o s i t i o n a l parameters (B taken as 3.0 A f o r a l l hydrogen atoms). 2  Hydrogen atom  H(l) H(2) H(3) H(4) H(5) H(6) H(7) H(8)  Attached to  C(l) C(2) C(3) C(4) 0(5) C(6) G(6) C(3)  x  0.392 0.275 0.225 0.125 0.233 0.100 0.200 0.158  y  0.417 0.600 0.042 0.433 -0.017 0.000 0.117 0.150  z  0.325 0.358 0.375 0.208 0.167 0.033 0.000 0.467  38 TABLE V I I Bond Lengths and Valency Angles 1  i  Cl(6) Cl(4) 0(1) 0(1) 0(2) 0(3) 0(5) 0(5) C(l) C(2) c(3) C(4) C(5)  C(6) C(4) C(7) C(l) C(2) C(3) C(l) C(5) C(2) C(3) C(4) e(5) C(6)  tr  s  0.04 A  D(1.1) 1.75 A 1.81 1.43 1.42 1.43 1.42 1.39 1.44 1.52 1.50 1.55 1.53 1.52  1  J  01(4) Cl(4) Cl(6) C(6) C(6) 0(3) 0(3) 0(2) 0(2) C(7) 0(1) 0(1) 0(5) C(l) C(2) C(3) C(4) C(5)  C(4) C(4) C(6) C(5) C(5) C(3) C(3) C(2) 0(2) C(l) C(l) C(l) C(l) C(2) C(3) C(4) C(5) 0(5)  k C(5) c(3) C(5) C(4) 0(5) C(4) C(2) C(3) C(l) C(l) 0(5) C(2) C(2) C(4) C(5) 0(5) C(l)  Angle (i.1k) 107.9° 108.3 114.2 112.5 106.0 108.3 110.7 108.6 108.6 113.7 114.0 109.7 108.1 109.4 108.0 110.3 107.3 113.0  Bond Lengths and Angles I n v o l v i n g Hydrogens  1  3  H(l)  C(l)  1.0 A  0(1) | 0(5) C(2)  113° 105  H(2)  C(2)  1.1  |C ( l )  112  D(U)  Ic  C(3)  1.0  H(4)  C(4)  1.1  106  C(3)  109  C(2) |c(4)  117  0(3)  103 109  C(3)  105  C(4) | 0(5) C(6)  128  0(2)  H(3)  Angle ( l j k )  |C(5) Cl(4)  109  118 107  103  H(5)  C(5)  0.9  H(6)  C(6)  1.3  l(6) i Cc(5)  92 118  H(7)  C(6)  1.1  {Cl(6)  c(5)  109 108  H(8)  0(3)  1.3  C(3)  102  Mean  1.1  A  99  109°  TABLE VIII Shorter Intermolecular Distances X  Y  1  1  1  DU -! ) 1  0(2)  0(3)  III  2.70  0(2)  0(3)  iv  3.08  0(3)  0(2)  III  3.08  0(3)  0(2)  IV  2.70  0(2)  C(3)  III  3.17  0(3)  0(7)  V  3.31  C(2)  0(3)  III  3.40  0(3)  C(3)  III  3.*8  Cl(6)  C(6)  II  3.*9  C(2)  0(1)  II  3.53  Symmetry Code I II  •  x  y  z  X  y + 1  Z  _ ,I  .  1  _ , n  1  A  41  TABLE IX D e t e r m i n a t i o n of the Absolute C o n f i g u r a t i o n ( C u K r a d i a t i o n ) w  |P (hkl)l  2  c  h k l 110 111 112 1 1 4 115 1 1 11 3 10 3 15 3 11 3 1 10 5 12 5 12 5 1 12 7 15 7 16 7 1 10 9 10 9 15 9 16 11 1 8 0 2 0 0 2 1 0 2 10 4 2 2 6 2 5 8 2 3 10 2 9 12 2 7 12 2 12 11 3 1 4 4 3 4 4 4  |F (hkl)| 0  6.9 *5.3 17.7 15.2 6.0 2.1 10.4 27.6 62.4 12.3 68 27.1 10.2 44.6 17.5 12.1 16.5 10.9 13.3 9.9 30d 31.3 10.7 21.1 11.5 13.5 4.4 12.4 7.7 6.2 11.4 12.6 e  |F (hkI)| 0  6.3 43.* 15.9 13.7 5.* 1.5 11.7 28.8 64.2 11.2 7.4 24.7 8.9 46.5 16.4 13.4 15.5 9.* 14.4 10.7 32.9 28.9 12.0 22.8 10.4 12.5 5.1 11.4 7.1 6.9 10.4 13.5  |Fc(hkl)| 1.20 1.09 1.24 1.23 1.24 1.96 0.79 0.92 0.95 1.21 0.84 1.20 1.31 0.92 1.14 0.82 1.13 1.35 0.85 0.86 0.84 1.17 0.80 0.82 1.22 1.17 0.74 1.18 1.18 0.81 1. 20 0.87  I (hkl) Q  2  Io(hkl 1.11 1.09 1.30 1.18 1.09 1.44 0.67 0.93 0.91 1.24 0.83 1.18 1.16 0.97 1.15 0.91 1.14 1.26 0.88 1.02 0.85 1.13 0.84 0.87 1.22 1.09 0.85 1.23 1.04 0.73 1.08 0.86  42  The The  XZ P r o j e c t i o n o f the Gluooside by D i r e c t Methods  s e t of f o u r programs ( d e s c r i b e d  s o l v i n g centrosymmetric p r o j e c t i o n s were w r i t t e n  a f t e r the g l u c o s i d e  later) for  by d i r e o t methods  s t r u c t u r e had been  s o l v e d by t h e c o n v e n t i o n a l methods d e s c r i b e d  earlier.  However, the d i r e c t methods programs were t r i e d on t h i s s t r u c t u r e b o t h t o t e s t the i n i t i a l v e r s i o n s  o f the p r o -  grams and t o suggest a l t e r a t i o n s and a d d i t i o n s to them. the  The i n i t i a l r e s u l t s w i l l n o t be presented but  following  glucoside  to be made  i s a d e s c r i p t i o n o f a r u n made on the  XZ p r o j e c t i o n w i t h t h e programs i n t h e i r f i n a l  forms The  PREDIR program was r u n w i t h a l l the three-  d i m e n s i o n a l d a t a w i t h sin$/X placed  l e s s than 0.5 (596  i n t o 10 ranges o f s i n ^ / A .  A p r i m i t i v e c e l l was  assumed by f i t t i n g the d a t a t o a s t r u c t u r e 2 molecules i n the u n i t c e l l . first  reflexions)  c o n s i s t i n g of  The weights used f o r the  two ranges were 0.0 and 1.00 r e s p e c t i v e l y .  The s c a l e  c o n s t a n t found was 2.45, the average temperature f a c t o r found was 5.00, and the p r o b a b i l i t y c o e f f i c i e n t was 0.26.  CT}/^^ 2  The s t a t i s t i c s f o r the 596 r e f l e x i o n s a f t e r  s c a l i n g were (|E|) = 0.84, (|E( ) = 0.99. 2  |E(h»,0,l)|  where h* = h/2 were then put out on tape f o r those 66 r e f l e x i o n s where The  JEj^.1.0.  35 r e f l e x i o n s w i t h  ]E| £ 1.4 were i n t r o d u c e d  into  the Sayre program and 68 Sayre r e l a t i o n s h i p s were found.  *3  When the relationships whioh included reflexions #21 and 22  ((4,7) and (4,8) respectively) were deleted as these  reflexions each occurred In only 2 Sayre relationships of " r e l a t i v e l y " low p r o b a b i l i t y , the number of r e l a t i o n ships was reduced to 64.  Each r e f l e x i o n which occurred  i n t h i s smaller group occurred i n at least 2 relationships and where a r e f l e x i o n occurred i n only 2, those r e l a t i o n ships were of " r e l a t i v e l y " high p r o b a b i l i t y .  The proba-  b i l i t y that no more than 8 relationships f a i l i n 64 was calculated to be approximately 0.998. At t h i s stage the signs of these 33 reflexions f o r the c o r r e c t l y solved structure were calculated to assure that the o r i g i n f i x i n g reflexions would be assigned phases to y i e l d the i d e n t i c a l solution to that already solved by the oonvential methods. As a r e s u l t r e f l e x i o n #1 (0 0 5) was assigned as +, and # 3 2 (7 0 -2) as - f o r the SIGNS program run next.  Out of 31931 solutions r e g i s t e r i n g no  more than 4 f a i l u r e s i n the f i r s t group, 1818 solutions s a t i s f y the additional condition that no more than 8 relationships f a i l i n a l l .  Of the l a t t e r number the 24  solutions which also s a t i s f y the condition that f o r no r e f l e x i o n "n* i s the sum over 1? of )E^||  | Ett-t>| (the  sum taken only over r e l a t i o n s that f a i l ) greater than 10.0. This corresponds to the statement that i n no possible s o l u t i o n i s any sign indicated to be the opposite of that predicted to a p r o b a b i l i t y of greater than 0.995.  A linear  44  dependence arose such that f o r any f a i l u r e s r e f l e x i o n #34 + or  - sign.  could  A p a r t from the  combination of  be a r b i t r a r i l y a s s i g n e d two  perfectly  a  consistent  s o l u t i o n s where no f a i l u r e of Sayre r e l a t i o n s h i p occur, the c o r r e c t s o l u t i o n has test.  the lowest v a l u e of the above  However, t h e r e are  3 s e t s of s o l u t i o n s  s o l u t i o n s ) w i t h the same minimum v a l u e .  (i.e. 6  Nevertheless,  the c o r r e c t s o l u t i o n would be r e a d i l y apparent  on  drawing up a l l the above 8 p o s s i b l e s o l u t i o n s s i n c e a l a r g e number of s i g n s  (33)  are determined.  f o r the c o r r e c t s o l u t i o n w i t h 1? extracted  + s i g n s and  The 16  from tape by the ESIGND program and  -  such  E -  signs  drawn up by  CONTUR program i s shown i n F i g u r e 9 w i t h the model of c o r r e c t s o l u t i o n superimposed  (Note a* *  a/2).  map  the  the  0 F i g u r e 9.  E-map of x z - p r o j e c t i o n (contours r e f i n e d s o l u t i o n superimposed.  60  Z AXIS on a r b i t r a r y s c a l e ) w i t h  final  46  3.  THE STRUCTURE OF METHYL 4 . 6 - D I C B L 0 R 0 4.6-DIDSQXY-tt-D-GAI^CT0PYHAN0Sl5g Introduction 4,6-diohloro-4j6-dideoxy-ot-D-galactopyra-  Methyl  n o s l d e i s prepared by r e a c t i o n of methyl oC-D-glucopyranos l d e w i t h s u l p h y r y l c h l o r i d e f o l l o w e d by d e s u l p h a t i o n . * ? 1 3  1  The steps i n the r e a c t i o n a r e s i m i l a r t o those i n v o l v e d i n the p r e p a r a t i o n of the g l u c o s i d e whose s t r u c t u r e a n a l y s i s precedes  t h i s one.  Although c h e m i c a l e v i d e n o e  1 3  had e s t a b l i s h e d the  a b s o l u t e c o n f i g u r a t i o n of the d i c h l o r o - d l d e o x y hexose p r o d u c t , the a c t u a l c r y s t a l s t r u c t u r e and t h e nature of the hydrogen bonding  i n the s o l i d were unknown.  This  compound a l s o showed promise f o r a p p l i c a t i o n of d i r e c t methods to i t s s t r u c t u r e d e t e r m i n a t i o n . Experimental Crystals  (from chloroform) of t h i s g a l a c t o s l d e are  c o l o u r l e s s needles elongated i n the c - d i r e c t i o n . a b l e c r y s t a l was c u t t o about 0.10 mm. needle of diameter 0.05 work.  mm.  A suit-  from a w e l l formed  and used i n a l l subsequent  U n i t c e l l and space group d a t a were determined  r o t a t i o n and Weissenberg goniometer.  (Approximate  obtained from f i l m .  from  photographs and on the G.E. s p e c t r o v a l u e s of the c e l l dimensions  Using these,18  arbitrarllly  were  selected  medium i n t e n s i t y r e f l e x i o n s were found on the c o u n t e r , and t h e i r 26 v a l u e s a c c u r a t e l y measured.  More aocurate values  47  of a, b, and o were then found by a p p l y i n g t h r e e c y c l e s of r e f i n e m e n t by l e a s t - s q u a r e s t o these parameters  using  the Z9 d a t a i n a program (CELDIM) w r i t t e n by Simon Whitlow t o do  this).  C r y s t a l Data  (X, MoK* - 0.7107 A)  Methyl C  7 12°4 H  m.p.  4,6-diohloro-4,6-dideoxy-0C-D-galactopyranoside C 1  2»  M  158 °C,  Orthorhombioi  31.1  2  =  W  =  D  a »  +184  23.12  (cr »  b - 8.18  Dm  » 1.59  gm  (o- =  o • 5.091  ( or*  U - 962.8  A  cm"3  0.05)»  0.02)  3  (suspended  Z * 4 , DJJ - 1.595  0.004)A  i n C C I 4 , fz(f  • 1.595)  gm-cm-, "3  A b s o r p t i o n o o e f f l o i e n t f o r X-rays, (CuK^ P(000) « Absent  ) =» 60 cm"  1  ^(MoK„) = 6.6  cm"  1  480  s p e c t r a l . h 0 0 when h =* 2n + 1 0 k 0 when k • 2n + 1 and  Space group i s The  0 0 1 when 1 = 2n + 1 P2^2 2 1  1  (Dg^)  i n t e n s i t i e s of the r e f l e x i o n s were measured on  a G e n e r a l E l e c t r i c XRD  6 automated (Datex c a r d c o n t r o l l e d )  spectrogoniometer, w i t h a s c i n t i l l a t i o n counter,  MoK^  r a d i a t i o n ( Z r f i l t e r and p u l s e - h e i g h t a n a l y s e r ) , and 26 scan.  The c r y s t a l  ( o f l e n g t h 0.10  mm.  and  a  diameter  48  0.05  nun.) was mounted w i t h c p a r a l l e l t o the ^ a x i s o f  the g o n i o s t a t .  Of  807  r e f l e x i o n s w i t h 20(MoK«)4  (minimum l n t e r p l a n a r spacing intensities  0.92  45.58°  A ) , 201 whose net  ( c o r r e c t e d f o r background which was recorded  f o r each r e f l e x i o n b e f o r e were l e s s than  (800)), were  30 counts  of ~ 2 ° )  and a f t e r the scan (maximum counts of  29440  c l a s s i f i e d as "unobserved" and were  for  included  In the a n a l y s i s (but not i n c a l c u l a t i o n of R-values) w i t h  JF l • 0.6F ( t h r e s h o l d ) . 0  L o r e n t z and p o l a r i z a t i o n f a c t o r s  were a p p l i e d but no a b s o r p t i o n Struoture  c o r r e c t i o n s were made. Analysis  a. D i r e c t Methods on the x y - p r o j a c t i o n . The  s h o r t n e s s of the c - a x i s  i n d i c a t e d that the mean  p l a n e of the moleoule l a y p e r p e n d i c u l a r  t o the c - a x i s . I t  was hoped t h a t i f d i r e c t methods were c a r r i e d out on the xy p r o j e c t i o n , and s e v e r a l s o l u t i o n s were p o s s i b l e f o r the s t r u c t u r e , the c o r r e c t one would be apparent on simple Inspection  of a l l these s o l u t i o n s ( a program had p r e v i o u s l y  been w r i t t e n which c o u l d r a p i d l y draw contoured F o u r i e r maps on U.B.C. Calcomp 565 12" drum p l o t t e r ) . Using the PREDIR program ( l a t e r d e s c r i b e d ) ,  the f u l l  t h r e e d i m e n s i o n a l d a t a was d i v i d e d i n t o nine ranges of sin^/> lated  f o r each of which the average i n t e n s i t y was c a l c u (^L^).  The average temperature f a c t o r , B, and the  o v e r a l l s c a l e , K, were determined by l e a s t - s q u a r e s  using  49  versus s i n 0/^ data (the f i r s t range was  the ^ i ) ^  excluded as I t included too few reflexions) i n the equation  Zf  = K exp [ B ( s i n Q/*) ] (l)  2  where S f  2  2  = 8f  2  + l 6 f ' + 28 f 2  c l  Q  2 Q  e  + 48 f  B was found to be 6.824 and K to be 22.9.  2 H  These con-  stants, however, are normally quoted f o r scaling of • B/2 « 3.*2 and K^- « Vfc • 4.79).  and not I (Byj  As  the reasonableness of the temperature factor indicated that the s c a l i n g oould now be aooepted, (B(hkl)j's where E ( h k l ) - Khkl). exp ( B ( s l n f l A ) ) 2  2  were calculated.  ,  E(hkO) data where |E|^1.0, were output  on tape f o r subsequent work by d i r e c t methods. The average value of|E| f o r the three dimensional data was 0.852, a c l e a r i n d i c a t i o n of an acentric d i s t r i b u t i o n ( < | E l ) i s 0.886 f o r acentric and 0.798 f o r centric d i s t r i b u t i o n s ) , and further i n d i c a t i o n f o r acceptance of the above s c a l i n g . A l l possible Sayre relationships among the 27 reflexions (hko data only; plane group pgg) with were found by the SAYRE  ]E)^1.30  program ( i f t h e i r p r o b a b i l i t y of  holding was greater than 0.60) which was run next. four relationships (  ~:  Fifty-  ) were found  i n which each of the 26 reflexions occurring i n r e l a t i o n ships occur i n at least two relationships (reflexion #22, (11 6 0) with  E  =1.68  occurs i n no r e l a t i o n s h i p s ) .  50  Solutions  were then generated by the SIGNS program.  Reflexion  #12 (9 3 0) and #21 (9 2 0) were g i v e n signs o f +  to d e f i n e  the o r i g i n as they were strong  o c c u r r e d i n the g r e a t e s t The  number o f Sayre r e l a t i o n s h i p s .  p r o b a b i l i t y t h a t , i n the c o r r e c t s o l u t i o n , no more  than t e n Sayre r e l a t i o n s h i p s in  r e f l e x i o n s and  (out of 5*)  f a l l was c a l c u l a t e d  the p r e v i o u s program t o be approximately 0.88.  maximum number o f f a i l u r e s i n the f i r s t  group that  As the oould  be handled was a t the time of t h i s work l i m i t e d t o f o u r , a l l s o l u t i o n s s a t i s f y i n g the c o n d i t i o n f o u r r e l a t i o n s h i p s f a i l i n the f i r s t ten f a i l  i n a l l , were examined.  that no more than  group and no more than  Out o f the 880 s o l u t i o n s  s a t i s f y i n g these c o n d i t i o n s ,  only 16 s o l u t i o n s a l s o  the c o n d i t i o n  ITEST, that i s , that f o r no  t e s t e d f o r by  r e f l e x i o n la i n a p o s s i b l e  s o l u t i o n i s the s i g n  satisfy  Indicated  be t h e o p p o s i t e of that i n the s o l u t i o n to a p r o b a b i l i t y greater  than 0.985 ( i . e . JjR | Efjl I Egll E f i . j | > H » 5 » the  summation being over r e l a t i o n s that f a i l ) . these were p l o t t e d , but only i.e.  the f i r s t  A l l 16 of  (the "most p r o b a b l e , "  w i t h the lowest v a l u e o f the o p p o s i t e i n d i c a t i o n of  s i g n ) had a d i s t r i b u t i o n of peaks t o which a model oould be f i t t e d .  That s o l u t i o n , which proved to be c o r r e c t i n  every s i g n , had only two f a i l u r e s of Sayre r e l a t i o n s h i p s ,  #21 E(10 1 0 ) * E(9 2 0)* E(19 3 0 ) « + w i t h p r o b a b i l i t y 0.785; and  #36 E(9 2 0 ) « E(19 3 0 ) * E(10 5 0 ) « w i t h p r o b a b i l i t y 0.782.  51  F o r t h a t s o l u t i o n , no r e l a t i o n s i n the f i r s t group f a i l e d , and  two signs  opposite  (#17 and #21) were i n d i c a t e d t o be the  of t h a t i n the s o l u t i o n t o a p r o b a b i l i t y of 0.93  (sEEE = 7.0).  The E-map (a F o u r i e r whose c o e f f i c i e n t s  are t h e EfhkOJ's of knownrphase) f o r t h i s s o l u t i o n i s given  i n F i g u r e 10 w i t h the s t r u c t u r e i n i t i a l l y  postulated,  superimposed. Five oyoles  o f r e f i n e m e n t by the method of l e a s t -  squares o f o n l y the i s o t r o p i c temperature f a c t o r s and s c a l e were c a r r i e d out (50# of the c a l c u l a t e d s h i f t s a p p l i e d a f t e r each c y e l e ) . C(2) and  A l l behaved w e l l except 0(1),  and C(4) whose temperature f a c t o r s went t o 10.5» 10.0 16.6 A , r e s p e c t i v e l y . 2  A F o u r i e r summation based on  the c a l c u l a t e d phases o f the remaining t e n atoms was c a r r i e d out and t h e m i s s i n g t h a t C(7)  atoms were r e l o o a t e d  ( F i g u r e 11).  Note  i s n o t i c e a b l y s h i f t e d towards 0(1) from the  p o s i t i o n i n which i t was i n c l u d e d F i v e c y c l e s of l e a s t - s q u a r e s  i n the F o u r i e r summation.  refinement o f the p o s i t i o n a l  parameters (x and y) and I s o t r o p i c temperature f a c t o r s (B = 3.0 A  2  I n i t i a l l y ) of a l l 13 non-hydrogen atoms,  w i t h the s c a l e , K, were c a r r i e d out, a p p l y i n g c y c l e , 50# o f the i n d i c a t e d s h i f t s .  together  a f t e r each  The s u c c e s s i v e  values  of B weret 0.283 ( I n i t i a l l y ) , 0.17*, 0.130, 0.113, 0.110 and  0.109.  The f i n a l F o u r i e r map f o r the x y - p r o j e c t i o n  appears i n F i g u r e 12 w i t h the r e f i n e d s t r u c t u r e  superimposed.  GALACTQSIDE..  1600  E -  MAP..  X T  PROJECTION  CO  o  1500 moo X  1300 12D0 1100  CD  1000  A  RXI  800  X  9oa  700  LO  BOO 500 •  400 300 200  •  1Q0 F i g u r e 10.  CD  CD  E-map of x y - p r o J e c t l o n (contours on a r b i t r a r y s c a l e ) w i t h the i n i t i a l l y p o s t u l a t e d s t r u c t u r e superimposed.  GflLflCTOSIDE..  F i g u r e 11.  F -  NRP..  X T  PROJECTION.. 0 - 1 .  C-2,  C-4  MISSING  E l e c t r o n d e n s i t y map of x y - p r o J e c t i o n (contours on a r b i t r a r y s c a l e based on phases c a l c u l a t e d using a l l non-hydrogen atoms except 0 ( 1 ) , C(2) and C ( 4 ) .  F i g u r e 12.  F i n a l e l e c t r o n d e n s i t y map of x y - p r o j e c t i o n (contours on a b s o l u t e s c a l e : e/A x 100) w i t h the r e f i n e d s t r u c t u r e superimposed. 2  55  As the z - a x i s I s such a s h o r t a x i s some doubt initially  e x i s t e d as t o whether the space group was  P 2 i 2 2 o r P 2 2 2 , the absence of o n l y 0 0 1 and 0 0 3 1  1  1  1  not b e i n g c o n c l u s i v e proof o f the former.  A f t e r the  s o l u t i o n of the p r o j e c t i o n , the former space group i s confirmed t o be c o r r e c t s i n c e i n the l a t t e r space group C l ( 6 ) . . , C 1 ( 6 ) a c r o s s a c e n t r e i n p r o j e c t i o n would be a c r o s s a t w o - f o l d a x i s i n t h r e e dimensions and would put 01(6).,.C1(6) non-bonding  distance at  2.8 A.  Attempts were made t o s o l v e the s t r u c t u r e three d i m e n s i o n a l l y by superimposing a model on the p r o j e c t i o n and, t o f i x the z - c o o r d i n a t e of the molecule, using the p o s t u l a t e t h a t 0(3) of one molecule i s hydrogen bonded t o 0(2) o f the n e i g h b o u r i n g molecule (hydrogen bond d i s t a n c e ~ 2.7 A ) .  As these attempts proved u n s u c c e s s f u l , i t was  d e c i d e d t o t r y d i r e c t methods on the xz p r o j e c t i o n as i n t h a t d i r e c t i o n there i s no o v e r l a p of one molecule on another, as the x - o o o r d i n a t e s o f a l l the atoms are known, as the phases of the h 0 0 d a t a a r e known, and as the moleoule o c c u p i e s a r o u g h l y p r e d i c t a b l e p o s i t i o n  because  of the hydrogen bonding of 0(3) t o 0 ( 2 ) . b. D i r e c t Methods on the x z - p r o J e c t i o n P R E P IB.  was a g a i n r u n w i t h the same input  parameters  as b e f o r e , b u t t h i s time normal s t r u c t u r e f a c t o r s  ( E ^ ) of  the type (h 0 1) where | E | >, 1.0 were output on tape. A l l p o s s i b l e Sayre r e l a t i o n s h i p s  (59)  among the 26  56  reflexions with  JB(> 1.0 were found by SAYRE but the  number of r e l a t i o n s h i p s was reduced to 5 5 by e x c l u s i o n of those r e l a t i o n s h i p s i n v o l v i n g r e f l e x i o n s # 1 5 ( 1 0 0 3 ) and #16  ( 8 0 5 ) as t h e i r s i g n s cannot be determined to a  sufficient probability.  As a r e s u l t , no r e f l e x i o n o f  e i t h e r even-odd o r odd-even p a r i t y o c c u r r e d In a Sayre relationship.  Reflexion  #14  ( 2 0 1 ) w i t h |E1  = 1 . 9 3 was  a r b i t r a r i l y g i v e n a + s i g n even though i t o c c u r r e d i n no relationship.  The o t h e r o r i g i n determining r e f l e x i o n  chosen was # 2 1 ( 1 1 0 3 ) because of i t s magnitude ( ] E | = 1.55)  and. because of i t s f r e q u e n t occurrence i n r e l a t i o n -  ships. #1  The phase of the s t r u c t u r e  invariant reflexions  ( 8 0 0 ) , # 2 ( 1 0 0 0 ) , # 3 ( 1 6 0 0 ) and #4 (24 0 0 ) were  already  known from the s o l u t i o n of the x y - p r o j e c t i o n .  The  SIGNS program was r u n w i t h the above o r i g i n  d e t e r m i n i n g r e f l e x i o n s a s s i g n e d as + and the other f o u r r e f l e x i o n s a s s i g n e d t h e i r proper s i g n s . s o l u t i o n s which s a t i s f i e d  the c o n d i t i o n t h a t no more than  f o u r Sayre r e l a t i o n s h i p s f a i l more than 1 5 f a i l  In t h e f i r s t group and no  i n a l l (Q0% p r o b a b i l i t y of f i n d i n g the  c o r r e c t s o l u t i o n In t h i s s e t ) , o n l y s a t i s f i e d the a u x i l i a r y c o n d i t i o n is  Out of 5 1 *  eight  solutions  that f o r no r e f l e x i o n  i t s s i g n i n d i c a t e d t o be o p p o s i t e to a p r o b a b i l i t y of  greater The  than 0 . 9 8 3  (sEEE > 1 1 . 0 ) .  two most probable s o l u t i o n s , i . e . the two w i t h  the lowest v a l u e s of  ITEST, d i f f e r r e d only  i n the s i g n  57  of  one minor r e f l e x i o n , #24 (21 0 3,  I E l = 1.23).  the E-maps o f both s o l u t i o n s would be almost  As  Indistin-  g u i s h a b l e , o n l y one was drawn up, t h a t shown i n F i g u r e 13 w i t h the p o s t u l a t e d S t r u c t u r e superimposed. refinement  Subsequent  of t h i s p o s t u l a t e d s t r u c t u r e e s t a b l i s h e d t h a t  the second most probable s o l u t i o n which contained 14 + s i g n s and 10 - s i g n s was o o r r e c t i n every s i g n . Four c y c l e s of l e a s t - s q u a r e s refinement of o n l y the z - c o o r d i n a t e s of the 13 non-hydrogen atoms was c a r r i e d out g i v i n g s u c c e s s i v e R-values 0.180, 0.170, and 0.168.  of 0.252 ( i n i t i a l l y ) ,  0.204,  A F o u r i e r based on a l l 13 atoms  w i t h the parameters of the l a s t c y c l e was summed and, as the s h i f t i n d i c a t e d (but not a p p l i e d ) t o the f a c t o r o f C(7)  was abnormally  h i g h (+6.2  temperature  A ) , t h i s atom 2  was r e l o c a t e d from the r e s u l t i n g contour map (not shown). F i v e more c y c l e s of l e a s t - s q u a r e s refinement were then c a r r i e d o u t , a g a i n s h i f t i n g o n l y the z - c o o r d i n a t e of each atom (50#  of c a l c u l a t e d s h i f t s a p p l i e d a f t e r each c y c l e ) .  The s u c c e s s i v e R-values were 0.167 ( i n i t i a l l y ) , 0.138, 0.137, 0.136, and 0.137.  0.145,  The f i n a l xz p r o j e c t i o n  F o u r i e r map w i t h the r e f i n e d s t r u c t u r e superimposed Is Shown i n F i g u r e 14 f o l l o w i n g . c. F u l l three dimensional  refinement.  The xy- and x z - p r o j e c t i o n d a t a were combined w i t h s u i t a b l e t r a n s l a t i o n s of the c o o r d i n a t e s s i n c e the proj e c t i o n s o f the screw axes of P2i2i2]Which become the  58  GRLflCTOSI.DE  16D0 1500 1400 X  —  X Z PROJ  X AXIS  E NRP  30 '  <  o  1300 1200 1100  CD 1000 900 BOO  A  700  rvi ZD X  y—i  LO  600 500 <T> 400 300 t—'  200  •  100  Figure 13.  ro o  E-map of x z - p r o j e c t i o n (contours on a r b i t r a r y s c a l e ) w i t h the i n i t i a l l y p o s t u l a t e d s t r u c t u r e superimposed.  59  GflLflCTOSIDE  —  X " z PROJ  13 A T O M S ,  5  CYCLES  1700 1600 1500  X  O  1100 1300 1200  CD 1100 1000 900 800  hJ D X  t—i  CO  700 BOO 500 400 300  t—*  ro o  CD 200  F i g u r e 14.  F i n a l e l e o t r o n d e n s i t y map of x z - p r o j e c t i o n (contours on a b s o l u t e s c a l e s e/A x 100) w i t h the r e f i n e d s t r u c t u r e superimposed. 2  60  o e n t r e s o f i n v e r s i o n i n two dimensions, a r e not a t 0,0 as they a r e i n the plane group pgg. s i o n a l refinement on a l l parameters  P u l l three dimen( a p p l y i n g 50% of  c a l c u l a t e d s h i f t s ) w i t h P* = 25,0 i n the standard weighting scheme noted e a r l i e r , was c a r r i e d out y i e l d i n g , f o r 7c y c l e s of r e f i n e m e n t , s u c c e s s i v e R-values tially), 0.143.  of 0.186 ( i n i -  0.162, 0.155, 0.151, 0.148, 0.146, 0.144, and Refinement was c o n t i n u e d i n c o r p o r a t i n g a n i s o t r o p i c  temperature  f a c t o r s , and y i e l d i n g , f o r f o u r c y o l e s ,  s u c c e s s i v e R-values 0.126, and 0.125. comparison  of 0.143 ( i n i t i a l l y ) ,  0.133, 0.128,  As t h i s R-value was r a t h e r l a r g e i n  t o the expeoted  acouraoy  of the d a t a , a r e -  a p p r a i s a l was made of the v a l u e which should be c l a s s i f i e d as a minimum o b s e r v a b l e i n t e n s i t y .  I t was noted t h a t the  background was of the order of 300 counts, (the maximum i n t e n s i t y r e f l e x i o n (8 0 0) on t h i s s c a l e had a scan of 29440 c o u n t s ) .  A v a l u e of 100 as the n e t counts f o r a  minimum o b s e r v a b l e r e f l e x i o n was s u b s t i t u t e d f o r 30 which was p r e v i o u s l y used to  (On t h e average, 100 would correspond  a r e f l e x i o n whose standard d e v i a t i o n i s VlOO + 2 x 300 =  V700 *=* 26 *=* 100/4).  On t h i s b a s i s , o n l y r e f l e x i o n s w i t h  net counts g r e a t e r than 4o*are c l a s s i f i e d as observed. Of the 807 r e f l e x i o n s r e c o r d e d , o n l y 335 (4l.5#) were now c l a s s i f i e d as o b s e r v a b l e .  Using the parameters  which  p r e v i o u s l y gave an R-value  o f 0.125, a r e c a l c u l a t i o n of  R u s i n g the new o b s e r v a b l e r e f l e x i o n s y i e l d e d a v a l u e  61  of 0.077. applying  Pour c y c l e s o f refinement by l e a s t - s q u a r e s , 50% o f the c a l c u l a t e d s h i f t s a f t e r each c y c l e  and w e i g h t i n g r e f l e x i o n s by the standard  scheme (see  b e f o r e ) where P* » 25.0, y i e l d e d t h e R-values1 0.077  ( i n i t i a l ) , 0.071# 0.070, 0.069 and 0.068.  A difference  F o u r i e r summed over o n l y o b s e r v a b l e r e f l e x i o n s i n d i c a t e d the p o s i t i o n s o f the s i x hydrogens g i v e n The  i n Table XI.  hydrogens on 0(2) and 0(3), however, were not found.  A f t e r r e f l e c t i n g the moleoule through z « \ t o make the s o l u t i o n c o n t a i n the c o r r e c t o p t i c a l enantiomorph, and a f t e r i n c l u d i n g the p r e v i o u s l y found hydrogens a l l w i t h i s o t r o p l o temperature f a c t o r s of 3.0 A , a s t r u c t u r e f a c t o r c a l c u l a t i o n revealed t o 0.0596.  The measured and f i n a l c a l c u l a t e d s t r u c t u r e  factors are l i s t e d synthesis The  t h a t the R-value had decreased  i n T a b l e X.  A f i n a l difference  showed f l u c t u a t i o n o f -0.3e/A  3  t o +0.3e/A . 3  f i n a l p o s i t i o n a l and thermal parameters a r e i n Table XI,  bond l e n g t h s  and v a l e n c y  angles a r e i n Table X I I , and the  shorter intermolecular distances  a r e i n Table XIII.  Discussion a. Moleoular S t r u c t u r e and Dimensions The  foregoing  a n a l y s i s has e s t a b l i s h e d the s t r u c t u r e  of methyl 4 6 - d i o h l o r o - 4 , 6 - d i d e o x y - a - D - g a l a c t o p y r a n o s i d e . t  That the c r y s t a l c o n t a i n s  the oC-anomer of the g a l a c t o s i d e  has been e s t a b l i s h e d , b u t that i t c o n t a i n s  the D-enantlo-  62  morph has not.  As the l a t t e r can be I n f e r r e d from the  p r e p a r a t i o n , the anamolous d i s p e r s i o n method was not used on t h i s c r y s t a l to a s c e r t a i n i t s a b s o l u t e c o n f i g u r a t i o n . A l l drawings d e p i c t the c o r r e c t enantiomorph a r i g h t handed  r e f e r r e d to  s e t o f axes.  F i g u r e 15 shows the c o n f o r m a t i o n and c o n f i g u r a t i o n of the m o l e c u l e In p r o j e c t i o n a l o n g the z - a x i s .  The  conformation adopted i s the c h a i r form of the pyranose r i n g on which s u b s t l t u e n t s a r e a t t a c h e d i n the manner ( i . e . , the expected CI c o n f o r m a t i o n i n Reeves*  Ia2e3e4a5e  notation ®). 1  The p a c k i n g of molecules In the u n i t c e l l i s shown i n Figure  16. The bond l e n g t h s and v a l e n c y angles i n the molecule  are g i v e n i n Table X I I .  The ranges f o r the C-c  i s 1.51-1.54 A - ( 0 v « 0.02  A ) , of whioh the average v a l u e i s  1.532  A( cr= 0.01  A).  bond l e n g t h s  The two C - C l bond l e n g t h s have an  average v a l u e bf 1.80  A ( c r = 0.01).  The C-0 bond l e n g t h s  a r e i n the range 1.48-1.41 A( (r = 0.02) w i t h t h e l e n g t h s i n v o l v i n g the g l y c o s i d i c oxygen, 0 ( 1 ) , a t the extremes  (Jefferey  and R o s e n s t e i n ^ have noted t h a t i n monosaccharides, C ( l ) - 0 ( 1 ) 1  tends t o be s h o r t e r than the normal C-0 bond), the other C-0 bond l e n g t h s c o v e r i n g a narrower range. bond l e n g t h i s 1.45  A( CT» 0.01).  The average  C-0  The mean v a l u e f o r C-C i s  as found i n o t h e r c a r b o h y d r a t e s ^ , but the C-0 v a l u e i s a t 1  the upper range of those found.  Except, perhaps, f o r those  i n v o l v i n g 0 ( 1 ) , none of the i n d i v i d u a l bond l e n g t h s d i f f e r s i g n i f i c a n t l y from t h e i r means.  63  Figure 1 5 .  Superimposed s e c t i o n s of the e l e c t r o n d e n s i t y d i s t r i b u t i o n (contours a t 1 , 2 , 3 . . . e / A 3 ) and a drawing of the molecule.  ON  65  Within the ring the oarbon valency angles range between 109.2°and 110.3° ( c r = 1.3°) with a mean value of 109.7 ( c r - 0.7°).  The angle at 0(5) i s 115.0°, larger  than the tetrahedral angle as i s commonly found i n other simple sugars. ^ 1  The external angles are i n the range  104°-ll6° (CT= 1.3°).  Table XII gives the bond lengths  and valency angles f o r six hydrogens, calculated from t h e i r coordinates as they appeared  on a difference synthesis.  They range i n bond length between 0.93 A and 1.22 A with a mean value of 1,0k  A.  The valency angles i n which they  occur range between 97° and 134° with a mean value of 109.9°. The standard deviation of the mean values quoted i n Table XII i s the root-mean-square-deviation  from the mean.  b. Hydrogen Bonding i n the Structure Table XIII contains the intermolecular distances which are less than 3.6 A .  The shorter distances represent  possible hydrogen bonding and these are Included i n Fig.17, a view along the y-axis of the near o r i g i n region of the unit c e l l .  Only two Independent hydrogens per molecule are  available f o r hydrogen bonding: one on 0(2), the other on A possible hydrogen bonding soheme i s  0(3).  IV o(2) - H I V  I ..-o(i) o(3) - H . : ; T T T 1 1 1  J  O(Z)  111  - H  0(3) - H etc.  F i g u r e 17.  Hydrogen bonding; view along b.  o\ ON  67  The hydrogen on 0(3) of moleoule (I) i s postulated to be directed between 0(1) and 0(2) of molecule III to form a bifurcated ^* 1  2 0  hydrogen bond.  Two reasons make a  bifurcated hydrogen bond reasonable! 1. The distances 0 ( 3 ) . . . 0 ( 2 ) J  m  and 0 ( 3 ) . . . O ( l ) 1  are both within the l i m i t s of hydrogen found i n carbohydrates (2.68-3.0* A ) 2. If the hydrogen on 0 ( 3 )  1  1 1 1  bonding  1 6  i s directed between  0(1) and 0(2) then the angle H-0(3)-C(3) would be closer to the tetrahedral angle then i t would be were the hydrogen directed to only one oxygen. One i n t e r e s t i n g short approach existing i n the structure i s that of 0 ( 2 ) . . . C 1 ( * ) IV  1  (3.28 A). It i s  tempting to postulate hydrogen bonding between the two atoms, possibly as a bifurcated system i n which 0 ( 2 ) ^ Is hydrogen bonded to both 0 ( 3 J and C i t * ) . 1  1  However, t h i s  oxygen-chlorine distance i s longer than that usually found 3 i n hydrogen bonding (2.86-3.21 A; mean 3.07 A), and more probably corresponds to only van der Waals i n t e r a c t i o n between the two atoms.  The other intermolecular distances  i n Table XIII correspond to van der Waals separations.  TABLE X Measured and c a l c u l a t e d s t r u c t u r e amplitudes (x 10). -0.6 F ( t h r e s h o l d ) . Unobserved r e f l e x i o n s have F,  21! 17B  -43 -57 ~TTZ 261 IM 383 14B 233 -?52— 106 138 -67 256 J 30  48 1 3 I75 250 1)2 372 146 2 33 266 121 165 13 272 349 154 211  -44 -65 ~TT0 3^9 15(1 35ft 203 -69  114 18 T34 403 ih6 I M 206 62 T T " 74  ay i  1^2 -60 22f 109  l?8 5*. 717 73  ~TT7~ I'll 164  ~\nn—nn~ 176 204 147  164 212 151  2aa *>?.?. 216  ? 3-0 2  177  2  -->G  207 278 -77  -  2<n 104 126  250 137 125  237 199 337  -  142 114 146 17a 155 194  164 126 224  1)1 127 2)B  -b'J -6" 120 224 144  l.)H  TTj'j  'J3  227 141  -7 ) -80 -82 l<.5 7 126  172 -82 -83  J3H  222 - 15 -8u 174  165 250 -76  24 3 467 154 30C -72  -65 147  I  19 29 6 266  69 TABLE XI FINAL POSITIONAL PARAMETERS ( f r a c t i o n a l ) . ISOTROPIC THERMAL PARAMETERS ( A ) . AND ANISOTROPIC THERMAL PARAMETERS 2  (exp - | b  i : L  h  2  + b hk + b ^ h l+ b 1 2  2 2  k  + b ^ k l + b ^1 ( >. 2  t o g e t h e r w i t h estimated standard d e v i a t i o n s In p a r e n t h e s i s , r e f e r r i n g t o the l a s t decimal p o s i t i o n s of the parameters. Atom Cl(4) Cl(6) 0(1) 0(2) 0(3) 0(5) C(l) C(2) C(3) C(4) C(5) C(6) C(7)  B 0.13114(15) 0.24867(17) 0.0912(4) -0.0039(4) 0,0190(4) 0.1535(4) 0.0977(6) 0.0521(5) 0.0598(5) 0.1217(6) 0.1653(5) 0.2276(6) 0.1218(7)  0.8545(5) 0.8354(6) 0.3636(12) 0.4807(13) 0,8233(11) 0.4975(11) 0.4213(16) 0.5526(17) 0.6982(16) 0.7667(16) 0.6295(16) 0.6713(17) 0.2077(18)  D  Cl(4) Cl(6) 0(1) 0(2) 0(3) 0(5) C(l) C(2) C(3) C(4) C(5) C(6) C(7)  0.00170(6) 0.00217(8) 0.0024(2) 0.0016(2) 0.0024(2) 0.0012(2) 0.0019(3) 0.0006(2) 0.0009(3) 0.0022(3) 0.0010(3) 0.0016(3) 0.0031(4)  12  b  0.7650(8) 0.2494(11) 0.283(2) 0.538(2) 0.487(2) 0.576(2) 0.5*1(3) 0.601(3) 0.417(3) 0.442(3) 0.400(3) 0.455(3) 0,246(4)  13  -0.0006(4) • •0.0008(9) -0.0014(5) • •0.0036(11) 0.0007(10) 0.004(2) •0.0057(11) 0.000(2) 0.0027(11) 0.002(2) 0.0006(10) 0.005(2) •0.0027(14) 0.009(3) •0.0026(14) 0.003(2) -0.0024(13) 0.004(3) 0.0027(15) 0.013(3) 0.0002(12) 0.001(2) -0.0024(15). •0.004(3) 0.0017(18) 0.013(5)  p  22  3.35(7) 4.67(10) 3.7(2) 3.9(3) 3.7(3) 2.9(2) 3.4(4) 2.7(3) 2.4(3) 3.0(3) 2.7(3) 3.5(*) 5.3(5)  222  0.0156(5) 0.009(3) 0.0203(6) 0.002(3) 0.0105(14). •0.003(7) 0.0209(19) 0.006(7) 0.0132(17) 0.014(6) 0.0134(16) 0.003(6) 0.0089(21) 0.007(7) 0.0128(24)- •0.021(8) 0.0095(24). •0.011(7) 0.0082(21) 0.007(7) 0.0060(20)- •0.030(7) 0.0124(24). •0.013(9) 0.0136(26) 0.004(12)  b  33  0.027(1) 0.056(2) 0.043(5) 0.049(5) 0.046(5) 0.035(4) 0.019(6) 0.035(7) 0.042(7) 0.022(6) 0.038(6) 0.046(8) 0.071(10)  70  POSITIONAL PARAMETERS OF HYDROGENS (Not r e f i n e d ; B taken 2 as 3.0 A f o r a l l hydrogen) Hydrogen atom  Attached t o  H(l)  C(l)  H(2)  y  z  0.1037  0.321  0.700  C(2)  0.0691  0.618  0.800  H(3)  C(3)  0.0648  0.630  0.267  H(4)  C(4)  0.1317  0.842  0.300  H(5)  C(7)  0.0994  0.145  0.133  H(6)  C(7)  0.1512  0.182  0.367  X  71  TABLE X I I Bond Lengths and V a l e n c y Angles  m i l Cl(6) Cl(4) 0(1) 0(1) 0(2) 0(3) 0(5) 0(5) C(l) C(2) C(3) C(4) C(5)  C(6) C(4) C(7) C(l) C(2)  c(3)  cd)  c(5)  C(2)  c(3)  C(4) C(5) C(6)  CT = 0.02 A  1.78* 1.817 1.48 1.41 1.46 1.44 1.45 1.44 1.5* 1.5* 1.5* 1.53 1.51  1 Cl(4) Cl(4) Cl(6) C(6) C(6) 0(3) 0(3) 0(2) 0(2) C(7) 0(1) 0(1) 0(5) C(l) C(2) C(3) C(4)  c(5)  J C(4) C(4) C(6) C(5) C(5) C(3) C(3) C(2) C(2) 0(1) C(l) C(l) C(l) C(2) C(3) <5(4)  c(5) C(5)  k C(5) C(3) C(5) C(4) 0(5) C(4) C(2)  c(3)  C(l)  cd)  0(5) C(2) C(2) C(3) C(4)  c(5) 0(5)  cd)  0-= l.l°-l.3°  Angle (1.1k) 110.1 109.6 108.9 115.7 103.8 108.9 109.2 106.6 106.2 111.2 110.9 110.5 106.4 110.3 110.0 109.2 110.3 115.0  72  Bond LengthB  and Angles I n v o l v i n g Hydrogens  D(1.1) H(l)  C(l)  1.17  H(2)  C(2)  1.22  k  0(1) { 0(5) C(2)  Angle ( l j k )  115° 97 116  { C(3) 0(2)  105 97 131  C(2) { C(4) 0(3)  93 100 13*  ( C(3) { C(5)  112 102 113  C(l)  H(3)  C(3)  0.96  H(4)  C(k)  0.99  H(5)  0(7)  0.93  0(1)  107  H(6)  C(7)  0.9*  0(1)  117  €T  Mean  0.12  1.0*  .  (d(4)  12  109.9  TABLE X I I I Shorter Intermolecular Distances X  1  Y  (*3.6  1  1  A) D(X*-  Cl(*)  0(2)  IV  3.28  Cl(4)  C(4)  II  3.55  0(3)  0(1)  III  2.92  0(3)  0(2)  IV  2.78  0(3)  0(2)  III  3.00  0(3)  C(2)  IV  3.28  0(3)  C(7)  III  3.60  0(3)  0(2)  III  3.5*  Symmetry Code I  x  y  z  II  X  y  z + 1  III  -x  y + i  IV  -x  y +  1  -z + -z + 3/2  PART I I  DESCRIPTION OF PROGRAMS  7*  DIRECT METHODS PROGRAMS Introduction A Sayres r e l a t i o n s h i p I n a centrosymmetrlc space group r e l a t e s the s i g n s o f t h r e e l a r g e r e f l e x i o n s as S(Ffl) • S(F£)  • S(F£_£) «  where S means "the s i g n o f . " r e l a t i o n holding reflexions  + 1  The p r o b a b i l i t y of t h e  i s a f u n o t i o n of the magnitudes of the  involved.  Following  i s a d e s c r i p t i o n of a s e t of f o u r programs  which attempt t o s o l v e two d i m e n s i o n a l p r o j e c t i o n s  using  Sayre r e l a t i o n s h i p s i n the Vand and Pepinsky approach t o Q  the Cochran and Douglas procedure.  The s e t of programs  begins w i t h unsealed t h r e e - d i m e n s i o n a l (or two dimensional) I F 1•s as output by DATAPREP (our d a t a p r o c e s s i n g 0  and  program)  produces I n t h e end a tape s u i t a b l e f o r input t o FOURIE  (our F o u r i e r summation program) c o n t a i n i n g s o l u t i o n s a t one time.  up t o s i x p o s s i b l e  F o r working w i t h d l r e o t methods,  e i t h e r u n i t a r y s c a t t e r i n g f a c t o r s , U*s (Woolfson  p . * ) , or  n o r m a l i z e d s t r u c t u r e f a c t o r s , E's ( K a r l e & K a r l e  p.855) can  be used.  As the trend i s toward i n c r e a s i n g use of the l a t t e r ,  these a r e used i n a l l subsequent work. of  A simple d e f i n i t i o n  IEI i s t h a t i t i s the r a t i o of the a c t u a l observed  ( p r o p e r l y s c a l e d ) magnitude of F t o that expected f o r I t s v a l u e of s i n ^  which i s simply / z f | ^ where the summation  i s over atoms i n the u n i t c e l l . expression  2  n  In terms of E's the  used to c a l c u l a t e the p r o b a b i l i t y of the above  75  Sayre r e l a t i o n s h i p h o l d i n g i s P = £ + * tanh  {cr/(r3/2 | ^ 3  2  .  B^|}  where  <r /<r 3/2 3  2  i s a c o n s t a n t dependent upon the c o n s t i t u e n t s o f the u n i t  cell.  No allowance  i s made i n t h i s s e t of programs f o r  s p e c i f i c a t i o n o f any but the tape u n i t n o r m a l l y a l l programs, i . e . , 00, 01, 02, 0 3 , and 04.  for  e x c e p t i o n o f PHEDIH and ESIGND (see l a t e r ) , can be on d i f f e r e n t f i l e s from  specifiable With the  input and output  o f the same tape. The tape  these programs has been made t o €e^completely  output  compatible  w i t h our r e g u l a r programs (DPAUTO & LSSQR & PATTER) so t h a t output from any o f these programs, except of course ESIGND ( c f . L S S Q R ) can be i n t e r m i x e d w i t h r e g u l a r s t r u c t u r e f a c t o r d a t a , and so t h a t a l l f o u r d i r e c t methods programs,DPAUT0, LSSQR & PATTER a r e a b l e t o read t o a p p r o p r i a t e f i l e s on intermixed  tapes.  (1) PREDIR T h i s program accepts a t h r e e - d i m e n s i o n a l  (preferably  but not n e c e s s a r i l y ) s t r u c t u r e f a c t o r tape prepared by DATAPREP and s c a l e s the |P | *s based on a knowledge of the 0  composition of the u n i t c e l l . to  f i n d the l i m i t s of s i n  The d a t a tape i s f i r s t •  scanned  The tape i s then r e r e a d and  the unsealed  i n t e n s i t i e s p l a c e d i n t o a s p e c i f i e d number of  e q u a l ranges  of s i n g  and 1.2 of Woolfson range,  2  Q  .  Two t a b l e s s i m i l a r t o Tables 1.1  (p.8) a r e c o n s t r u c t e d , and f o r each  j j f / ( l ) i s computed. 2  76  Assuming an average temperature  f a o t o r (B) can be  used f o r a l l the d a t a , one can w r i t e f o r each range of sin %  (= S)»  Z^ / 2  <I>  - K exp  ( + BS )  (1)  2  T h i s can be r e w r i t t e n ast log  ( 2 f / ( i ) ) - l o g K + BS 2  (2)  2  N  L e a s t - s q u a r e s i s used to f i n d the 'best' v a l u e of K and B in  equation (2). T h i s program then computes and outputs  E *s both  p r i n t e d and on tape, the l a t t e r e x a c t l y i d e n t i c a l to the o r d i n a r y s t r u c t u r e f a c t o r tape produced by DATAPREP except t h a t J Pj becomes of  | E | and P  2  becomes E . 2  (For i n t e r p r e t a t i o n  EPSILON i n the p r i n t e d output, see the f o o t n o t e i n K a r l e &  K a r l e , p.855). 7  As a f i n a l check on the method of s o a l i n g the d a t a , average v a l u e s of both  JE|  and  |E| are output, the l a t t e r  i n d i c a t i n g the presence or absence of  of a c e n t r i c  distribution  atoms i n the s t r u c t u r e . Two  u s e f u l o p t i o n s are i n c l u d e d to ensure that  (and subsequently, c a l c u l a t i o n of (|B|^  scaling  and <^|E| ) ) i s  c a r r i e d out f o r o n l y the best p a r t of the d a t a .  2  These a r e i  (1) Weights can be s p e c i f i e d f o r the f i r s t two ranges of S (2) The l i m i t i n g v a l u e of S can be s p e c i f i e d to be s m a l l e r than a c t u a l l y c o n t a i n e d on tape. The n e c e s s i t y of the f i r s t ranges may  o p t i o n i s that the f i r s t  not c o n t a i n enough r e f l e x i o n s to make <^I^  two  c  77  statistically seoond  s i g n i f i c a n t there.  The n e c e s s i t y o f the  i s t h a t a t h i g h v a l u e s o f 3, many r e f l e x i o n s  become too weak t o be measured and a r e c l a s s i f i e d as "unobserved." for  However,  E s a r e c a l c u l a t e d and output #  a l l the d a t a on the i n p u t tape. The d a t a c a r d s f o r i n p u t t o the PEEDIB program a r e  as f o l l o w s i POSITION  DESCRIPTION  FORMAT  Card 1 1-2  INPUT tape u n i t no.  3-4  INFILE - f i l e no. (» 1 i f l e f t  blank)  12  5-6  OUTPUT tape u n i t no. ( i f any) (OUTPUT INPUT)  12  OUTFIL - Output f i l e no. (»1 i f l e f t blank)  12  NINTVL - no. of i n t e r v a l s of S (-10 i f l e f t blank)  12  IPROJ - i f output i s p r o j e c t i o n ( a l o n g l=x, 2=y, 3»z)  12  IHALF - i f an index i s t o be halved on tape output s p e c i f y here  12  STLMAX - maximum v a l u e o f S f o r s o a l i n g i f o t h e r than l i m i t of d a t a on tape  12.  MINEPR - minimum v a l u e o f E f o r p r i n t e r output  F5»2  MINETP - minimum v a l u e o f E f o r tape output ( u s u a l l y 1.0)  F5.2  7-8 9-10 11-12 13-14 16-20  21-25 26-30 31-35 36-40  WEIGHT (1) WEIGHT (2)  - weight f o r f i r s t for scaling - weight f o r second for soaling  12  range F5.2 range F5.2  78  Card 2 ( M u l t i p l i c i t y f a o t o r s f o r extending to whole o f r e c i p r o c a l l a t t i c e )  data  1-5  MULTAX - (as i n FOURIE) m u l t i p l i c i t y of axial reflexions  F5.3  6-10  MULTPL (1) - o f 0 k l d a t a  F5.3  11-15  MULTPL (2) - of h 0 1 d a t a  F5.3  16-20  MULTPL (3) - of h k 0 d a t a  F5-3  Card 3 ( S p e c i f i c a t i o n o f s y s t e m a t i c absenoes i n d a t a ; a blank card must be inoluded i f , as i n PT, no s y s t e m a t i c absences occur) 1-2  3-5  NEXT - no. o f s e t s o f e x t i n c t i o n s following  12  BLANK  3X  6  IEX (1,1)  \  S p e c i f i c a t i o n of  11  7  IEX (1,2)  [  1st s e t o f e x t i n c t i o n s  11  8  IEX (1,3)  I  9  EXMULT (1) '  0 0 1 l»4n  -» 0014  11  BLANK  h 0 0 h=2n  —> 1002  IX  10  e.g. h k 0 h=2n —» 1102  11-15  r e p e a t o f 6-10 f o r 2nd s e t of e x t i n c t i o n s  16-20  r e p e a t of 6-10 f o r 3rd s e t of e x t i n c t i o n s  11  etc. Card 4 (Composition of p r i m i t i v e u n i t c e l l )  1-2  NCURV - no. of atom types  12  3-4  NATOMS (1) - no. o f atoms of type 1 present  12  5-6  NATOMS (2) - no. o f atoms o f type 2 present  12  7-8 etc.  • • • •  •  •  • • • • • • (The s p e c i f i c a t i o n o f atoms must be i n the same order as f ' s a r e c o n t a i n e d on tape produced by DATAPREP)  • e • •  79  Cards 5 -  (4 + NCURV)  Scattering  f a c t o r oards i n o r d e r on c a r d k and  on i n p u t tape.  (The c o n t e n t s o f these c a r d s a r e  desoribed i n writings  f o r the DATAPREP program).  (2) SAYRE T h i s program a c c e p t s the p r o j e c t i o n d a t a output of PREDIR, and reads i n t o the f o u r p a r i t y groups those r e f l e x i o n s whose | E l i s n o t l e s s than a s p e c i f i e d v a l u e (MINE).  F o r I n t e r n a l workings  non-zero  index i s H, t h e seoond K.  g i v e n an i d e n t i t y ( r e t a i n e d  i n the program, the f i r s t Each r e f l e x i o n i s  i n SIGNS and ESIGND) which i s  i t s p o s i t i o n on the tape when o n l y those r e f l e x i o n s not l e s s than MINE a r e counted.  The program then systema-  t i c a l l y f i n d s a l l Sayre r e l a t i o n s h i p s group t o which the d a t a belongs are handled, p2, pmm,  knowing the plane  (only the f o l l o w i n g  pmg (pgm), o r pgg).  four  The p r o b a b i l i t y  w i t h which eaoh r e l a t i o n h o l d s i s computed and allowance i s made f o r r e l a t i o n s of the type s i g n  (HK) « t 1 (2^  type)  as t h e i r p r o b a b i l i t y i s n o t g i v e n by t h e same e x p r e s s i o n as t h a t o f a g e n e r a l Sayre r e l a t i o n . Eaoh r e f l e x i o n i s then l i s t e d  i n p a r i t y groups t o -  g e t h e r w i t h the number o f r e l a t i o n s h i p s  i n which i t  oocurs n o n - t r i v l a l l y ( i . e . w i t h i t s s i g n not squared). The Sayre r e l a t i o n s a r e p r i n t e d seoond b e i n g an o p t i o n a l  out i n two ways, the  addition  t o the f i r s t t  80  1, a l i s t i n g In which each r e l a t i o n s h i p  occurs  u n i q u e l y and In t h e order In which i t i s generated, and 2. a l i s t i n g by r e f l e x i o n , i n descending  value  of I E l , o f a l l r e l a t i o n s h i p s i n which t h a t r e f l e x i o n occurs. The  Sayre r e l a t i o n s can a l s o be output on tape i n a  simple b i n a r y form which the next program i n the s e r i e s (SIGNS) can use as i n p u t f o r d e t e r m i n i n g the p o s s i b l e signs of r e f l e x i o n s . T h i s program t e r m i n a t e s by beginning a g a i n ; t h e r e f o r e , s e v e r a l d i f f e r e n t o p t i o n s may be s p e c i f i e d and output can be on s e p a r a t e f i l e s o f the same tape, d e l a y i n g the d e c i s i o n of how b e s t t o handle the d a t a u n t i l the output  i s seen f o r each c y c l e .  The l i m i t s o f the v a r i o u s d i m e n s i o n a l a r r a y s a r e g i v e n In comment c a r d s a t the beginning o f the source deck f o r t h i s program.  As the output o f t h i s program i s  the i n p u t o f t h e next, these dimensions  a l s o apply t h e r e .  Three o p t i o n s a r e b u i l t i n t o the program t o e l i m i n a t e unwanted r e l a t i o n s h i p s  ( b e s i d e s the obvious r e d u c t i o n  made by s p e c i f y i n g a d i f f e r e n t v a l u e of the minimum |E| (MINE) t o be r e a d from the i n p u t t a p e ) .  In the order i n  which they w i l l be a p p l i e d t o the d a t a , these a r e i 1. S p e c i f i c a t i o n o f a minimum p r o b a b i l i t y a c c e p t a b l e for a relation.  T h i s Is done by s p e c i f y i n g a  minimum v a l u e o f the t r i p l e product of E's  81  IE 1)  lE l* 2  (ACCEEE).  g o i n g Into a r e l a t i o n  3  The  main purpose of t h i s Is  e l i m i n a t e most 2^ because of sion, 2.  be  tend to have low  of r e f l e x i o n s  NSCRAT).  expres-  which are not  to  (ISCRAT ( I ) ,  T h i s Is done on a r e r u n of  the  program and  used i n a case where MINE i s very  s m a l l , e.g.  1.0,  low  v a l u e of  and  some r e f l e x i o n s  | E l have an  of  the  i n s u f f i c i e n t number of  relationships  determining t h e i r  Specification  t h a t a c y c l i c prooess i s to  carried 1. and  out 2.  on  the  relations  one  remaining  The  end  the  i s to be  need f o r 3.  i s obvious when one  almost i d e n t i c a l s o l u t i o n s i d e n t i c a l except the  occurs i n o n l y one  found two  relationships.  method of g e n e r a t i o n of s o l u t i o n s  s i g n s are  cycle  r e s u l t of t h i s prooess i s t h a t  SIGNS program, occurs i n at l e a s t  different The  after  that r e l a t i o n i s e l i m i -  eaoh r e f l e x i o n , f o r which a s i g n by  be  i s found o c c u r r i n g i n only  Sayre r e l a t i o n and  nated.  sign.  have been a p p l i e d , d u r i n g each  of which a r e f l e x i o n  Two  which,  probabilities.  considered for r e l a t i o n s h i p s  1*1,  3.  - type r e l a t i o n s h i p s  t h e i r modified probability  Specification  to  by  the  looks at  the  next program.  of a s t r u c t u r e i n which a l l s i g n of  r e l a t i o n w i l l , on  the  reflexion  elimination  of  which that  r e l a t i o n , be r e p l a c e d by o n l y one s o l u t i o n i n which t h a t sign i s indeterminate.  (Note that the only  difference  between the two s o l u t i o n s i s t h a t the r e l a t i o n s h i p r e f e r r e d t o w i l l h o l d f o r one s i g n of the r e f l e x i o n and f a i l f o r the o t h e r ) .  O p t i o n 3*  s h o u l d , t h e r e f o r e , be  used except when a r e l a t i o n s h i p of the above type has a (~*98) l a r g e enough t o assume that i t does  probability not f a i l .  F o r t h i s c a s e , t h a t r e l a t i o n should be  r e t a i n e d but o t h e r l e s s p r o b a b l e r e l a t i o n s of the type should be e l i m i n a t e d  s e l e c t i v e l y by the use of o p t i o n  The d a t a cards f o r i n p u t as  2.  to the SAYRE program are  followst  Card 1 1-2  INPUT tape  12  3-*  INFILE  12  5-6  OUTPUT tape i f any. (OUTPUT - or + INPUT)  12  7-8  OUTFIL  12  9-10  IPROJ - the type of p r o j e c t i o n on tape ( l * x , 2=y, 3=z)  12  11-12 13-14 15-16  17-18 19-20  ISPACE  1 f o r p2; 2 f o r pmm; 3 f o r pmg, 4 f o r pgg, 5 f o r pgm  IPRINT -1 suppress p r i n t o u t of r e l a t i o n s h i p s by r e f l e x i o n IONE  -1 i f e l i m i n a t i o n of r e f l e x i o n s o c c u r r i n g i n only one r e l a t i o n s h i p i s d e s i r e d ( o p t i o n #3)  12 12  12  NSCRAT -no, o f r e f l e x i o n s t o be soatched ( o p t i o n #2)  12  BLANK  2X  83  21-30  PHOBCP - p r o b a b i l i t y c o e f f i c i e n t as output by PBEDIR  P10.0  31-40  MINE - minimum v a l u e of E f o r a c c e p t a b l e r e f l e x i o n i n p u t i n t o the program from tape  F10.0  ACCEEE - minimum a c c e p t a b l e v a l u e of t r i p l e product f o r a c c e p t i n g a relationship  P10.0  41-50  51-52  ISCBAT (1)  - the no. o f a r e f l e x i o n t o be eliminated  12  53-54  ISCBAT (2)  - the no. of another r e f l e x i o n to be e l i m i n a t e d  12  I  ISCBAT (NSCBAT)  Cards 2,  3.  12  3 e t e . i r e p e a t o f Card 1 f o r s p e c i f y i n g d i f f e r e n t parameters i n r e c y c l i n g of program.  SIGNS T h i s program  the  NSCRAT * 10  produces s o l u t i o n s from the output of  SAYRE program by the Vand & Pepinsky method (Woolfson  8  pp.101-6) which oan be viewed as a time s a v i n g v e r s i o n of the  Cochran & Douglas method (Woolfson  pp. 167-171).  8  9 pp.94-100; R o l l e t t 7  No attempt w i l l be made to d e s c r i b e these  as they a r e v e r y adequately d e s o r i b e d i n the r e f e r e n c e s quoted. the  The o r i g i n a l v e r s i o n of t h i s program was  based on  Cochran & Douglas method but as the t e s t l a t e r d e s c r i b e d  was v i s u a l i z e d , the program was  r e w r i t t e n to c a r r y out the  f a i l u r e t e s t s by the Vand & Pepinsky method.  84  A b r i e f description of the l a t t e r program follows » Individual Sayre r e l a t i o n s h i p s are stored l n binary form, up to four words, l n a way s i m i l a r to that pictured i n B o l l e t t ^ (p;170) except that provision i s made f o r up to 105 relationships among up to 35 reflexions.  These  relationships are stored i n the variable 1X8, dimensioned as IXS (4, 105).  The 4 s i g n i f i e s that up to 4 words can  be used to store a single r e l a t i o n s h i p .  The f i r s t word  i s used exclusively f o r indicating which x's ( i n the notation of Woolfson) oocur i n that relationship. The f i r s t b i t of the seoohd word i s the sigh associated with the r e l a t i o n , and each subsequent b i t extending to 3 words i s used consecutively  to Indicate S's (again Woolfson's  notation), e.g. - x j X a X j ^ = S37 would be represented ass  IXS (1,37) »  01000000010000010...0...00  IXS (2,37) -  10000...  ...0...00  IXS (3,37) =  00100...  ...0...00  IXS (4,37) =  ( i f less than 70 relationships occur, this word would not be used)  85  The m a n i p u l a t i o n s of " a d d i t i o n s of remainders modulo 2" ( i . e . a d d i t i o n o f b i t s modulo 2) a r e accomp l i s h e d i n t h i s program by the use of the b u i l t - i n f u n c t i o n s AND, OR, and COMPL a v a i l a b l e f o r the 7040/7044 system as d e s c r i b e d i n the programming m a n u a l  2 1  (p.38).  The a c t u a l a d d i t i o n modulo 2 i s c o m p l i c a t e d by the f a c t t h a t the above a r e " r e a l " f u n c t i o n s . The a d d i t i o n of I t o J modulo 2, i n t h e sense that each b i t of I i s added modulo 2 t o each b i t  of J , t o  produce K, would be accomplished by the f o l l o w i n g  state-  ments: EQUIVALENCE  (XI,I), (XJ,J),  (XK,K)  X -AND ( I , J ) X = COMPL (X) Y » OR ( I , J ) XK - AND  (X,Y)  The c o m p l i c a t i o n Introduced by EQUIVALENCE  i s necessary  s i n c e the v a r i a b l e s t o be manipulated by AND, OR, and COMPL, when used i n o t h e r p a r t s of the program, must be used i n i n t e g e r mode but w i t h o u t the c o n v e r s i o n accomp l i s h e d by a statement such as XK = K The i d e n t i t y of a g i v e n r e f l e x i o n here Is the same as i n SAYRE, i . e . i t i s i t s p o s i t i o n on the tape cont a i n i n g E*s when o n l y those r e f l e x i o n s w i t h JEJ p r e s e t v a l u e (MINE i n SAYRE) are counted.  a  86  It sometimes happens that i n t r y i n g to systemat i c a l l y solve the set of equations f o r eaoh of the z's (by the procedure described i n R o l l e t t ) , a l i n e a r dependenoy of x's which cannot be resolved, Is found for  the f i r s t group.  In t h i s eventuality, Instead of  only one s o l u t i o n e x i s t i n g f o r one set of f a i l u r e s of u  r e l a t i o n s l n the f i r s t group, there now exists 2" s o l u tions f o r that s e t , where N equals (the number of r e f l e xions) minus (the number of equations l n the f i r s t group). This program can handle N ^ 4, and w i l l output up to 16 solutions f o r any one group of f a i l u r e s . 8  The program now follows Woolfaon  9  (p,101-5) c l o s e l y .  The r e l a t i o n s that f a i l In the seoond group when none f a l l 2,4]. r e l astored t i o n s that f a i l when r e l a(37.1)t tion iIn =the f i rThe s t are In IVP1(I), I •e.g. 1,3 the [ cNth f . IXS i n the f i r s t group f a i l s i s given by IVP (I,N), I = 1,3 [again  c f . IXS ( 3 7 » D , I = 2,4-]. Note that I VP (I,N) shows  also that the Nth r e l a t i o n l n the f i r s t group f a l l s . No allowance, though, i s made to r e j e c t a p a r t i c u l a r s o l u t i o n on the basis of a p a r t i a l "summation" as indicated in R o l l e t t  9  (p.105).  Each s o l u t i o n which i s within the l i m i t s of a c e r t a i n test described below  (ITEST) and which obeys a preset  l i m i t on the number of f a i l u r e s i n the f i r s t group ( £ 5 ) and a preset l i m i t on those i n a l l , i s printed out together with the value of that t e s t , the number of plus signs l n  87  the  s o l u t i o n , the numbers of the p a r t i c u l a r Sayre  r e l a t i o n s which f a l l ,  I K  and the v a l u e of  dfe l E j j i i E g i l E R - s l )  (3)  2  where h* I s a r e f l e x i o n c o n t a i n e d In a Sayre r e l a t i o n t h a t f a l l s , and |Bg| lEg«,£l I s t h e v a l u e o f the t r i p l e product o f g's f o r a Sayre r e l a t i o n s h i p c o n t a i n i n g n.  I E R I  There i s a l s o an o p t i o n a l for  the v a r i o u s r e f l e x i o n s  output on tape o f the s i g n s  i n solutions.  T h i s output i s  compatible w i t h the next program which, by merely s p e c i f y i n g the number o f the s o l u t l o n ( s ) d e s i r e d , slmilated structure Fourier  f a c t o r tape ( o f E's) f o r input  t o the  program.  The ITEST  produces a  c h i e f t e s t incorporated  i n t o SIGNS i s c a l l e d  and w i l l now be d e s c r i b e d . ITEST  w i l l r e j e o t any s o l u t i o n f o r which, f o r any h,  the f o l l o w i n g  e x p r e s s i o n exceeds a p r e s e t  valuei  lEKl |E£l lEfJ.^I where H i s a r e f l e x i o n c o n t a i n e d i n a Sayre r e l a t i o n s h i p that f a l l s and lEgl IE^I \BC*rf|I s the v a l u e o f the t r i p l e product of E's f o r t h a t r e l a t i o n s h i p . For a s o l u t i o n which i s w i t h i n above, the maximum v a l u e a t t a i n e d out  t h e bounds imposed  f o r any K w i l l be p r i n t e d  under t h e heading of SMAX. This  t e s t , f o r any n, i n d i c a t e s  which i t s s i g n i s i n d i c a t e d which i s p r e d i c t e d .  the p r o b a b i l i t y w i t h  t o be the o p p o s i t e of that  I t i s i n the n a t u r e of the s o l u t i o n s  88  produced by  the Vand A Peplnsky method (or Cochran &  Douglas method f o r that m a t t e r ) , t h a t list the  f i r s t group and  that  as  w i t h each s i g n  p r o b a b i l i t i e s of the r e l a t i o n s  s o l u t i o n are o o r r e o t , then i t i s v e r y  a r e l a t i o n of say 0.99  that all  f a i l u r e s i n a l l , there e x i s t s  s o l u t i o n t o the s t r u e t u r e  the p r e d i c t e d  for  Improbable.  t h a t one t o be  the  The  unlikely  Sayre r e l a t i o n s h i p  is  of  indicated  probabilities  99#  or b e t t e r .  test i n  be  extended  individual relation This extension,  ITEST, f o l l o w s  from  the  e x p r e s s i o n s f o r the p r o b a b i l i t y of Sayre r e l a t i o n s p r o b a b i l i t y of one  r e l a t i o n Indicating  r e f l e x i o n h t o be p o s i t i v e i s g i v e n P+(h*) »  tanh C3  But  beoause t h i s f u n c t i o n  the  e q u a t i o n can  that  the  1  Incorporating  However, t h i s t e s t can  those oases where no  a p r o b a b i l i t y of say  The  Is  99#.  of Sayre r e l a t i o n s h i p s .  which i s the a c t u a l  rejected  •solution  program which uses the a c t u a l  to i n c l u d e  hence  at t h i s f a i l u r e  p r e c e d i n g I n d i c a t e s a simple way  a t e s t i n t o the  further  of l o o k i n g  o p p o s i t e s i g n t o that g i v e n l n the  to a p r o b a b i l i t y of  correct.  p r o b a b i l i t y f a i l s and  Another way  r e f l e x i o n i n the  the  holding  s o l u t i o n s where such a r e l a t i o n f a i l s can be  has  the  s a t i s f y i n g the l i m i t i n g c o n d i t i o n s on f a i l u r e s i n  correct If  somewhere i n  the  holding. sign  by  (T2"3/2 j j j gg  (i^  E {  is  be r e w r i t t e n  of  antisymmetric about P = to express the  £•  probability  s i g n of EfJ, whatever l t I s . i s g i v e n by  the  89  p a r t i c u l a r Sayre r e l a t i o n i n question, as follows,  P(K) « H t a n h a  ff  2"  ]Eg) ) E £ h E | .  3/2  M  (5)  When more Sayre/relationships are used to indicate the sign of h  (4) becomes,  P+(h*)«£+£ t a n h ^ 3 2 v  "  3 / 2  (6)  E | E f f | Eg Ej^g  (see H o l l e t t ^ or Karle & K a r l e ) 7  and  i f a l l the r e l a t i o n s indicate the same sign f o r h  (5)  becomes i n the general case P(K) »  W  tanh ^3 &2  "  3 / 2  Elsgl  jEgl lEg^gl  0  (7)  Now, by the nature of the method of forming solutions, the actual r e l a t i o n s which f a i l f o r any s o l u t i o n are known. If (6) oontained oniy $ i y r e r e l a t i o n s that f a i l e d , then (7) becomes the p r o b a b i l i t y that the sign of Eg i s predicted to be the o p p o s i t e ^ f that which appears i n the s o l u t i o n . The foregoing now,indicates the test i n i t s most general form.  Because of the form of equation  (7)» i t i s easier to  work with a value of the summation of t r i p l e  products,  rather than an a c t u a l value of the p r o b a b i l i t y , and hence, the c r i t e r i o n becomes a maximum on the value of t r i p l e products of E's (EMAX i n the program). Note that a better expression f o r the p r o b a b i l i t y that the sign of Ej* Is opposite to that predicted Is P ( i a ) « £ + i tanh 0-3 <*2 ~  3  /  2  (Eft |Egl (Eg||Ep* g| failures =  '  Iff  jEHllEgllEpj^l) suocesses  but the simpler form where only the f i r s t term i n brackets  90  Is used, should be s u f f i c i e n t i f i t s l i m i t i n g v a l u e i s s e t h i g h enough, (e.g. a v a l u e o f the t r i p l e  product  c o r r e s p o n d i n g t o a p r o b a b i l i t y of ~ 0.99). A l s o note, t h a t the t e s t i s o n l y a method o f r e j e c t i n g a l a r g e number o f improbable  s o l u t i o n s and does  not n e c e s s a r i l y i n d i c a t e which of t h e remaining  solu-  t i o n s i s the c o r r e c t one. However, i t I s n e v e r t h e l e s s suggested  t h a t the r e m a i n i n g s o l u t i o n s be t r i e d i n the  order o f i n c r e a s i n g v a l u e o f SMAX.  The t e s t ' s  u s e f u l n e s s i s t h a t i t permits one t o extend  chief  the Sayre  r e l a t i o n s h i p s t o low v a l u e s of E (as low as say,  1.0),  and p r o v i d e s a good c r i t e r i o n f o r the r e j e c t i o n of the v a s t m a j o r i t y o f p o s s i b l e s o l u t i o n s which a r e produced when, as i n t h i s case, i n d i v i d u a l Sayre r e l a t i o n s have a p r o b a b i l i t y o f h o l d i n g o n l y a l i t t l e removed from  50#.  The d a t a c a r d s f o r t h e SIGNS program a r e as f o l l o w s t Card 1 1-2  INPUT tape u n i t  12  3-4  INFILE  12  5-6  OUTPUT tape u n i t n o . ( I f any) ( p r e f e r a b l e » INPUT)  12  7-8  OUTPIL  12  9-10  NFAILl  l i m i t i n g v a l u e o f no. of f a i l u r e s i n f i r s t group ( i 5 )  12  11-12  NFAIL2  l i m i t i n g v a l u e o f no. o f f a i l u r e s i n a l l ( £ 20)  12  13-20  EMAX - upper l i m i t of sEEE i n  ITEST  P8.0  91  Card 2 1-2  NCON - number o f r e f l e x i o n s whose s i g n Is t o be s p e c i f i e d ( £ 1 0 )  3-5  ICON (1)  6-9  ICON (2)  9-11  ^  12-14  12  - i the no. of the 1st r e f l e x i o n t o be g i v e n s i g n  13  - - t h e no. o f the 2nd r e f l e x i o n t o be g i v e n s i g n  13 13  .  /the s i g n t o be  .  yused f o r a r e f l e x i o n ) w i l l be the s i g n  ICON (NCON)  13  ' a t t a c h e d here  4. ESIGND program T h i s program acoepts a tape of | E l ( h k l ) ' s and a tape (which may be t h e same as the l a s t ) solutions suitable  from SIGN program.  containing  I t produces another tape  f o r the POUBIE program, c o n t a i n i n g E-values w i t h  t h e i r proper s i g n s ( i f any) f o r up t o s i x s o l u t i o n s a t onoe s p e c i f i e d o n l y by the number of the s o l u t i o n as i t appears i n the SIGNS program.  The s i x s o l u t i o n s  on the  output tape are put i n c o n s e c u t i v e words a f t e r the f l o a t i n g point  h,k,l's.  Each s o l u t i o n i n the F o u r i e r 1-6, Bo,  i s , t h e r e f o r e , capable of being c a l l e d  program by s p e c i f y i n g  as c o e f f i c i e n t s f o r F o u r i e r  d i f f e r e n t numbers,  summation (Fo, F c , Ac,  Be now no l o n g e r have t h e i r o r i g i n a l meaning but a r e  just E *s f o r different 0  program).  (up t o 6) s o l u t i o n s  o f the SIGNS  92  A t y p i c a l r u n would have E»s i n f i l e 14 of P 6 9 on u n i t 03 and have s i g n s i n f i l e 16 o f the same tape; the output o f f i v e d i f f e r e n t s o l u t i o n s would be the s c r a t c h u n i t 02.  The i n p u t f o r t h e F o u r i e r program r u n immediately  a f t e r on IBSYS, would be 02 w i t h output on the d i s k u n i t 11 for  the f i r s t  pass  ( c o e f f i c i e n t = 1 ) ; the next f o u r passes  would be output on the same u n i t 11, w i t h the F o u r i e r cards d u p l i c a t e d f o r each pass except t h a t t h e c o e f f i c i e n t s s p e c i f i e d would be 2, 3 , 4, and 5 f o r r e s p e c t i v e passes. U n i t 11 then p r o v i d e s the Input f o r t h e CONTUR program where one s p e c i f i e s t h a t t h a t u n i t c o n t a i n s f i v e to  passes  be drawn (IPBOJ.« +1 f o r l a b e l l i n g ) , and the contoured  map would be output as u s u a l on U n i t 04 f o r which a s m a l l L - tape should s u f f i c e . Note t h a t t h e c o n t o u r i n g I n t e r v a l t o be used f o r the CONTUB program i s r o u g h l y p r e d i c t a b l e . of  ~ 2 5 r e f l e x i o n s o f average  and rnF(OOO) as 0.0. in  F o r the case  E ~ 1 . 5 » s p e c i f y C/V = 1 . 0 ,  Then, as the t r i g o n o m e t r i c f u n c t i o n s  t h e summation oan never exceed a v a l u e o f 1.0, t h e  F o u r i e r summation c a n never exceed 40 ( a v a l u e w i t h F0URIE outputs as 4000). to  A h i g h e s t v a l u e o f 1000 should s u f f i c e  contour any E-map t h a t r e s u l t s .  The d a t a c a r d f o r the  ESIGND program c o n t a i n s t h e f o l l o w i n g i n f o r m a t i o n 1 1-2  INE - i n p u t tape u n i t f o r E»s  12  3-4  I F E - f i l e # on INE  12  5-6  INS - i n p u t tape u n i t f o r s i g n s (solutions)  12  93  7-8  IPS - f i l e # on INS  12  9-10  OUTPUT - tape u n i t no.  12  11-12  NPOSS - no. of s o l u t i o n s t o be output (£6)  12  13-20  MINE - same as i n SAYRE (but not as i n P8.0  PBEDIR) 21-25  IPOSS (1)  - t h e no. of the f i r s t  26-30  IPOSS (2)  - the no. of the second s o l u t i o n  solution  15 15  31-35  •  • IPOSS (NPOSS)  The f o l l o w i n g two p o i n t s should be noted 1 1.  the numbers i n IPOSS must be i n i n c r e a s i n g order.  2.  I F E I s u s u a l l y the same as IFS.  • 15  9*  HOT PROGRAM T h i s program was w r i t t e n e x l u s i v e l y f o r the methyl 2-chloro-2-deoxy-or-D-galactopyranoslde  structure to f i n d  the c o r r e c t s o l u t i o n I n t h e xy p r o j e c t i o n knowing the p o s i t i o n of o n l y the c h l o r i n e and the r e l a t i v e (in to  positions  r a d i a l c o o r d i n a t e s ) of up t o s i x carbon atoms and up s i x oxygen atoms,  ^ h l s program c a l c u l a t e s the B-  v a l u e f o r h k 0 p r o j e c t i o n d a t a (^ 300) w i t h  |Fo|(h k 0) ^  a s p e c i f i e d v a l u e , as the molecule i s r o t a t e d by s m a l l increments about the f i x e d c h l o r i n e p o s i t i o n .  The v a r i o u s  (R,8) a r e output on tape u n i t 11 In p r e p a r a t i o n f o r p l o t t i n g a R v e r s u s © curve by a U.S.C. l i b r a r y program. program i t I s assumed t h a t | P o | ( h k l ) d a t a  (In t h i s  2000  r e f l e x i o n s i n c l u d i n g end o f group symbolsj Is i n f i l e of  #3  a tape mounted on l o g i c a l tape u n i t 03), The d a t a c a r d s f o r the ROT program a r e as f o l l o w s i  POSITION  DESCRIPTION  FORMAT  Card 1 1-10  A - l e n g t h o f a - a x l s (A)  F10.0  11-20  B - l e n g t h o f b - a x i s (A)  F10.0  21-30  THETA - i n i t i a l  31-40  THEINC - increment i n &  F10.0  41-50  THEMAX - maximum v a l u e o f 0  F10.0  FOMN - minimum l F o ( h k 0)1 t o be used  F10.0  TCL - temperature  F10.0  v a l u e o f <9 ( r a d i a n s )  F10.0  Card 2 1-10 11-20  factor  (B) o f CI  95  21-30  TO - temperature  f a c t o r (B) o f 0  F10.0  31-40  TC - temperature  f a c t o r (B) o f C  F10.0  41-45  NO - no. of 0- atoms i n molecule i n asymmetric u n i t (<6)  45-50  NC - no. o f C- atoms l n molecule  51-55  IFOBS - 0  (46)  no p r i n t o u t of i n p u t F ( h k 0)*B 0  56-60  15 15  15  IFCAL - 0 ^ n o p r i n t o u t o f Fo/Fc f o r s t r u c t u r e w i t h minimum B  15  Card 3 1-10  CLX - x/a c o o r d i n a t e o f C l  F10.0  11-20  CLY - y/b c o o r d i n a t e o f C l  F10.0  1-10  RADO(l) - r f o r 0#1  F10.0  11-20  ANGO(1) - 0 f o r 0#1  F10.0  Card 4  e  Cafd 4+NO 1-10  RADO(NO) - r f o r 0#N0  F10.0  11-20  ANGO(NO) - 6 f o r 0#N0  F10.0  Card 5+NO 1-10  BADC(l) - r f o r C#l  F10.0  11-20  ANGC(l) - 6 f o r C#l  F10.0  Card 5+NO+NC 1-10  RADC(NC) - r f o r C#NC  F10.0  11-20  ANGC(NC) - & f o r C#NC  F10.0  96  CONTUR PROGRAM T h i s program accepts  a tape (IN12) prepared by the  FOURIE program c o n t a i n i n g a s p e c i f i e d , number of passes (NPASSS) and produces contoured maps f o r s p e c i f i e d oontours ( C ( I ) , I » 1, NCONTU) on U.B.C.'e Caloomp 565 12  i n c h drum p l o t t e r .  Each map (pass) w i l l normally be  contoured i n t u r n , a l l s e c t i o n s of one pass being done before  the next pass i s begun.  An o p t i o n , however,  e x i s t s which w i l l a l l o w two passes t o be j o i n e d i n each s e c t i o n w i t h the r e s u l t t h a t corresponding two  sections f o r  passes a r e read c o n s e c u t i v e l y and drawn up as one  larger section.  Another o p t i o n  (NEWZ) allows  t i o n o f a d i f f e r e n t axis, o f s e c t i o n s t o that on the i n p u t tape, b y - p a s s i n g t h e need f o r  specificacontained  repreparing  the s t r u c t u r e f a c t o r tape. The  s i z e o f the maps a r e s p e c i f i e d i n cm./A (SCALER).  I f not s p e c i f i e d , t h e maps w i l l be drawn t e n inches wide, the l i m i t  o f U.B.C.'s Calcomp p l o t t e r .  If a scale i s  s p e c i f i e d which r e q u i r e s more than the t e n i n c h width of the p l o t t e r , t e n inches be drawn f i r s t ,  o f the map f o r a l l s e c t i o n s  will  t h e r e a f t e r , u n i t s (PARTS) of up t o t e n  inches w i l l be drawn as many times as i s needed t o complete the map. Each PART ( a " p a r t " o f a s e c t i o n n o t g r e a t e r t e n inches)  than  i s f i r s t read i n from IN12 and the number of  p o i n t s i s i n c r e a s e d f o u r - f o l d (BHOO(6l,6l)) by l i n e a r  97  interpolation,  i n t r o d u c i n g one p o i n t between every two  a d j a c e n t p o i n t s of the o r i g i n a l F o u r i e r g r i d .  On t h i s  f i n e r g r i d c o n t o u r i n g i s commenced by s e a r c h i n g f o r p o s s i b l e contours which b e g i n on the o u t s i d e of the map of  (and thus f i n i s h on the o u t s i d e ) .  A f t e r contours  t h i s type a r e drawn, i n t e r i o r contours (which f i n i s h  a t the same p l a c e they begin) are then searched f o r along the v e r t i c a l d i r e c t i o n  o n l y , and drawn i f they  have not been drawn a l r e a d y . are  Regions between g r i d p o i n t s  r e p r e s e n t e d i n ICON (61,121) and when, f o r Instance,  an Nth contour i s drawn between two g r i d p o i n t s , note i s made of i t i n ICON by adding 2^"^  t o the a p p r o p r i a t e word  of c o r e ( t u r n i n g the Nth b i t o n ) . In s e a r c h i n g f o r the s t a r t of a contour between 2 g r i d p o i n t s , a l l NCONTU contours are t r e a t e d s i m u l t a n e o u s l y (but o n l y i f they ooour between p o i n t s such t h a t the second has a h i g h e r v a l u e than the f i r s t ) , b e f o r e g o i n g on to the next i n t e r v a l .  In c o n t i n u i n g the drawing  of a contour l i n e , a note i s made of the d i r e c t i o n i n which the contour has approached f a c i l i t a t e finding  direction  —•  a grid quadrilateral  a new e x i t p o i n t f o r the oontour.  (1,0)  new d i r e c t i o n | (0,-1)  to  98  Only t h r e e p o s s i b l e such e x i t p o i n t s e x i s t f o r the c o n t o u r d e p i c t e d above and i t becomes a simple matter of c h e c k i n g which can be used. back on i t s e l f  When a contour comes  (or i n the case of e x t e r i o r c o n t o u r s ,  when a contour a g a i n reaches the o u t s i d e ) , i t i s complete and s e a r c h f o r new oompleted  contours can recommence where the  one s t a r t e d .  now  Contour l i n e s c o n s i s t of s t r a i g h t  l i n e s between edges of the q u a d r i l a t e r a l g r i d ,  their  p o s i t i o n on the edges b e i n g determined by l i n e a r  inter-  polation. L a b e l l i n g of the c o n t o u r maps c o n s i s t s of i d e n t i f i c a t i o n of each s e c t i o n by i t s h e i g h t i n 1/120'ths and of each t h i r d contour ( b e g i n n i n g w i t h C ( l ) ) w i t h s p e c i a l symbols noted a t the b e g i n n i n g of the p l o t .  When a l l  c o n t o u r i n g t o be done on a s p e c i f i e d i n p u t tape i s complete, the message, END  OF ALL PASSES, i s drawn out on the p l o t t e r  paper. As o n l y l o g i c a l u n i t s 03 and 04 can be used f o r l o a d i n g and u n l o a d i n g t a p e s , and as a p l o t t e r tape must always be mounted on 04 f o r the CONTUB program (at U.B.C. p l o t t i n g i s o f f - l i n e ; p l o t t i n g i n s t r u c t i o n s are f i r s t output on tape u n i t 04 b e f o r e a c t u a l p l o t t i n g i s done ), it  i s i m p o s s i b l e t o r u n FOURIE and CONTUR c o n s e c u t i v e l y  p l o t t i n g out a F o u r i e r map  and a t the same time s a v i n g the  tape output of the FOURIE program. alternatives t  T h i s l e a v e s two  99  1. Saving the F o u r i e r map - The FOURIE program Is r u n one day I n p u t t i n g  the s t r u c t u r e  f a c t o r tape on 04, and o u t p u t t i n g map on 03.  the F o u r i e r  The next day t h i s prepared F o u r i e r  map I s remounted on 03 t o be used by the CONTUR program f o r p r e p a r i n g  a p l o t tape on 04.  2. Not s a v i n g t h e F o u r i e r map - The FOURIE and CONTUR programs a r e r u n c o n s e c u t i v e l y and conc u r r e n t l y w i t h t h e s t r u c t u r e f a c t o r tape on 03 and  output o f t h e F o u r i e r map on s c r a t c h d i s c  u t i l i t y 11 (or 12).  The l a t t e r u n i t  provides  Input t o the CONTUR program which prepares a p l o t tape on u n i t 04. NOTEi A program (PROJ) whose i n p u t w i l l not be d e s c r i b e d here, was a l s o w r i t t e n which together  with a  s p e c i a l v e r s i o n of t h e CONTUR program (PR0JCN), produces p r o j e c t e d views o f t h e three  dimensional  e l e c t r o n d e n s i t y maps ( F i g u r e s , 6 and 15)* 3  T h i s was done t o save the l a r g e amounts of paper and  computer time r e q u i r e d f o r oontouring on a  large soale, f u l l  three-dimensional  maps which would  otherwise have t o be produced f o r t h i s by the r e g u l a r CONTUR program.  100  The data cards f o r the CONT UR program are as follows t POSITION  DESCRIPTION  FORMAT  Card 1 IN12 - Input unit,no. (02, 03, 11 oi> 12 only)  12  3-4  NPASSS - no. of passes on IN12  12  5-6  NPAIRS - no. of p a i r s of passes to be joined i n each section beginning at pass #1  12  1-2  7-8  NEWZ - new a i l s of sections, i f any (1 f o r x, 2 f o r y, 3 f o r z)  12  Card 2 1-80  ANYTHING f o r i d e n t i f i c a t i o n  1 3 A 6 , A2  Card 3 1  IDENTITY OF AAXIS )  II  \l f o r x, 2 f o r y,3for z 2  IDENTITY OF BAXIS J  II  3-4  NC0NTU - no. of contours ^16  12  5-6  IPASS - -fl i f program to begin again a f t e r p l o t t i n g IN12 12 ILAB - -1 suppresses a l l non-essential labeling 12 IPR - +1 i f Fburiers are a series of projections 12 AAXIS - length of axis (A) along p l o t t e r paper F10.0 BAXIS - length of axis (A) across 10 inch width F10.0  7-8 9-10 11-20 21-30 31-40 41-50 51-60  THETA - angle (deg.) between AAXIS + BAXIS (90.0 i f BLANK)  F10.0  SCALE - cm./A (plot f i l l s width of paper i f BLANK)  F10.0  CLKMAX - time allowed f o r this program (normally BLANK)  F10.0  101  Card 4 1-10  C ( l ) - f i r s t contour  P10.0  c(8) - e i g h t h contour (read o n l y i f  71-80  NC0NTU»8)  P10.0  Card 5 ( i n c l u d e d o n l y i f NC0NTU>8) 1-10  C(9)  71-80  - n i n t h contour  F10.0  C ( l 6 ) - s i x t e e n t h contour  P10.0  The f o l l o w i n g p o i n t s should be noted f o r the CONTUR program t 1. Repeat c a r d s 1 through 4 ( o r 5) i f l a s t s e t of 4 ( o r 5) cards had IPASS = +1. 2. AAXIS + BAXIS a r e w.r.t. UNIT CELL, not ASYMMETRIC UNIT. 3. Contours must be i n i n c r e a s i n g o r d e r . 4. P l o t t e r tape i s always mounted on 04. 5.  I f two passes a r e t o be J o i n e d , they must be i n n a t u r a l o r d e r ; they must be of equal dimensions a l o n g a l l t h r e e d i r e c t i o n s ; and, the end of one pass must be the same as the s t a r t of the other pass along one a x i s i n t h e plane of s e c t i o n s .  **********  s  102  B I B L I O G R A P H Y 1. H. L l p s o n and W. Coohran, "The Determination o f C r y s t a l S t r u c t u r e s , " G . B e l l and Sons L t d . , 3rd edn., 1966. 2. J.M. Robertson, "Organic C r y s t a l s and M o l e c u l e s , " C o r n e l l U n i v e r s i t y P r e s s , 1953» 3.  G.H. Stout and L.H. Jensen, "X-ray S t r u c t u r e D e t e r m i n a t i o n A P r a c t i c a l Guide," Macmillan Co., 1968.  4. M.J.Buerger, "Vector Space," John Wiley and Sons L t d . ,  1959. 5. G.N. Ramachandran, ed., "Advanced Methods o f C r y s t a l l o g r a p h y , " Academic P r e s s , 1964. 6.  H. Hauptman and J . K a r l e , "The S o l u t i o n of the Phase Problem - I . The Centrosymmetrio C r y s t a l , " American C r y s t a l l o g r a p h i o Ass., 1953*  7.  J . K a r l e and I.L. K a r l e , Aota C r y s t . , 1966, 21, 849.  8. M.M. Woolfson, " D i r e o t Methods i n C r y s t a l l o g r a p h y , " Oxford U n i v e r s i t y P r e s s , 1961. 9.  J.S. R o l l e t t , Clarendon  10.  "Computing Methods i n C r y s t a l l o g r a p h y , " P r e s s , Oxford. 1965.  R. Hoge and J . T r o t t e r , J.Chem.Soc.(A), 1968, 267.  11. H.M. Berman and S.H. Kim,  A c t a C r y s t . , I968, B24, 897.  12.  J.K.N. Jones, P r i v a t e Communication, 1967.  13.  J.K.N. Jones, M.B. P e r r y and I.C. Turner, Canad.J.Chem., I960, 3_8, U 2 2 A J.M. B i j v o e t , A.P. Peerdeman and A . J . van Bommel, Nature, 1951, 168, 271.  14. 15.  " I n t e r n a t i o n a l Tables f o r X-Bay C r y s t a l l o g r a p h y , " Kynoch P r e s s , Birmingham, 1962, v o l . I I I .  16.  G.A. J e f f r e y and R.D. R o s e n s t e l n , Advanc.Carbohyd.Chem., 1964, 19, 1.  17e P.D. Bragg, J.K.N. Jones, and J.C. Turner, Canad.J.Chem., 1959, 37, 1412.  Bibliography (cont'd.)  18. B.E. Reeves, J.A.C.S., 1950, 72, 1499. 19. W.C.  Hamilton and J.A. Ibers, "Hydrogen Bonding i n S o l i d s , " W.A. Benjamin, Inc., i 9 6 0 .  20. J.D. Oonohue i n "Structural Chemistry and Molecular Biology," Ed. A. Rich and N. Davidson, Freeman Press, 1968, pp.450-456. 21. "IBM 7040/7044 Operating System (16/32K) Fortran IV Language," IBM Corp., Programming Systems Publications, 1964.  **********  APPENDIX  (Source deck l i s t i n g s of programs i n P a r t I I )  9 9 L 8 6 °'l  TT Zl A  P R E D I R  V 12'_  1J_ 10  9 8  7  6_ 5  4 3  P R O G R A M  ,  S I B F T C PREDIR R E F » DECK C T H I S PROGRAM I S I D E N T I C A L INTEGER EXMULT INTEGER OUTPUT * O U T F I L  TO  THAT  DATED  08/02/68  07/09/68  R E A L MAXSS, M I N S S , MAXSL, M I N S L , MINEPR• MINETP*MULTAX,MULTPL DIMENSION F X ( 3 ) » N R E F L ( 5 0 ) * S U M F 2 < 5 0 ) » S U M N F ( 5 0 ) » AVRGF2(50) DIMENSION S T O L S 2 < 5 0 ) » SSOLS2(50.)» S I G M A 2 ( 5 0 ) » RAT 1 0 ( 5 0 ) , N A T O M S ( 5 0 ) DIMENSION M U L T P L ( 3 ) » IEX(10»3)» EXMULT(IO) DIMENSION F C U R V ( 8 ) » FO(8)» P(8)» F ( 8 » 1 4 ) DATAPREP  1 44 45  2 00  READ  201  FORMAT (16F5.3) PRINT 48  48  FORMAT  153 154 155 .  4  3  WEIG+T IPROJ,I HALF,STLMAX, WEIG+T  READ 4 5 » N E X T » ( ( ( I E X ( I , J ) , J = 1 , 3 ) » E X M U L T ( I ) ) , I = FORMAT ( 12, 3X, 1 0 ( 4 I 1 » I X ) ) / READ 24»NCUR\£, ( N A T O M S ( I ) , 1=1,NCURV) FORMAT DO 2 0 0  152  WEIG+T  R E A D 4 4 , M U L T A X , ( M U L T P L l I ) ,1 = 1 , 3 ) FORMAT I 4F5.3)  24  151  > W  DIMENSION W E I G H T { 2 ) » O U T T Y P U ) ' DATA OUTTYP / 24H H K L O K L H O L H K O / R E A D 1. I N P U T , I N F I L E , O U T P U T , O U T F I L , N I N T V L » 1 MINEPR, MINETP, W E I G H T ( l ) , WEIGHT(2) FORMAT (712, IX, 5F5.2)  1,NEXT) •  (912) 1 = 1 ,NCURV  201,  P(I.)»  ( 11H  DATAPREP FO(I),  DATA  ( F ( I , J ) »J = 1 , 1 4 ).  DATAPREP DATAPREP  CARDS  )  PRINT 151, INPUT, I N F I L E , OUTPUT, O U T F I I , 1 MINEPR, MINETP, W E I G H T Q ) , WEIGHT(2) FORMAT 15X, 6 1 2 , 3X, 5 F 5 . 2 ) PRINT 152, M U L T A X , ( M U L T P H I ) , 1 = 1 , 3 ) FORMAT ( 5X, 4 F 5 . 3 )  NINTVI,  PRINT 153» N E X T , ( ( ( I E X ( I , J ) , J = l , 3 ) » EXMULT<I)),I= FORMAT ( 5X, 12, 3X, 1 0 ( 4 1 1 , I X ) ) PRINI 154, NCURV, ( N A T O M S ( I ) , 1=1,NCURV) FORMAT (5X, 912) PRINT 1 5 5 , NCURV, ( F O ( I ) , I = 1 , NCURV.) FORMAT <5X, 1IVE INITIAL INTVL = 0 IfESI 1 = 0 ITEST2 = 0  4 H P L U S , 1 3 , 6 1 H CARDS OF S C A T T E R I N G MAGNITUDES,' 8(1X, F6.2))  STIMAX.  IPRn.J.  1,NEXT)  FACTORS  OF  RESPECT  :  2 4 8  3  5  6  7  69  68  ITEST3 = 0 A S S I G N 4 TO I E N D F C A L L EOF ( I N P U T * IENDF) REWIND INPUT NFILE = INFILE I F ( N F I L E . L E . 1 ) GO TO N F I L E = N F I L E - 1. R E A D ( I N P U T ) 11 . G O TO 8  iF(iTESTi  .NE.  O>GO  TO  •  '  _ _ _ _ _ _ _ _  3 ; .  6  ITEST1 = 1 • ' MINSS = 10.0 MAXSS = 0 . 0 R E A D ( I N P U T ) I I » I G P E N » S S O L S » F H »FK,» F L > F R E L » F S Q R » ( F C U R V ( I ) » I = 1 » 8 ) • I F ( I G P E N . N E . 0 ) GO TO 5 I F ( I I . N E . 0 ) GO TO 2 I F ( S S O L S .GT. M A X S S ) MAXSS= S S O L S . . I F ( S S O L S . L T . TMINSS) M I N S S = SSOLS G O TO 5 I F ( I T E S T 2 . N E . 0 ) GO TO 2 8 . M A X S L =• S O R T ( M A X S S ) MINSL = SQRT(MINSS) PR I N T 7» M A X S L * M I N S L • FORMAT I 3 6 H 1 S I N E THETA OVER, LAMBDA» MAXIMUM = » F 7 . 4 , 12H» M I N I 1MUM = » F7.4 ) I F ( S T L M A X . L E . 0 . 0 ) GO TO 6 8 . " MAXSL = STLMAX P R I N T 69* STLMAX FORMAT (/66H AS I N S T R U C T E D * . A L L DATA_WITH S I N E THETA OVER LAMBDA G 1 R E A T E R THAN , F 7 . 4 » 3 7 H WILL BE R E J E C T E D FROM WILSON S C A L I N G 2 / 5 X , 1 1 6 H A N D F R O M C A L C U L A T I O N S O F A V E R A G E E@S A N D E 2 @ S » B U T W I L L 3 B E I N C L U D E D I N C A L C U L A T I O N S A N D O U T P U T T I N G • O F I N D I V I D U A L E@S /) DIVSL =10.0 I F ( N I N T V L .GT. 4 ) D I V S L = N I N T V L I F ( N l NT V L . L T . 5) N I N T V L = 1 0 ' X I N T V L = ( M A X S L - M I N S L . ) /• D I V S L ITEST2 = 1 DQ 2 3 1 = 1» N I N T V L .. ^ ; ' S U M F 2 ( I ) = 0.0 SUMNF(I) =0.0  s 9  23 9  _  14  10  12 13 f  1  Y  12  16  1JL 10  9 8  15 17  7 6 5 4  3  11 18  NREFL(I) = 0 READ (INPUT)  II * IGPEN * SSOLS» 1 ( F X ( I ) » I = 1 » 3 ) » FREL*FSQR»(FCURV(I)»I = 1»8) I F ( I G P E N . N E . O ) GO TO 9 ' I F ( I I . N E . 0) GO TO 11 5T0LS = SQRT(SSQLS) IF (STOLS . G T . MAXSL) GO TO 9 I = (STOLS - MINSL) / XINTVL + 1.0 , IF (STOLS . E Q . MAXSL) I = NINTVL ~ . IF (STOLS . E Q . MINSL) 1 = 1 . NREFL ( I ) = N R E F H I ) + 1 ' . NZEROS = 0 DO 14 J = 1. 3 IF ( F X ( J ) . G T . 0 . 2 5 . O R . F X ( J ) . L T . ( - 0 . 2 5 ) ) GO TO 14 ~~ NZEROS = NZEROS +1 JZERO = J CONTINUE IF (NZEROS . N E . 0) GO TO 10 ADDF2 = FSQR ADDNF = 1 GO TO 17 . IF (NZEROS . N E . 2) GO TO 12 ADDF2 = FSQR * MULTAX • ADDNF = MULTAX GO TO 13 ADDF2 = FSQR * MULTPL(JZERO) ADDNF = MULTPL(JZERO) IF (NEXT . E Q . 0) GO TO 17 DO 15 J= 1» NEXT DO 16 K= 1* 3IF ( I E X ( J » K ) . E Q . 0 . A N D . F X ( K ) . N E . 0 . 0 ) GO TO 15. CONTINUE ADDNF = ADDNF * F L O A T ( E X M U L T ( J ) ) GO TO 17 CONTINUE S U M F 2 U ) = S U M F 2 U ) + ADDF2 ' SUMNF(I) = SUMNF(I) + ADDNF GO TO 9 PRINT 18 F O R M A T ( / / / 8 H RANGE 8H STOLS »12H REFLEX IONS , 10H SUMREFL »  L 8 6  Ol  s 9  1  21 20 400 50  2 03 202 204 205 2 07  •  41 40  13H SUMF0BS**2 , 1 7 H AVERAGEF0BS**2 ) SL = MINSL +XINTVL / 2 . 0 DO 20 I = 1 •NINTVL AVRGF2(1 ) = SUMF2( I ) / SUMNF(I) PRINT 21» I » S L * N R E F H I ) » SUMNF I I ) * SUMF2 ( I.) • AVRGF2( I ) . FORMAT (3X» I3» 2X» F 7 . 4 » 4 X , I 5 » 4X» F 8 . 2 * 2X • F 1 0 . 1 . 5X^ F 1 0 . 3 ) SL = SL + XINTVL NINTVL = NINTVL - 1 DQ 400 1=1• 8 FCURV(I)=0. PRINT 50 F 0 R M A T ( / / / 8 H RANGE 8H STOLS »12H REFLEXIONS * 10H SUMREFL * 1 13H SUMF0BS**2 • 17H AVERAGEF0BS**2 2 8H SIGMA2 » 17H SIGMA2/AVRGEF2 ) DO 22 J = 1 » NINTVL X = J N R E F L ( J ) = N R E ' F L U ) + NREFL ( J + l ) SUMNF(J) = SUMNF ( J ): + SUMNF ( J + l ) S U M F 2 U ) = S U M F 2 U ) + S U M F 2 U + 1) AVRGF2(J ) = SUMF2(J) / SUMNF(J) S T 0 L S 2 ( J ) = MINSL + X * XINTVL SS0LS2(J)= ST0LS2(J) ** 2 STOLS = S T 0 L S 2 I J ) SSOLS = SSOLS2 1J) IF (STOLS - 0 . 1 ) 203»204»204 DO 202 1=1 •NCURV FCURV(I) = F 0 < I ) / E X P ( P ( D * S S 0 L S ) GO TO 105 IF (STOLS - 1.0) 205*206^206 KO = 1 K l = KO + 1 El = Kl • F l = 0.1*E1 IF (STOLS - F l ) 4 0 , 4 1 » 4 1 KO = KO + 1 GO TO 207 EO = KO FO = 0 . 1 * E 0 K2 = KO + 2 K3 = KO + 3  I  i  8-  6  011 T T  Zl  DATAPREP DATAPREP  DATAPREP DATAPREP DATAPREP DATAPREP DATAPREP DATAPREP DATAPREP DATAPREP DATAPREP DATAPREP, DATAPREP DATAPREP DATAPREP DATAPREP DATAPREP DATAPREP  A  t  = ( z < *o J  402  206 209  43 42 502 105 25 22 51 65  RANGE=(STOLS-FO)/.l RANG2=RANGE*(RANGE-1•)*0.5 RANG3=RANG2*(RANGE-2.1*0.33333 DO 402 I=1»NCURV F C U R V ( I ) = F ( I * K O ) ,+ ( F ( I • K l ) - F ( I • K O ) ) * R A N G E 1 • ( F•( I »K2 ) - 2 . * F ( I »K1 )+F ( I »K0) )*RANG2 + 2 ( F( I »K3 ) - 3 . * F ( I »K2 >+3«*F( I • K1 ) - F ( I • KO ) ) *RANG3 GO TO 105 KLOW = 10 KHI GH= KLOW + 1 EH IGH= KHIGH FHIGH= 0 . 1 * EH IGH IF (STOLS - F H I G H ) 4 2 » 4 3 » 4 3 KLOW = KLOW + 1 GO TO 209 DO 502 1 = 1 •NCURV FCURV(I) = F(I•KHIGH) + (F(I•KLOW)-F(I•KHIGH) )*(FHIGH-STOLS)* 10. SIGMA2U) = 0.0 DO 25 I = I t NCURV S I G M A 2 U ) = S I 6 M A 2 ( J ) + FLOAT ( NATOMS ( I ) ) * ( FCURV ( I.) • * * 2) " RATIO ( J ) = S I G M A 2 ( J ) / A V R G F 2 ( J ) PRINT 5 i t S T 0 L S 2 ( J ) ^ N R E F L ( J ) » SUMNF(J)* SUMF'2(J)^ A V R G F 2 ( J ) * 1 S1GMA2 ( J ) •. RAT I 0( J ) FORMAT (3X^ 13* ZX* F7«4» * X i 15* 4X* F 8 . 2 * 2X» F l O . l * 5X* F l 0 . 3 » 1 4 X . F 7 . 1 * 5X» F 7 . 2 ) PRINT 65* WEIGHT ( 1) » .WEIGHT(2) FORMAT ( 7 45H WEIGHTS OF FIRST TWO RANGES IN REFINEMENT = • 1 F 5 . 2 * 5H AND » F 5 . 2 , 13H RESPECTIVELY ) X I = ALOG(RAT 10(1) ) X2 = ALOG(RAT 10(2) ) Y l = SS0LS2(1) Y2 = S S 0 L S 2 ( 2 ) A l l = NINTVL - . 2 A l l = A i l +WEIGHTU) + WEIGHT(2) A12 = WEIGHT(l) * Y l + WEIGHT(2) * Y2 A22 = WEIGHT(l) * Y 1 * Y l + WEIGHT(2) * Y2 *Y2 B I = WEIGHT (1) * X I + WEIGHT(2) * X2 B2 = WEIGHT(l) * Y l * X I + W E I G H T 1 2 ) ' * Y2 *X2 DO 26 I = 3*NINTVL X = ALOG(RAT 1 0 ( I ) )  DATAPREP DATAPREP DATAPREP DATAPREP DATAPREP DATAPREP DATAPREP DATAPREP DATAPREP DATAPREP DATAPREP DATAPREP DATAPREP DATAPREP DATAPREP DATAPREP DATAPREP  WEIGH WEIGHT WEIG+T WEIG+T WEIG+T WEIG+TWEIG+T WEIG+T WEIG+T WEIG+T WEIG+T -WEIGHT WEIG+T WEIG+T •  .•  • .  Y= SS0LS2( I ) A12 = A12 + Y . A22 = A22 + Y * * 2 BI = BI + X B2_ = B2 + Y * X . . DETERM = A l l * A22 - A12 * A 1 2 X LOGK. = ( B I * A22 - B2 * A12 ) / DETERM B = (B2 * A l l - BI * A12 ) / DETERM . . . XK. = EXP(XLOGK) PRINT 52» A l l * A12» A22* Bl» B2» DETERM* XLOGK.* B F0f_MATj/5H A l l = * F 8 . 4 . 5H A12=» F 8 . 4 * 5H A22=* F 8 . 4 * 4 H Bl=> F 9 . 4 * 1 4H B2=t F 8 . 4 * 5H. DE t =» F8 • 4» 7H X|_OGK=.» F 8 . 4 » 3H B= * F 8 . 4 ) PRINT 63 FORMAT ( / / 26H CONSTANTS FOR INTENSITIES ) . . • PRINT 27» XK » B FORMAT ( 5 X , 1 8 H SCALE CONSTANT = » F 1 0 . 4 * 5X» 23H TEMPERATURE FACT _10R = F1C_.4_) :• PRINT 64 FORMAT ( / / 32H CONSTANTS FOR STRUCTURE FACTORS ) X = SQRT (XK) . ; • .. Y = B / 2.0 PRINT 27» X , Y  26 " :  ;  52  •  :  63 27 64  ••  •  SIG3 = 0 . 0 • • . " ' DO 61 I = 1» NCURV SIG2 = SIG2 +, FLOAT (NATQMS ( I )') * ( F O ( I ) * * 2) SIG3 = SIG3 + FLOAT (N A TOMS ( I ) ) * ('FO(I) 3) PROBCF = SIG3 / (S.IG2 * * 1.5) • PRINT 62 » PROBCF FORMAT (/ / 51H PROBABILITY COEFFICIENT* SIGMA3 / SIGMA-2 3/2 = 1 . F8.5) ' G 0 TO 2 • • . ' ^ PRINT 35 FORMAT (4H1 H» 4X,1HK»4X,1HL»8X»2HF0•5X»5HF0**2»4X,7H/F0**2/• 1 3X» 2HE2»-5X» 1HE» 3X * 7HEPS I LON / ) SUME =0.0 SUME2 =0.0 XNO = 0 . 0 NO = 0 SSLMAX = MAXSL * * 2 r  61 , "62.  PROBCF PROBCF PROBCF PROBCF PROBCF PROBCF PROBCF PROBCF  :  :  28 35  ' WEIG+T  46 47 34  29 31 32  IF (OUTPUT . E Q . 0) GO TO 34 REWIND OUTPUT . . ASSIGN 46 TO IENDF CALL EOF (OUTPUT. IENDF) N F I L E = OUTFIL I F . ( N F I L E . L E . 1) GO TO 34 NFILE = NFILE - 1 READ (OUTPUT)I I . GO TO 47 READ (INPUT) I I»IGPEN » SSOLS•FH » FK » FL»FREL»FSQR»(FCURV(I) • I = 1 » 8 ) IF( I I . N E . 0 . O R . IGPEN . N E . 0 ) GO TO 3.7 ' ABSF2 = FSQR * EXP(.( 6) * SSOLS) * XK IEPSLN =1 IF (NEXT . E Q . 0) GO TO 31' IF ( FH . N E . 0 . 0 . A N D . FK . N E . 0 . 0 . A N D . FL . N E . 0 . 0 ) GO TO 31 DO 29 J = 1» NEXT IF ( I E X ( J * 1 ) . E Q . 0 • A N D . FH . N E . 0.0) GO TO 29 IF ( I E X ( J » 2 > . E Q . 0. . A N D . FK . N E . 0.0) GO TO 29 IF (I EX(J» 3 ) . E Q . 0 • A N D . FL . N E . 0.0) GO TO 29. IEPSLN = EXMULT(J) GO TO 31 CONTINUE E2 = ABSF2 • SIGMAS = 0 . 0 DO 32 I = 1» NCURV SIGMAS = SIGMAS + F L O A T ( N A T O M S ( I ) ) * ( F C U R V ( I ) ** ?) E2 = E2 / SIGMAS IF ( I E P S L N . E Q . 1) GO TO 33 EPSLN = IEPSLN E2 = E2 / EPSLN E = SQRT(E2) IF (SSOLS . G T . SSLMAX) GO TO 7 0 1 = 10 IF (FH . E Q . 0 . 0 ) I = I -9 IF (FK . E Q . 0 . 0 ) I = I -8 IF (FL . E Q . 0 . 0 ) I = I -7 X = 1.0 IF (I . G T . 3) GO TO 67 IF (I . L T . 0) X = MULTAX IF (I . G T . 0) X = M U L T P L ( I ) >  •  -  •  -  33  WEIG+T WEIG+T WEIG+T WEIGHT WEIG+T WEIG+T WEIGHT WEIGHT  I 67  70 36  57 58 5 9. 60 71 72 73 56 37 f  38  12 1 1  66  Pio 9 8  P 1 6 5  P  4'  •  39  NO = NO + 1 WEIG+T XNO = XNO + X WEIG+T SUME = SOME + ABS(E) * X WEIG+T SUME2 = SUME2 + E2 * X WEIGHT CONTINUE IF (E . G E . MINEPR) PRINT 3 6 , F H , F K , F L , F R E L , FSQR, A B S F 2 , E2 ,E» IEPSLN ' FORMAT ( 3(1X» F 4 . 0 ) , 3 X , F 7 . 1 , F 8 . 1 , F 1 2 . 1 » 2 F 6 . 2 , 4 X , 12) I F ( O U T P U T . . L E . 0 ) GO TO 34 IF ( I P R O J . E Q . 0) GO TO 56 PROJ IF ( I P R O J - 2) 5 7 , 5 8 , 59 PROJ FPROJ = FH PROJ GO TO 60 PROJ FPROJ = FK PROJ GO TO 60 PROJ FPROJ = FL PROJ IF (FPROJ • N E . 0 . 0 ) GO TO 34 . PROJ IF (I HALF . E Q . 0 ) GO TO 56 GO TO ( 7 1 , 7 2 , 7 3 ) , I HALF FH = FH / 2 . 0 GO TO 56 FK = FK / 2 . 0 GO TO 56 FL = FL / 2 . 0 IF (E . G E . MINETP) WRITE(OUTPUT) I I , IGPEN, S S O L S , F H , F K , F L , E , PROJ 1 E2» ( F C U R V ! I ) , 1 = 1 , 8 ) GO TO 34 IF (OUTPUT . G T . 0 ) WRITE(0UTPUT) I I , IGPEN» SSOLS, F H , F K , F L , E* 1 E2, (FCURV(I),1=1,8) IF ( I I . N E . 0) GO TO 38 > GO TO 34 END F I L E OUTPUT IF (OUTPUT . G T . 0) PR I NT 66» O U T T Y P U P R O J + 1) , MINETP, OUTPUT WEIGHT • FORMAT ( A 6 , 30H DATA WITH @E@.NOT LESS THAN , F 5 . 2 , 24H HAS BEEN WEIGHT 10UTPUT ON T A P E , 13 ) WEIGHT REWIND INPUT REWIND OUTPUT PRINT 39 FORMAT 1 / / 2 5 H END DATA TO BE PROCESSED ) X2 = SUME / XNO WEIG+T  17  L  8 6 Ol TT Zl A  t  3  I  53  54 55 .  X I = SUME2 / XNO PRINT 5 3 , N O , SUME,- SUME2 > X2 > X I ' ; FORMAT ( / / 11H NO. REFL = » I 7 » 3 X , 8H SUM E =» F 9 . 1 » 3X 1 »' 9H SUM E2 =» F 9 . 1 * 3X» 12H AVERAGE E =» F 6 . 3 , 3 X . • 2 13H AVERAGE E2 =» F 6 . 3 ) _____ PRINT 54 FORMAT ( / 102H ( N O T E . . . I D E A L L Y , ©AVERAGE E@ HAS THE VALUE 0 . 7 9 8 F 10R CENTRIC AND 0 . 8 8 6 FOR NON-CENTRIC DISTRIBUTIONS ) PRINT 55 FORMAT ( 1 0 X , 49H WHILE ©AVERAGE E2@ HAS THE VALUE 1.000 FOR BOTH 1) ) ' • • -  S  -  T  0  END SENTRY  p  -  •  —  •  •  -  -  •  •  '  '  —  =  5AYRE PROGR.AM  V  12. 11_  ho 9  5 4  3  $IBFTC SAYRE DECK C THIS PROGRAM IDENTICAL TO 07/15/68 EXCEPT FOR FORMATS OF TAPE C . AND THAT EMPTY PARITY GROUPS ARE ALLOWED FOR ' C ISPACE I S . . . . 1 FOR P 2 » 2 FOR PMM» 3 FOR PMG, 4 FOR PGG» AND 5 FOR PGM C NO MORE THAN 35 REFLEXIONS IN ALL C NO MORE THAN 20 REFLEXIONS PER PARITY GROUP C NO MORE THAN 105 SAYRE RELATIONS TO BE GENERATED C NO MORE THAN 10 REFLEXIONS .TO BE SCRATCHED BY ©ISCRAT© INTEGER O U r p U T , OUTFIL INTEGER "PLUS PRINTOUT REAL MINE DATA PLUS* MINUS / 1H+, IH- / PRINTOUT DIMENSION F ( 3 ) » FCURV(8>* I COUNT(4)» IH(4»20)» I M 4 , 20) » E U » 2 0 ) DIMENSION I0CCUR(4» 2 0 ) , IDENT(4» 20) DIMENSION I2N(35)» IXS(4»105)» PROBIB(105) DIMENSION IREFL(35)» EREFL(35)» ID(3»105)» ISIGID(105)» E E E I D ( 105) PRINTOU DJ MENS I ON IRK20I.I IR2(20)» EE(20)» I S ( 2 0 ) , PRO.' 20) PRINTOUT "DIMENSrON"NOCCUR( 3 5") • ISCRAT(10) INTEGER OPLUSf OMINUS • DATA OPLUS, OMINUS / QOOOOOOOOOOOO» 0400000000000 / DIMENSION NA(35) FRR 1 ,3H 2»3H 4,3H DATA NA/3H 3..3H 5 ,3H 6, 3H 7,3H 8,3H 9, 3H IFOR 10, 3H 11*3H 12»3H 13»3H 14.3H 15*3H 16» 3H 17»3H 18»3H 19» 3.H IFOR 20» 3H 21»3H 22,3H 23.3H 24.3H 25,3H 26.3H 27,3H 28,3H 29,3H 2F0R 30, 3H 31,3H 32,3H 33,3H 34,3H 35 / FOR EQUIVALENCE ( X L , I L ) DUMMY = 0 . 0 52 READ 9 , INPUT, I N F I L E , OUTPUT, OUTFIL, I PROJ, ISPACE, IPRINT 1 .TONE, NSCRAT 2 . , PROBCF, MINE, ACCEEE, ( I S C R A T ( I ) , 1 = 1 , NSCRAT) 9 FORMAT ( 9 1 2 , 2X, 3F10.0, 1012) C © A C C E E E ® IS ACCEPTABLE VALUE OF TRIPLE PRODUCT CALL POSN ( INPUT, INFILE) DO 20 I - 1 * 4  (  I » 1 ) =0 = 0 E (1,1) = 0.0 ICOUNT(I) = 0 DO 23 I = 1,4 DO 23 J = 1, 20  .I-H  IK(I,1)  20  9  23 55.  29  46 47 7  8  I O C C U R d . J) = 0 DO 55 I = 1. 35 NOCGUR( 1) = 0 I2N(35) =1 • DO 29 I =. It 34 J = 35 - I I 2 N ( J ) = I2N(J+1) * 2 CONTINUE IPH = 1 . IPK = 3 IF ( I P R O J . E Q . 1) IPH = 2 IF ( I P R O J . E Q . 3) IPK = 2 IDEN = 0 PRINT 46* MINE. FORMAT (53H1THE REFLEXIONS CONTAINED ON THE- INPUT TAPE. WITH @E@ • ) 1 13HGREATER THAN » F 5 . . 2 . 9H ARE . . . PRINT 47 FORMAT(/6H I DENT* 5X» 1HH* 3X» 1+K* 4X» 1HE ) READ (INPUT) I I . IGPEN* SSOLS* ( F U ) » I = 1*3). E l » E2» ( F C U R V ( I ) 1 I = 1*8) IF (IGPEN . N E . 0) GO TO 7 IF ( I I . N E . 0) GO TO 8 IF ( E l . L T . MINE) GO TO 7 IDEN = IDEN + 1 I R E F L ( I DEN) = IDEN E R E F L ( I DEN) = E l IHO = F ( I P H ) IKO = F ( I P K ) PRINT 2 1 * . I D E N * IHO* IKO* E l 1 = 1 IF (IHO . N E . IHO / 2 * 2 ) 1 = 3 1 = 1 + 1 IF (IKO . N E . IKO / 2 * 2 ) I C O U N T U ) = ICOUNT(I) + 1 IQ = ICOUNT( I ) I H ( I » IQ) = IHO I K ( I » IQ) = IKO E ( I • IQ) = E l I DENT(I» IQ) = IDEN GO TO 7 PRINT 10  * * T T  PRINTOUT PRINTOUT  PRINTOUT PRINTOUT PRINTOUT  10  FORMAT (6H1 HI * 2 X , 2HK1* 4 X , 2HH2» 2 X , 2HK2* 4X» 2HH3» 2 X , 2HK3 * 3X» 8HE1*E2*E3» 4X» 5HSAYRE » 7X» 11HPROBABILITY / ) * AVPROB = 1.0 . NSAYRE = 0 DO 6 I = 1 • 4 IQ1 = ICOUNT(I ) IF (IQ1 . E Q . 0) GO TO 6 DO 6 J = 1• I Q 1 . 11=1 DO 6 K = I I * 4 TQ2 = ICQUNT(K) IF ( IQ2 . E Q . OT GO TO 6 • Jl = J IF ( K . N E . II ) J l = 1 ,. • .DO 6 L= J l * IQ2 I ALPHA = 1 _ K K _ _ IK< I » J ) + IK.(K»L) ' DO" 2" IA = 1* 2 I I = I H ( I » J ) + I ALPHA * IH(K»L) IF ( IA . N E . 2) GO TO 54 • • IF ( I H ( I » J ) . E Q . 0 . O R . I K ( I * J ) • E Q . 0) GO TO 2 I 15.= 1. IF ( I I . L T . 0 " . AND. . KK. . N E . 0) I I S = -1 IF (ISPACE . G T . 1) II = I A B S ( I I ) IF (I . N E . K) IF IND =. 9 - I - K IF (I . E Q . 1) I FIND = K IF (I . E Q . K) IFIND = 1 IC = ICOUNT(IFIND) IF ( IC . E Q , 0) GO TO 3 DO 1 M = 1* IC IF ( I I . N E . I H ( I F I N D » M) ) GO TO 1 IF (KK . N E . ' IK( IFIND* M) ) GO TQ 1 EEE = E ( I » J) * E(K» L) * E l I F I N D * M) IF (EEE . L T . ACCEEE) GO TO 3 IF (K . N E . I . O R . L . N E . J ) GO TQ 82 EEE = (EEE - E U F I N D * M)) / 2 . 0 IF (EEE . L T . ACCEEE) GO TO 3 IOCCUR( IFIND* M) = I OCCUR ( I F I ND , M) + 1 • GO TO 84 IF (I . N E . IFIND . O R . J . N E . M) GO TO 83 . 1  54  82  83 84  36 37  EEE = (EEE - E( K» L . ) ) / 2 . 0 IF (EEE . L T . ACCEEE) GO TO 3 IOCCURU , L) = I O C C U R U • L) + 1 GO TO 84 I OCCUR ( I » J) = IOCCURd > J) + 1 IQCCUR(K , L) = IOCCUR(K » L) + 1 IOCCURUFIND» M) = I OCCUR(IFIND» M) + 1 PRQB = 0 . 5 + 0 . 5 * TANH(PROBCF * EEE) AVPROB = AVPROB * PROS N5AYRE = NSAYRE + 1 IQ = I DENT CI » J ) NOCCUR(IQ) = NOCCURdQ) + 1 IR = I DENT (K. • L) NOCCUR(IR) = NOCCUR(IR) + 1 "• IF (IQ . E Q . IR) NOCCURdQ) = NOCCURdQ) - 2IR = I DENT ( I F I N D * M) NOCCUR(IR) = NOCCUR(IR) + 1 IF (IQ . E Q . IR) NOCCURdQ) = NOCCURlIQ) - 2 PROBIB(NSAYRE) = PROB I D l = IDENT(I» J) ID2 = I DENT(K» L) ID3 = I DENT(IFIND» M) I X S ( 1 » NSAYRE) = I 2 N I I D 1 ) + I 2 N ( I D 2 ) + I 2 N U D 3 ) IF ( I D l . E Q . ID2) I X S ( 1 » NSAYRE) = I 2 N ( I D 3 ) IF ( I D l . E Q . ID3) I X S ( 1 » NSAYRE) = I 2 N ( I D 2 ) IF (ID2 • E Q . ID3) I X S ( 1 » NSAYRE) = I 2 N*( I D 1 ) IF ( I D 2 . G E . I D l ) GO TO 36 IQ = I D l I D l = ID2 ID2 = IQ IF ( ID3 . L E . I D l ) GO TO 37 IF ( ID3 . L T • ID2) GO TO 38 GO TO 39 IQ = ID2 ID2 = ID3 ID3 = IQ IQ = I D l I D l = ID2 ID2 = IQ GO TO 3 9  '  * * * * *  ' .  ;  07/04/68 n7/04/ftfl PRINTOUT PRINTOUT PRINTOUT PRINTOUT PRINTOUT PRINTOUT PRINTOUT PRINTOUT PRINTOUT PRINTOUT PRINTOUT PRINTOUT PRINTOUT PRINTOUT  38  IQ = ID2 ID2 = ID3 103 = 1 0 CONTINUE I D (-It N S A Y R E ) = I D 1 I D ( 2 * NSAYRE) = ID2 IDC 3» N S A Y R E ) = I Q 3 ISIGID(NSAYRE) = PLUS EEEID (NSAYRE). = EEE IXS( 3, NSAYRE) = 0 ~ I X S ( 4 , NSAYRE) =0 MULT = 1 GO TO (30» 3 0 » 3 1 , 3 2 , 8 1 ) , I S P A C E IF ( K.NE. L A N D . K .NE. 3 .AND.'IALPHA  39  81 1  32  33  30 5 •1 3 2 6 85  '  .EQ.  (-1 ) ) MuL i  PRINTOUT PRINTOUT PRINTOUT PRINTOUT PRINTOUT PRINTOUT PRINTOUT PRINIOUT PRINTOUT  = MuLi * i - l ) ( I F I N D . N E . 1 . A N D . I F I N D . N E . 3 ) MULT = MuL f * H i TO 3 3 <K . G T . 2 . A N D . I A L P H A . E Q . ( ~ D ) MULl = MULl * ( -1) ( I F I N D . G T . 2 ) M U L l = MuL T * lb TO 33 ( K . N E . L A N D . K . N E . 4 . A N D . I A L P H A . E Q . (-1 ) ) 1 M u L i = MuLi * ( - 1 ) I F ( I F I N D . N E . 1 . A N D . I F I N D . N E . 4 ) MuLT = MoLT * I I I D 1 = I D 1 * MULT IF ( I D 1 . L T . 0 ) I S I GI D ( N S A Y R E ) = M I N U b PRINTOUT I X S ( 2 , NSAYRE) = OPLUb I F ( M U L T . L T . 0 ) I X b I 2 > N^A T R E ) = ' O M I N u o • . P R I N T 5» I H ( I , J ) , I K I I » J ) » I H i K » L ) , I K i K , L ) , I I , K.K, E E E 1 , T D 1 , I D 2 , I D 3 , PROB F O R M A T ( 2 X , 3 ( 2 1 4 , 2 X ) , F 6 . 1 » 3 X , 2 ( 1 3 , 2 H *)» 1 3 , 3 X , F 7 . 4 ) * GO TO 3 CONTINUE I F ( I S P A C E . E Q . 1 ) GO TO 6 IALPHA = -1 • CONTINUE CONTINUE PRINT 85 F O R M A T ( 1 2 7 H ( N O T E T H A T @EEE@ FOR S I G M A 1 I Y P E R E L A l I Q N b H I P b H A b B E 1 E N M O D I F I E D SO T H A T © P R O B A B I L I T Y ® C A N B E C O M P U T E D B Y O N L Y ONE E X P R 2ESSION) ) IF GO IF IF GO IF  28 27 22  25 21 24 ~2"6"  57  XSAYRE = NSAYRE AVPROB = AVPROB »* (1.0 / XSAYRE) • PRINT 28. NSAYRE .. FORMAT.(// 30H NO. OF SAYRE RELATIONSHIPS = » 14) PRINT 27. AVPROB • ' . •• FORMAT ( // 25H ©AVERAGE® PROBABILI 1Y = , F7.4) PRINT 22 FORMAT (6H11 DENT» 5X» 1HH * 3X> 1HK. 4X> 1HE> 3X> 9HOCCURANCE / ) DO 24 I = 1. 4 J l .= ICOUNT( I ) DO 25 J = 1* J l PRINT 21» I DENT I I» J ) , I H ( I . J ) . I K ( I'» J)» E ( I , J)» IOCCuR( I » J ) FORMAT (I5» 4X. 13. 14. F 7 . 2 . 4A» 12) PRINT 26 "FORMAT (~2H ~) ' ' ' CALL PROBN (NSAYRE. AVPROB) IF (NSCRAT .EQ. 0 ) GO TO 56 ' * IQ = 0 * DO 57 I = 1. NSCRAT * I R = ISCRAT ( I ) . . ' . * IQ = IQ + I2N(IR) • • * DO 58 I = 1. NSAYRE * XL = AND ( IQ. IXS( 1 » I ) ) •- , IF ( I L .EQ. 0) GO TO 58 I X S ( 1 . I) = 0 * DO 59 J = 1. 3 . . ' » IR = ID(J» I ) * NOCCUR(IR) - NOCCUR(IR) - 1 * i D d . i ) = 1000 ; ' # CONTINUE " . * PRINT 60. NSCRAT. U S C R A T ( I ) , I = 1 . N5CRAI) * FORMAT (/61H0AFTER ELIMINATING RELA I I ONbH I Pb WHICH INCLUDE THE FOLL* 10WING » I3.14H REFLEXI.ON(-) . luiI3» 1H»)) * PRINT 61 * FORMAT ( 13H WE HAVE...'.. / ) '  |  —  :  60  61 62 63 56  PRINT 62. (NA(I)» I = 1. IDEN) FORMAT. (5X, 11H REFLEX I ONb , 35A3) PRINT 63 » < NOCCUR ( I ) » I = 1. IDEN) FORMAT (5X. 11H OCCURANCE » 3513) IF (IONE .NE. (-1)) GO TO 64  . •' "  '  I •  j \ J ! [ i j i  FOR .  : •  :  59 ^ 58  '  I  *  '  "! *  PRINT 6 5 FORMAT ( / / 9 7 H  65 1 2 80  REMOVES  ONE  THE FOLLOWING REFLEXION  CYCLE_  OCCURRING  WERE CARRIED Q u i , EACH OF  ONLY  ONCE  // 5X» 5 3 H T H E F O L L O W I N G ' L I - 1 " oHO.wo PRINT 80* (NA(I)» I = 1 , IDEN) . FORMAT. ( 7 X » N  =  2H  N»5X,  * wHICH*  »  OCCuRANCEo  .* AFTER  EACH  CYCLE)* FOR  35A3)  * *  0  70  PRINT  71  FORMAT (6X» I3» 5 X . 3 5 I 3 ) DO 6 6 I = ! • I D E N •  71»  N»  (NOCCURlI),  I  =  1»  IDEN)  FOR  * * * *•  :  66  IF  (NOCCUR(I)  IQ GO  = I 2N(I) TO 6 7  .NE.  1)  GO  TO  66  CONTINUE GO  67  N  69  TO =  * *  64  N  +  1  I  =  DO  68  IF  (  IXS(1»  1,  XL  =  AND(IQ*  IF  ( I L .EQ.  DO  69  IQ  =  J  =  NSAYRE I) 0)  1»  ID ( J »  NOCCUR(IQ)  .EQ.  0)  IXS(1» GO  GO  10  68  I)).  TO  68  *  3 I)  =  NOCCUR(IQ)  -  *  1  #  ID(1» I) = 1000 IXS(1, I) = 0 GO  TO  68  CONTINUE PRINT 72  72  FORMAT  64  IF 1  ( 1 3 H  (IONE 73  PRINT 74  .NE.  NS  » 7X» = 0  AVPROB NSA DO  = 75  (-1)  AT  72  )  .AND.  25H1FINAL  F0RMAT(4X» 1  ERROR  NSCRAT  •EQ.  0  .AND.  OUIPUI  .LE.  0)  2H  8X»  18HSIORAGE  =  OF  DATA  5HCSATRE» FOR  OUIPUI  Ui>ED  7A ,  ///)  HHPROBABILI i'Y,  TO  *  7H  EEE  / )  1.0  (NSAYRE I  N,  FORM  GO  * *  74  FORMAT ( PRINT 76  76  * * * *  70  =  1,  -  1)  NSAYRE  /  35  +  2  *  '  77  75  73  34  35 48 49  * IF ( IXS(1» I ) .EQ. 0) GO 10 75 NS = NS +1 IQ = (NS - 1) / 35 + 2 IR = NS - (IQ - 2) * 35. XL = 0 R ( I X S ( I Q . I ) • I 2 N ( I R ) ) I X S ( I Q , I) = IL PRINT 77, NS, I S I G I D ( I ) , . <ID(J.» I ) , J = 1 , 3 ) , P R Q B I d l I ) , E E E I D ( I ) 1 , ( I X S ( J , I ) , J = 1 , NSA) FORMAL ( 3X» I 3»4X»Al»12» 2H *» I3» 2H *» 13, 3'X » F 7 . 4, 3 A , F 5 . 1 , 1 10X, 4013) * AVPROB = AVPROB * PROBIB.U) CONTINUE * IF (IONE .NE. (-1) .AND. NSCRAl .EQ. 0 ) GO TO 73 * XS = NS AVPROB = AVPROB '** (1.0 / XS) * PRINT 28, NS * *• PRINT 27, AVPROB CALL PROBN (Nb, AVPROB) I F d P R I N T .EQ. (-1)) GO 10 53 * DO. 35 I = 1, IDEN PRINTOUT JINI1 =1 PRINTOUT EMAX = 0 PRINTOUT DO 34 J = J I N I T , IDEN PRINTOUT IF ( E R E F L ( J ) . L E . EMAX) GO TO 34 PRINTOUT EMAX = E R E F L ( J ) PRIN1 OUT PRINTOUT IREFJ = J . CONTINUE PRINIOUI IF (I .EQ. IREFJ) GO TO 35 PRINIOUT IQ = I R E F L ( I ) PRINIOUI IREFL(I) = IREFL(IREFJ) PRINIOUI I R E F L ( I R E F J ) = IQ PRINIOuI XQ = E R E F L ( I ) PRINIOUI EREFL(I) = EREFL(IREFJ) PRINIOUI E R E F L ( I R E F J ) = XQ PRINIOUT CONTINUE PRINIOUI PRINT 48 PRINIOUI FORMAT ( 3H1HK, 3.X»3H(E)» 7X, 3 1 7 A , 5H^ArRE» 5 A11H , i EEE » P R O B ) » 3 A ) / ) P R I N l O u DO 40 I = 1, IDEN PRINiOui PRINT 49, I R E F L ( I ) , E R E F L ( I ) PRINIOUI F0RMATI/I3, 2H (, F5.2, 2H) )  INS = 0 DO 4 1 J = 1» N S A Y R E DO 4 2 K = 1* 3 I F ( I R E F L ( I ) . L T . ID(K» IF ( I R E F L l I ) . N E . I D ( K , INS = INS + 1 I R K I N S ) = ID(1» J ) IR2(INS) = ID(3 » J ) I F IK •EQ. 1) I R l l l N b ) I F (K .EQ. 3 ) I R 2 ( I N S ) EEUNS) = EEEID(J) PRO(INS)  42 41  50  44 51 43  45 40 53  =  J)) J))  GO GO  = ID(2* = ID(2»  70 41 i d 42  J) J)  PROBIB(J)  IS(INS) = ISIGID(J) GO TO 4 1 CONTINUE CONTINUEI F ( I N S . N E . 0) GO TO 4 4 P R I N T 50 FORMAT ( 1 1 X , 4 7 H N 0 S A Y R E R E L A V I O N S H I P i E A I _ I " FOR • H I o R E F L E A I O N 1 ////) GO TO 40 I NI T = 1 LIM = 3 IF ( I N S • L T • LIM) L I M = INo P R I N T 43» (IS(J)» I R K J J . t I R 2 U ) » .EE'i J)» P R O i J ) , J = I N I T , L I M ) FORMAT (16X» 3( 5X » Al» I3» 2H *» I3» 2H i , F 5 . 1 .1H» , 1 F 6 . 3 , 1H)» 2 X ) I N I T = I N I T .+ 3 LIM = LIM + 3 I F ( I N S - L I M .G1 . t - 3 ) ) GO i 0 51 P R I N T 45 FORMAT I / 2H ) I F ( I N S / 3 * 3 .NE. I N 6 ) P R I N l 45 CONTINUE REWIND INPUT I F (OUTPUT .EQ. 0 ) GO 10 52 C A L L POSN ( O U I P U I . O u i F I L ) WRITE ( O U T P U T ) I D E N , N6» P R O B C F , iDUMMY I = 4, 16) NR = (NS - 1) / 35 + 2 N = NR + 2  PR] PR] PR] PR] PR] PR] PR] PR] PR] PR]  N t0o i • NIOUI NIOUI NIOUI NIOUI NiOui NIOUI  NiOui N IOU i NIOUI  PR] N I O U 1 PR] N I O U I PR] N I O U I PR] I N i O u t PR] [ N I O U I PR] [ N I O U I PR] [ NTOUT PR] [•NT O U T PR] [ NTOuT PR [ N i O u i PR [ N I O U I PR] [Ni'Oui PR] [ N i O u i PR [ N T O U T PR t N I O U 1 PR] [ N I 0 u j PR [ N i O u i PR [ N i O u i PR] [ N I O U I PR [ N i O w f PR [ N I O U 1 PR NTOUT  s ' 9  %  1  V  12  1J_ • 10  9 8 7 6 5 4 3  DO 78 I = 1. NSAYRE IF (IXS(1» I) .EQ. 0 ) GO TO 7 8 WRITE (OUTPUT) ( I X S U , I ) , J = l . N R ) . E E E I D U ) * (DUMMY » J = N» 16) 78 CONTINUE * END F I L E OUTPUT * REWIND OUTPUT PRINT 4» NS» OUTPUT» . O U 1 F l L 4 FORMAT(// 4H THE» 13. 1 63H RELATIONSHIPS AS DESCRIBED. EARLIER HAS NOW BEEN OUTPUT 2 ON UNIT * 13* 5H F I L E . 13) GO TO 52 END S I B F T C POSN DECK S U B R O U T I N E POSN ( I N P U I . I N F I L E ) A S S I G N 14 10 I E N D F C A L L EOF ( I N P U T , I E N D F ) 12 REWIND INPUT NFILE = INFILE 14 I F ( N F I L E . L E . 1) GO 10 13 NFILE = NFILE - 1 18 • READ ( I N P U T ) I I GO TO 18 13 RETURN END S I B F T C PROBN DECK ' • S U B R O U T I N E PROBN ( N S A Y R E . AVPROB) PRINT 2 Z FORMAT ( 1 0 2 H 1 P R O B A B I L I l Y T H A i CORRECT o~" R u C i u R E I N v O L v E o NO MORE 1THAN N F A I L U R E S OF I N D I V I D U A L oAi'RE R E L A I O N S H I P o ) DIMENSION P ( 1 0 0 ) . I ADD(lu) X S A Y R E = NSAYRE P(l) = AVPROB * * X S A Y R E PI = P ( 1 ) X = 1.0 DO 3 1 = 1 . NSAYRE X = X * F L O A T ( N S A Y R E - I + 1) / F L O A T ( I ) P I = P I ' . / AVPROB * ( 1 . 0 - A V P R O B ) PU + 1)=P(I) + X*-P1 3 DO 4 I = 1 , 10 4 I ADD(I) = I - 1  L  A  8 6  Olg_,  TT~ Zl A  I  _ k  w  Ik  9 9  7  5 .6  SENTRY  PRINT 7» (I A D D ( J ) » J = I , 10) FORMAT ( // 9H FAILURES, 14, 917) NS = NSAYRE + 1 DO 5 1 = 1» NS ,10 IQl = I - 1 IQ2 = I 103 = IQ2 + 9 IF (IQ3 .GT. NS ) IQ3 = NS PRINT 6* I Q l , ( P ( J ) » J = IQ2, IQ3) FORMAT ( / 15, 2H /» 2X» 10F7.4) RETURN END  L | 8 6 1  Oli  TT Zl  ! (  [ f s " 9  L 8  ' 6 01  S I G N S  HKUGKAIVI  SIGNS REF »DECK 08/U2/68 THIS PROGRAM IDENTICAL TQ 0 7 / 1 5 / 6 8 . EXCEPT FOR FORMA IS OF IAPE RELATIONSHIPS OF RANK DOWN lO FQuR LEoo THAN iHE NO."OF REFLEXIONS OCCURRING IN iHEM CAN BE HANDLED THE ©SECOND GROUP© MUSI NO I BE COMPLETELY EMP i Y UP TO F I V E FAILURES IN fHE FIRoT GROuP 07/15/68 COMMON EEE» EMAX » I 2 N , IDMI__» I F A I L , I F I N , I M u L J , 1 I.SIG». I S I G S , I X b , I X l , N F A I L , NMuLT, 2 NPOSS, NS, OUTPUI DATA INEG* IZERO / 0 4 0 0 0 0 0 0 0 0 0 0 0 , 0 0 0 0 0 0 0 0 0 0 0 0 0 / INTEGER OUTPUT, OUTFIL , 'BLANK» PLub DIMENSION NA(35) FOR DATA NA/2H 1, 2H 2, 2H 3,. 2H 4 » 2H 5, 2H 6 , 2H 7 , 2H 8,2H 9»3H lu,FOR 1 2H 1, 2H 2, 2H 3, 2H 4 , 2H 5, 2H 6, 2H 7, 2H' 8 ,2H 9,3H 2u,F0R 2 . 2H 1, 2H 2,. 2H 3, 2H 4 , 2H 5, 2H 6, 2H 7, 2H 8,2H 9,3H 3u,F0R "3 . 2H 1, 2H 2, 2H 3, 2H 4 , 2H 5 / FOR DATA BLANK» PLUS, M I.NUS ' /2H 2H +, 2H - / DIMENSION I X S ( 4 , 1 0 5 ) , I2N(35)» E E E U 0 5 ) , IDMlSb»2u), I i ( 3 ) , I Q b t 3 ) DIMENSION I S K 3 5 ) , ISIG (35) DIMENSION ICON(10) DIMENSION I A R B ( 4 ) , ICOMPM(16)» IMuLii35» 1 6 ) , I o I G o ( 3 5 ) ARBIIRAR D I M E N S I O N I X T ( 1 0 5 ) » PEEE'lu5)» AOV3)» I v P l f 3 ) » A v P1\3 ) »  35IBFTC  C C C C C  •  1  •  10 4 51  •  I VP ( 3 , 3 5 ) , X V P ( 3 , 3 5 ) . •- " DIMENSION I F A I L ( 3 ) ,X F A I L 1 3 ) ' 1 »IFAIL1(3), XFAILK3) 2__ ,IFAIL2(3), XFAIL2(3) . 3 ,IFAIL3(3) , XFAIL3(3) 4 ,IFAIL4(3.) , XFAIL4(3) EQUIVALENCE ( X L , I L ) , ( I S , X S ) , ( I X , XX).»lXQl» I Q l ) , i A V P l , IvPl) E Q U I V A L E N C E ( I V P , X V P ) , II F A I L » X F A I L ) , ( I FA I L 1 , A F A I L 1 ) , ( I FA I L 2 , 1 XFAIL2),(IFAIL3, XFAIL3)»<IFAIL4, XFAIL4) R E A D 1 0 , I N P U T , I N F I L E , O U T P U I', Qu I F I L> N F A l L l , NFAI L 2 , E M A X  • "  FORMAT ( 6 1 2 , F 8 . 0 )  READ 4, NCON, ( I C O N ( I ) , I = 1, NCON) FORMAT ( 1 2 , 1 0 1 3 ) / P R I N T 5 1 , NCON, ( I C O N U ) , I = 1, NCON) FORMAT ( 1 4 H THE F O L L O W I N G , I 3 > 5 2 H R E F L E A I O N O 1 C I F I E D IN INPUI ... , 10113* CALL POSN ( I N P U T , INFILE) R E A D ( I N P U T ) N , M, PROBCF  1H,D)  "  , -  HAVE  THEIR  oIGNo oPE  17  s 9  c c  99 6  62  7 8  56  12 JJ_  ho 9 8  61 60 58  7 6 5  4  53  THE PROBABILITY C O E F F I C I E N l l b READ BuT I o IMU i' K K E - J _ N I " L I U O E D PEEE IS THE TRIPLE PRODUCT OF E@b PER R E F E A I O N . K = ( M - l ) / 3 5 + 2 DO 99 I = 1, M NuFILING READ (INPUT) d X S U . I ) , J = 1» K)» P E E E i l ) EEE(1) = P E E E l I ) I XT( I) = IXSd* I ) PRINT 6» INPUT. INFILE ' FOR FORMAT (/5H UNIT. I3» 5H F I L E . I3» FOR 1 54H CONTAINS THE FOLLOWING R E L A T I O N S H I P S (OC1AL NO 1 A d O N ) / ) FOR N S = ( M - l ) / 3 5 + l J = NS + 1 DO 62 K = It M FOR PRINT 30. ( I X S d . K) ». I = 1, J ) IF (N .EQ. 35) GO TO 8 FOR K = N + 1 FOR DO 7 I = K» 35 FOR NA(I) = BLANK FOR CONTINUE FOR I2N(35) = 1 DO 56 I = 1. 34 J = 35 - I I 2 N U ) = I 2 N ( J + 1) * 2 IF INCON •EQ. 0) GO TO 58 DO 60 I = 1. NCON I.AB =IABS.( ICON( I ) ) ISI = +1 IF ( I C O N ( I ) . L T . 0) ISI = -1 DO 61 J = 1. M XL = AND (I XS ( 1 » J ) . I 2 N.( IA B ) ) IF ( IL .EQ. 0). GO TO 61 I X S ( l . J ) = IXSC1.J) - I2N(IAB) I X S ( 2 . J ) = I X S ( 2 . J ) * ISI CONTINUE CONTINUE CONTINUE DO 53 I = 1. 20 I4MISS(I) = 0 NMISS = 0 DO 2 I = 1.  L 8 6 Ol  TT Zl  3  !  s 9  PROBMX JINIT =  -  DO  1  J  = I =  LM  0,0 - NMISS JINIT*  8  M  6  IF ( P E E E ( J ) . L E . PROBMX PROBMX = P EE E ( J )  • • •  JNOTE 1  1X5(1*  J)  /  I2NI.I)  .EQ.  U)  GO  10  1  J  .  (PROBMX  .NE.  0.0)  GO  TO  24  OTHERWISE REFLEXION. CONSIDERED NMISS = NMISS + 1 'IDMISS(NMISS) = 1 GO XQ  24  0 1  _  A_  CONTINUE • IF  c  =  .OR.  l b MlbbING  FROM  THE  oAiRE  RELATIONSHIP  L*  TO 2 = PEEE(JINIT)  PEEE(JINIT) PEEEIJNOTE) J = NS + 1  = =  PEEE(JNOTE) XQ  D O , 2 5 K. - 1» J IQ = IXS(K»JINIT) ••  25  #  0  I  5  •  IXS(K» DO 3 K  JNOTE) = 1* M  =  IQ  IF  (K  XL  =  .EQ.  IF  (IL  DO  26  XL XL X  = = =  .EQ. K.Q  FORMAT 1  5 4 3  2 8  0) 1*  GO  TO  JNOIE)  TO  M  3  I2N(I>). 3  J JINIT) ,  IXS(KQ»  K.))  JINII.)*  lXb(KQ»  K) )  XL = AND(XL* X ) I X S ( K.Q » K ) = I L CONTINUE  27  7  =  GO  K)»  AND(IXS(KQ» COMPL(XL) OR (IXS(KQ,  CONTINUE PRINT 27*  8  JINIT)  AND(IXS(1»  2  6  0  IXSIK*  12  9 !  =  26 3  10  •  JINIT)  Y  .LL :  IXS(K»  M %  M  •  ( 4H1THE*  AND RESTORED PRINT 28  IN  I4.105H 1 HE  SAYRE  FOLLOWING  FORMAT 15X* 8HIXS(1»M)» 1 9X, 8 H I X S ( 4 » M ) / ) DO 2 9 K = 1* M J = NS + 1  RELATI0N5HIPb MANNER  vGIvEN  HAVE IN  BEEN OCTAL  MANIPULATED NO i A l I O N ) / / ) _  9X,  8 H IXS.l 2 »M ) »  9X,  8HIXS(3*M)» 5 rc  U  J  29 30 C 120  31 32 C 121  • 33 70 C  10  73  74  PRINT 30, (1X5(1, K)» I = 1»J) FORMAT (4017) NOW TO FIND WHICH b@b OCCuR IN THE IFIN = N - NMISS DO 120 K = 1, NS IS(K) = l A B S U X S C K + 1, 1) ) DO 31 I = 2, IFIN DO 31 J = 1, NS I Q l =IABS( I XS ( J + . 1 , 1 ) ) X S U ) = ORdS(J) , IQl) CONTINUE PRINT 32, ( I S ( K ) , K = 1, NS) FORMAT 1/ 63H OCTAL REPRESENTATION 1ROUP , 3013) NOW TO I DENT IFIY THESE S@S 11 = 1 DO 121 K = 1, NS IQS(K) = I S ( K ) K = 1 DO 33 I = 1, M J = (I - 1 ) / 35 +. 1 L = 1 - (J - 1) * 35 IF CIQSIJ) / I2N(L) .EQ. 0 ) GO 10 I S1 ( K ) = I I Q S ( J ) = I Q S ( J ) - I2N(L) K = K + 1 CONTINUE PRINT 70, ( I S K I ) , I = 1, IFIN) FORMAT ( 20H THIS CORRESPONDS 10, NOW TO FIND WHICH REFLEX I ONb OCCUR IF (NMISS .EQ. 0) GO f0 75 IX = IXS(1,1) DO 73 I = 2, IFIN XX = 0 R ( I X , IXS(1 , I )) IQl = 0 DO 74 I = 1, NMISS J = IDMISS(1) IQl = I Q l + I2N(J) XL = AND(IX, I Q l ) IF ( IL .EQ. 0) GO TO 75 •  FIRoT GROuP  OF S@b' OCCURING IN  1 HE FIRST G  33  2'x» 3 5 U 2 , IH,) ) w.I TH ARBITRARY bIGN  *  ARB I IRAR  ARBIiRAR  ARB I IRAR ARB IIRAR ARB ITRAR ARB ITRAR ARBITRAR ARBIIRAR  t7  i  9  77 78  79  84 "1 r• 12 1  0  JJ_  10  .  85  9 1 I  9  8  7 6 5  86 83  9  I Q l = IL NARB = 0 ARBITRAR DO 7 7 I = 1. NMISS ARBITRAR J = I DM ISS( I ) ARBITRAR I F ( I Q l / I 2 N ( J ) .EQ. 0) GO TO 77 ARB I 1RAR NARB = NARb + 1 ARBIiRAR I ARB(NARB) = J ARBITRAR • IQl = I Q l - I2N(J) . ARBITRAR CONTINUE ARBITRAR PRINT 78 »NARB* ( I A R B ( I ) , I = 1, NARB) ARB I "1 RAR FORMAT (/86H EACH SET OF COCHRAN + DOUGLAS SOLUTIONb. 15 BASED ON AARBITRAR 1RB1TRARY SIGNS OF THE FOLLOWING »• I3» 17H R E F L E A I O N T O ) ARBIiRAR 2 4 ( 1 3 , 1H» ) ) ARBI1RAR NMULT = 2 * * NARB ARBIIRAR GO TO 76 ARBITRAR NARB = 0 ARBITRAR NMULT = 1 ARBIIRAR = I* DO 79 J = 1* NMULT NARBETRA I MULT(I > J ) = 1 ARBITRAR IF (NARB .LQ. 0 ) GO TO 96 1RBITRAR ICOMPM(l) = 0 ARBITRAR I = IARB(l) ARBITRAR ICOMPM(2) = I 2 N ( I ) ARBITRAR IF (NARB .EQ. 1) GO TO 8 3 ARBIIRAR J = IAR6(2) ; _A.RB.I_T.RAR. J = I2N(J) ARBITRAR DO 84 I = 1» 2 ARBITRAR ICOMPM(I + 2) = ICOMPM(I) + J ARBITRAR IF (NARB .t-Q. 2) GO TO 83 ARBIIRAR J = IARB(3) ARBIIRAR J = I2N(J) ARBIIRAR DO 85 I = 5» 8 ARBIIRAR ICOMPM(I) = ICOMPM(I - 4) + J ARBITRAR IF (NARB .EQ..3) GO TO 83 ARBITRAR J = IARB(4) ARBITRAR J = I 2 N .( J ) ARBIIRAR DO 86 I = 9, 16 ARBI1RAR ICOMPM(I) = ICOMPMd - 8 ) + J ARBI1RAR DO .80 J = 1» NMULT ARBITRAR  L 8 6 Oil  TT Zl  I'  3 !  81  82  80 C 96 38 39  41  54  59 97 .  98  87  L = 0 DO,80 K = 1. IFIN KL = K + L IF ( KL .NE. IDMISSCL + 1) ) GO lO 82 L = L + 1 GO TO 81 XQ1 = AND (IXS(1»K) » ICOMPM(J)) CALL I C O U N T d Q l , NONES) IMULT(KL, J ) = 1 , IF (NONES / 2 * 2 .NE. N0NE6) I M u L f i K L , J ) = -1 CONTINUE NOW TO CARRY OU1 1 HE iAYRE FAILuRE i E o T o PRINT 38 FORMAT ( 29H1SIG.NS OF POSSIBLE STRUCTURES //) PRINT 39, < NA(I)» I = 1, 35 ) FORMAT (3X» 2HNO, 2X» 3(9A2» A3)» 5A2» 2X 1 »3HNO+, 2X, 4HSMAX, 9H SEEE**2» 2X, 8HFAILURES /) NPOSS = 0 IF INK. = IFIN + 1 DO 41 I = IF INK, 3 5 ISIG ( I ) = 0 IF (NMISS .EQ. 0) GO TO 55 DO 54 1 = 1 , NMISS ' ' J = IDMISS(I) ISIG ( J ) = 0 IF (NCON .EQ. 0) GO TO 97 DO 59 I = 1, NCON IA6 = I A B S ( I C O N ( I ) ) I S I G ( I A B ) = +1 IF (I CON(I) . L T . 0) I S I G ( I A B ) = -1 CONTINUE CONTINUE IF (NARB .EQ. 0 ) GO TO 88 DO 98 I = 1, NARB J = I ARB ( I ) • * . . . • • • I S I G ( J ) = +1 J = I ARB(1) DO 87 I = 1,. NMULT., 2 IMULT ( J , I + 1) = -1 IF (NARB .EQ. 1) 60 TO 88 •  ARBITRAR ARBIIRAR ARBI1RAR ARBI ARBIiRAR ARBIIRAR  :  ARBIIRAR ARBIIRAR ARBI1RAR ARBITRAR FOR  ARBITRAR  ARB ITRAR ARBITRAR ARB ITRAR ARBIiRAR ARBITRAR ARBITRAR ARBI1RAR ARBI1RAR ARBIlRAR ARBIIRAR ARBITRAR ARBITRAR  9  '89  90 91  92 55 88 102  #  101 100 #. 4  107  12  108  1 1 010 9  9  105  8  i 6 5  W  4 3  C  J = I ARB (2) DO 89 I = 1, NMULT , 4 I M U L T U , I + 2) = -1 IMULT(J» I + 3) = -1 IF (NARB •EQ. 2) GO TO 88 J = IARB(3) DO 90 I = 5, 8 IMULT(J» I ) = -1 IF (NARB .LQ. 3) GO TO 88 DO 91 I = 13, 16 IMULT(J, I ) = -1 J = IARBU) DO 92 I = 9, 16 I MULT(J, I ) = -1 CONTINUE IF (OUTPUT .NE. 0) CALL POSN (OUTPUT, OUTFIL) NPOSSO = 0 DO 102 J = 1, NS I V P K J ) = IZERO DO 100 I = IFINK, M XL = AND(INEG» 1X5(2, I ) ) XL = COMPL(XL) IF ( I L . L I . 0) GO TO 100 DO 101 J = 1, NS X V P K J ) = OR ( I V P K J ) , I X S ( J + 1, I ) ) CONTINUE IVP1 (1 ) = I A B S ( I V P 1 ( 1 ) ) DO 107 J = 1, NS XL = C O M P L l I S ( J ) ) X V P K J ) = AND ( I V P K J ) , I D DO 108 I = IFINK, M I X S ( 2 , I) = I A B S ( I X S ( 2 , I ) ) DO 103 1 = 1, IFIN DO 105 K = 1, NS I VP ( K , I) = . I ZERO K = ISI(I) • L = ( K - 1) / 35 K = K - L * 35 L IS TO BE STORED UNTIL l i b UoE J u o f BEFORE b'i'A i EMEN i l u 3 L = L + 1  ARBITRAR ARBITRAR ARBITRAR ARBITRAR ARBITRAR ARBITRAR  ARBITRAR -  110 104 C  111 C 103  148  48  L L = I 2N ( K ) DO 104 J = I FINK, M XL = AND I I X S ( L + 1, J ) , L L ) I F l IL .EQ. 0) GO TO 104 DO 110 K = 1, NS XVP(K» I) = 0 R ( I V P ( K , I ) , IXS(K + I t CONTINUE NOW SUBTRACT S@S OF FIRST GROUP DO 111 K = 1, NS XL = COMPL(IS(K)) XVP(K, I) = AND(I V P ( K , I ) , I L ) THE FOLLOWING STATEMENT MAKES @IVP@ SHOW ALSO FAILURES I V P ( L , I) = I V P ( L , I ) + LL CONTINUE NFAIL = 0 DO 148 I = 1» N 3 I F A I H T ) = IVP1 ( I ) CALL ICOUNT ( I F A I L ( I ) , NONES ) NFAIL = NFAIL + NONES NINALL = 1 IF (NFAIL .GT. NFAIL2) GO. TO 48 NPOSSO = NPOSSO + NMULT CALL ITEST CONTINUE IF (NFAILI . L T . 1 )• GO TO 49 DO 47 11 = 1, IFIN NFAIL = 0 DO 147 I = 1, NS X = AND (I VP 1(I ) , I VP(I , 11) ) X = COMPL(X) . Y = 0R(I VP 1 ( I ) , IVP( I , 11 ) ) XFAIL ( I ) = AND(X , Y) CALL ICOUNT ( I F A I L ( I ) , NONES ) NFAIL = NFAIL + NONES NINALL = NINALL + 1 IF (NFAIL .GT. NFAIL2) GO TO 47 NPOSSO = NPOSSO + NMULT CALL ITEST CONTINUE IF (NFAILI . L T . 2) GO TO 49 •  -  147  47  -  IN GROUP 1  IF INI = I F I N 1 DO 4 5 I I = , 1 , T F I N 1 DO 1 4 5 I = 1 , N S X = AND ( I V P K I )> I V P ( I , X = COMPL(X) Y 145  =  OR ( I V P 1 ( I ) »  XFAILK I2INIT DO 4 5 NFAIL DO X X  245 = =  I VP ( I »  I) = AND(X» = 1 1 + 1 12 = = 0 I =  I D )  Y)  I 2 I N I 1' » 1*  11) )  IFIN  .  NS  AND (IF A I L K I )» COMKL(X)  IVPU,  12))  Y = OR(IFAIL1(I)» IV P ( I , 12) XFAIL ( I ) = AND I X * Y) CALL ICOUNI ( I F A I L * I ) , NONEo 245  NFAIL = NFAIL + NONEi NINALL = NINALL + 1 IF (NFAIL.GT. NFAIL2) NPOSSO = NPOSSO CALL ITtSI  45  +  GO  TO  ) )  45  NMULT  -  CONTINUE IF  (NFAILI  . L T . 3)  GO  TO  49  I F I N l = I F I N - 2 IFIN2  i  I  Y  142  10 9 8 7 5 4 3  =  IFIN  -  1  4 2 I I = 1, I F I N 1 " 1 4 2 I = 1, NS = AND ( I V P 1 ( I ) » I VP ( I • = COMPL(X) = O R ( I V P 1 ( I ) , IV P ( I » 1 1 ) ) A I L 1 ( I ) = A N D ( X » Y)  I2INIT = 1 1 + 1 DO 4 2 12 = I 2 I N I T , DO .242 I = 1 , N S '  12  1 1  6  DO DO X X Y XF  242  I D )  IFIN2 .  X X  = =  AND ( I F A I L K I ) , COMPL(X)  Y  =  O R ( I FA I L 1 ( I ) ,  I V P d ,  IV P ( I ,  X F A I L 2 ( I ) '= AND ( X , Y ) 13 I N I T = 12 + 1 DO 4 2 13 = 131 N I T , I F I N  12))  12)  )  342  42  134  234  3 34  NFAIL = 0 DO 342 I = 1. NS X = AND ( I F A I L 2 d ) » I V P d , 13)) X = COMPL(X) Y = 0 R ( I F A I L 2 ( I ) » I V P d , 13)) XFAIL ( I ) = AND(X• Y) CALL I COUNT ( I F A I L ( I ) , NONES ) NFAIL = NFAIL + NONES ' NINALL = NINALL + 1 IF (NFAIL .GT. NFAIL2) GO TO 42 NPOSSO = NPOSSO + NMULT CALL ITEST CONTINUE IF (NFAILI . L T . 4) GO TO 49 I F I N I = IFIN - 3 IFIN2 = IFIN - 2 IFIN3 = IFIN - 1 DO 34 11 = 1, IFIN1 DO 134 I = 1, NS X = AND ( I V P K I ) , I V P d , I D ) X = COMPL(X) Y = OR ( I V P K I ) , IVP(I» 11)) X F A I L K I ) = AND ( X , Y) 12 IN IT = I 1 + 1 DO 34 12 = I 2 I N I T , IFIN2 DO 234 I = 1, NS X = AND ( I F A I L K I ) , I V P d , 12)) . X = COMPL(X) Y = O R ( I F A I L 1 ( I ) , I V P ( I , 12) ) X F A I L 2 ( I ) = AND(X , Y) I3INIT = 1 2 + 1 DO 34 13 = I 3 I N I T , IFIN3 DO 334 I = 1, NS X = AND ( I F A I L 2 ( I ) , I V P d , 1 3 ) ) X = COMPLIX) Y = OR ( I FA IL2 ( I ) , I V P d , 13)) X F A I L 3 ( I ) = AND(X , Y) .I4INIT = 1 3 + 1 DO 34 14 = I 4 I N I T , IFIN NFAIL = 0  -  •  434  34  144  l 1  T 1  244  V  12  -J_L ho 9 8 1  7 6 5  *4  344  -DO 434 I = 1» NS X = AND ( I F A I L 3 1 I ) . - I V P ( I . 14)) X = COMPL(X) Y = OR(I FA I L 3 ( I ) • I V P d . 14)) XFAIL ( I ) = AND (X » Y) CALL ICOUNT ( I F A I L ( I ) . NONES ) NFAIL = NFAIL + NONES NINALL = NINALL + 1 IF (NFAIL .GT. NFAIL2) GO TO 34 NPOSSO = NPOSSO + NMULT CALL ITEST CONTINUE • ' IF (NFAIL1 .LT. 5) GO TO 49 I F l N l = I F I N - 4 .IFIN2 = IFIN - 3 IFIN3 = IFIN - 2 IFIN4 = IFIN - 1 DO 44 I I = 1, IF INI DO 144 I = 1» NS X = AND ( I VP1 ( I ) » I VP ( I » I D ) X = COMPL(X) Y = OR( I V P K I ) , IVP( I • 11 ) ) X F A I L 1 ( I ) = AND(X » Y) I2INIT = I 1 + 1 DO 44 12 = I 2 I N I T , IFIN2 DO 244 I = 1• NS X = AND (IFAIL1(I)» I V P ( I • 12)) X = COMPL(X) Y = OR( I FA I L K I ) » IVP( I » 12) ) X F A I L 2 ( I ) = AND(X » Y) . I 3 IN IT = 12 + 1 DO 44 13 = I 3 I N I T , IFIN3 DO 344 I = 1, NS .X = AND ( I F A I L 2 ( I ) • IVP(I , 13) ) X = COMPL(X) Y = OR ( I FA I L2 ( I ) * I V P U . 13)) X F A I L 3 ( I ) = AND(X » Y) I4INIT =13+1 DO 44 14 = I 4 I N I T , IFIN4 DO 444 I = 1, NS  3 I I  X =. AND (IFAIL3(I)» I V P d , 14)1 X = CQMPL(X) Y = OR ( I FA I L3 I I ) • I V P d . 14)) 444 X F AI L 4 ( I ) = AND(X» Y) I 5 IN I T = 14 + 1 ; • ,DO 44 15 = I 5 I N I T . IFIN NFAIL = 0 DO 544 1 = 1, NS X = AND d F A I L 4 ( I ) , I V P d , 15)) X = COMPL(X) Y = OR ( I FA I L4 ( I ) » I VP ( I , 15) ) _ XFAIL ( I ) = AND(X, Y) ' ' . CALL ICOUNT ( I F A I L ( I ) , NONES ) 544 NFAIL = NFAIL + NONES ; . NINALL = NINALL + 1 IF (NFAIL .GT. NFAIL2) GO TO 44 _. NPOSSO = NPOSSO + NMULT CALL ITEST " " : 44 CONTINUE 49 PRINT 150, N F A I L I , NINALL 150 FORMAT ( // 33H THE NO. • OF COMB I NAT IONS OF UP TO, 12, 55H FAILURE IS THAT WERE.CONSIDERED FOR THE FIRST GROUP WERE » 18) . ___ PRINT 50. NPOSSO. N F A I L I , NFAIL2, EMAX 50^ FORMAT ( /7H OUT OF, 17, 56H SOLUTIONS WHICH SATISFY THE-CONDITION ' 1 THAT NO MORE THAN , 13, 20H SAYRE RELATIONSHIPS 2 / 41H FAIL IN THE FIRST GROUP AND NO MORE THAN , 1 4 , 3 55H FAIL IN A L L , ONLY THE ABOVE PRINTED ONES ALSO SATISFY 4 / 83H THE CONDITION THAT FOR NO REFLEXION IS THE SUM OF EEE@S OVER 5_ER FAILURES GREATER THAN , F8.2 ) ; IF (OUTPUT .NE. 0) END F I L E OUTPUT * IF (OUTPUT .NE. 0) PRINT 5, OUTPUT, OUTFIL 5 FORMAT (/ 40H THOSE PRINTED HAVE BEEN OUTPUT ON UNIT , . 1 13, 5H F I L E , 13) STOP END . SIBFTC POSN DECK ~' — — — — — SUBROUTINE POSN ( INPUT.INFILE ) • ASSIGN 14 TQ IENDF CALL EOF (INPUT, IENDF) " ' ' 12 ' REWIND INPUT :  NFILE = INFILE IF ( N F I L E . L E . 1) 60 TO 13 NFILE = NFILE - 1 18 READ (INPUT ) I I GO TQ 18 ' 13 RETURN END SIBFTC ITEST DECK SUBROUTINE ITEST COMMON EEE* EMAX* I2N* IDMISS*. IFAIL* IFIN» I MULT» 1 ISIG* ISIGS* IXS* IXT* NFAIL* NMULT* 2 NPOSS» NS, OUTPUT DATA INEG» IZERO / 0400000000000 , QOOOOOOOOOOOO / INTEGER OUTPUT, OUTFIL, BLANK* PLUS ; . ~ ' DIMENSION I F A I L ( 3 ) » X F A I L ( 3 ) > I 2N(35)» N F ( 2 0 ) » I D X ( 3 5 ) »IXS(4 » 105) DIMENSION ISIG(35)» ISIGS(35)» IMULT(35» 1 6 ) , I D M l S S ( 2 0 ) , EEE(105) DIMENSION IXT(105) EQUIVALENCE ( I F A I L , X F A I L ) , ( I X , X X ) , ( I L , XL) DATA BLANK, PLUS,-MINUS, COMMA / 2H , 2H +» 2H -» I H , / DUMMY = 0.0 • ' NF(1) = 0 NF(2) = 0 _ _ ' J =0 :_______ I F ( N F A I L .EQ. 0) GO TO 36 IX = IZERO DO 1 I = 1, NFAIL • '. 2 J = J +1 K = ( J - 1) / 35 L = J - K * 35 . ' XL = AND ( I 2 N ( L ) , I F A I L ( K + 1 ) ) IF ( I L .EQ. 0 ) GO TO 2 14  NF  1 C C  (i) = J  XX = OR (I X, I X T ( J ) ) CONTINUE NOW TO IDENTIFY THE X@S IDX = IDENTITY OF X@S J =0  • -  •  : • -, • • •  5 . C C  7  6 36  52  51  68 37'  IF ( J .GT. 35) GO TO 5 XL = AND(I2N(J)> IX) IF ( I L .EQ..0 I 60 TO 4 IDX(I) = I2N(J) GO TO .3 NX = I - 1 NX NOW HAS IDENTITY OF NO. OF DISTINCT X@S IN FAILURES NOW TO TEST IF ANY X@S SUM TOO HIGH SUMMAX = 0 . 0 SSUME2 = 0.0 DO 6 I = I f NX SUME = 0.0 L = IDX(I) DO 7 J. = 1.-NFAIL K = NF(J) XL = AND (I X T ( K ) » L) I F U L .NE. 0) SUME = SUME + EEE(K) CONTINUE IF (SUME .GT. EMAX) GO TO 57 IF (SUME .GT. SUMMAX) SUMMAX = SUME SSUME2 = SSUME2 + SUME * * 2 CONTINUE CONTINUE ••' • • J = 0 IFAIL(l) = - IFAILll) DO 37 I = 1» IFIN K = I + J IF (K. .NE. IDMISS(J + 1 ) ) G 0 TO 51 J = J + 1 GO TO 52 NONES = 0 DO 68 L = 1. NS XL = AND(IXS(L + 1» I ) , I F A I L ( D ) CALL ICOUNT ( X L , N0NES1) NONES = NONES + N0NES1 ISIG (K) = +1 IF ( NONES / 2 * 2 .NE. NONES) ISIG ( K) = -1 DO 93 JK = 1, NMULT ' NPLUS = 0 DO 94 J L = 1, 35  *  •  ARB ITRAR ARB I TRAR ARBI TRAR ARB ITRAR ARB ITRAR  9  8  IQ = I S I G ( J L ) * I M U L T U L , JK ) I S I G S ( J L ) = BLANK. IF ( IQ •LT. 0 ) I S I G S ( J L ) = MINUS IF ( IQ . L E . 0) GO TO 94 I S I G S ( J L ) = PLUS NPLUS = NPLUS + 1 94 CONTINUE NPOSS = NPOSS + 1 P'R'INT 40, NPOSS, ( I S I G S ( I ) , I = 1, 3 5 ) , NPLUS, 1. SUMMAX, SSUME2* NF ( 1 ) » (COMMA, N F U > » I = 2, NFAIL) 40 . FORMAT ( I X , 14* 2X, 3(10A2, I X ) , 5A2» IX,13* 2X» 1 F 5 . 1* IX, F 8 . 0 , 2X, 10(12* A l ) / (102X, 10(12 » A l ) ) ) ( I S I G S ( I ) , I = 1, 16) WRITE (OUTPUT) ( I S I G S ( I ) , I = 17, 32) WRITE (OUTPUT) WRITE (OUIPUI) ( I S I G S ( I ) , I = 33* 3 5 ) , (DUMMY, I = 4, 16) CONTINUE 93 IF (NMULT .NE. 1) PRINT 95 95 FORMAT (/ i n ) 57 RETURN END $IBMAP I COUNT DECK ENTRY ICOUNT ICOUNT SAVE 1,2,4 I COUNT,4 LAC ANA =0777777777777 CAL* 2,4 TNZ *+3 STZ* 3,4 RET TRA LGR 36 AXT 36,1 AXT 36,2 ZAC LOOP LGL 1 -LBT TIX *+l,l,l TIX LOOP,2,1 PXA »1 S 1 0* 3,4 RET BRN ICOUNT-5 •  ARBITRAR ARBITRAR ARBITRAR ARBITRAR ARBITRAR ARBITRAR ARBITRAR ARBITRAR ARBITRAR  ARBITRAR ARBITRAR ARBITRAR  TT  I  j)  (Jl  Ol  si  CD  W  - h^ o  3  O  2  -  CC  3 tL -Q U Z L_ L U  >cc z  t—  (fl  UJ  U  ro  _ 3 J . i w n NIVUO  ~ i  d  ESIGND  PROGRAM  12_ 1J_  ho 9  8. 7 6_ 5 4  3  it  SIBFTC ESIGND DECK »REF REAL MINUS, MINE INIEGER OUIPUI DATA PLUS, MINUS, BLANK / 2H + » 2H ^» 2H / DIMENSION SIGNSC6* 3 5 ) • SE(6)» FH<3)* IP0SS(6) READ 1, INE, IFE» INS, I F S . OUTPUT, NPOSS, MINE* ( I P O S S ( I ) . I = 1, 1 NPOSS) • ' ... • FORMAT (612, F 8 . 0 , 615) 1 CALL POSN(INS, I F S ) K = 0 DO 15 I = 1, NPOSS 16 K = K + 1 READ (INS ) ( S I G N S U . J ) , J = 1, 16) READ (INS > ( S I G N S U . J ) , J = 17, 32) READ (INS ) ( S I G N S U , J ) , J = 33, 35) IF ( I P O S S ( I ) .NE. K) GO TO 16. DO 17 J = 1, 35 IF ( S I G N S U . J ) .NE. PLUS) GO TO 18 S I G N S U , J ) = 1.0 GO TO 17 18 IF ( S I G N S U . J ) .NE. MINUS) GO TO 19 S I G N S ( I . J ) = -1.0 GO TO 17 , S I G N S U . J ) = 0.0 19 17 CONTINUE 15 CONTINUE REWIND INS REWIND OUTPUT CALL POSN ( I N E . I F E ) DO 7 L= 1. 6 7 S E ( L ) = 0.0 PRINT U . INE. I F E , MINE. INS. I F S , OUTPUT 11 FORMAT ( 24H THE REFLEXIONS ON UNIT . 12. 6H F I L E » 12. 1 23H WITH @E@ NOT LESS THAN.. F7.3.34H W.ILL BE ASS IGN ED SIGNS AS 0 2N UNIT » 13. 5H F I L E » I3.4H ANDT / 10X. 24H WILL BE OUTPUT ON UN 3IT . 12. 12H AS FOLLOWS //) PRINT 12 12 FORMAT( IX. ,5HIGPEN. 3X, 2HFH, 4X, 2HFK, 4X, 2HFL, 8X,• 2HE1, 5X, 1 2HE2, 5X, 2HE3, 5X, 2HE4, 5X, 2HE5. 5X» 2HE6 /) DO 2 I = 1» 36 •  8  6  1  3  4  READ (INE ) I I , IGPEN, SSOLS, (FH(K) , K = 1 , 3 ) , ' E IF(IGPEN .NE. 0) GO TO 4 IF(I I .NE. 0) GO TO 14 IF (E . L T . MINE) GO TO 8 IF (I .EQ.36) GO TO 2 DO 6 K = 1, NPOSS SE(K) = E * SIGNS(K» I) WRITE-(OUTPUT) IGPEN, (FH(K)» K = 1» 3 ) , (SE(K)» K =. 1 » PRINT 13, IGPEN, ( FH( K ) , K = 1» 3)» (SE(K ) » K = 1 , FORMAT (2X» I2» 2X, 3 ( 2 X , F 4 . 0 ) , 3X, 6 ( 2 X , F5.2 ) ) GO TO 2 WRITE (OUTPUT) IGPEN, (F H(K)» K = 1, 3 ) , E, E» E» E, E, PRINT 13, IGPEN, (FH(K)» K = 1» 3 i , E » E » E , E, E» GO TO 8  6) 6)  E E  PRINT 10, MINE FORMAT (// 71H ERROR... TAPE HAS MORE THAN '35 REFLEXIONS ON IH @E@ NOT LESS THAN , F7.3 ) 14 REWIND INE END F I L E OUTPUT ; • ,. • REWIND OUTPUT. STOP END . ' $IBFTC"POSN DECK SUBROUTINE POSN ( INPUT,INFILE) ASSIGN 14 TO IENDF . CALL EOF (INPUT, IENDF) 12 REWIND INPUT; NFILE = INFILE _4 IF (NFILE . L E . 1) GO TO 13. NFILE = NFILE - 1 18 READ (INPUT) II . • ,• GO TO 18 13 RETURN END' SENTRY ' — •, . 10__  IT WIT  .  ROT PROGRAM  •I  i  t  Y  12..  11 10 2 z  5 4 3  SIBFTC  ROT DIMENSION DIMENSION DIMENSION DIMENSION DIMENSION IN = 3  :  _ 2 53 7 170 180  F F < 8 ) » FH<300)» F K ( 3 0 0 ) » FOBS-(300)» FCLQOO')* FCQOO) TFCL.4 3 0 0 ) " * T F C ( 3 0 0 . ) » R A D 0 ( 6 ) » R A D C < 6 ) » A N G 0 ( 6 ) » ANGC(6) I E V O D O O O ) , X C ( 6 ) ». • YC < 6 ) » F C A L C < 3 0 0 ) » F O B S S C ( 3 0 0 ) . F0(300)* T F O ( 3 0 0 ) * X Q ( 6 ) » YQ(6) FOBSMN-OOO) » F M I N O O O ) , X 0 M ( 6 ) » Y 0 M ( 6 ) » X C M ( 6 ) » Y C M ( 6 )  ' REWIND 11 ' C A L L P O S N (IN»- 3 ) : : NN = 0 ' R E A D 7* A * 6 » T H E T A » T H E I N C , THEMAX ' . . FORMAT ( 5 F 1 0 . 0 ) R E A D 1 7 0 * F O M N » T C L , T O , T C » NO, N C » IFOBS-, FORMAT ( 4F1Q.0, 415 ) ^ PRINT 1 8 0 * FOMN FORMAT ( I X , 7HF0MN = , F7.1 /////) DO 2 N = I * 2 0 0 0 READ ( I N ) I I , IGPEN, IF ( I I . N E . 0 ) GO TO IF IF IF NN  1  V  12  ,o 9 8  2  1 3  7  6 5 4  SSOLS, 1  4  TFC(NN) CONTINUE  :  '  ~  . . IFCALC  ' .  •  2 2 TO  XH,  XK,  XL,  XOBS,  X0BS2 »  ( F F ( I ) , I = 1,8)  ' 2 ;  •  .  XH  F K ( N N ) = XK = XOBS FOBS(NN) F C L ( N N ) == F F ( 1 ) FO(NN) = FF( 2 ) FC(NN) = FF(3) T F C L ( N N ) = EXP( -TCL TFO(NN) = E X P ( -TO-  f  1 1  =  :  1  ( I G P E N . N E . 0 ) GO TO (XL .NE. 0.0) GO TO ( X O B S . L T . FOMN ) GO = NN. + 1  FH(NN)  '  =  EXP(  -TC  •  #  SSOLS SSOLS  ) )  SSOLS  )  PRINT 3 FORMAT U 5 H THE 0 0 1 P R O J E C T I O N O F S P A C E GROUP P 2 1 , 2 1 , 2 / / ) I F ( IFOBS .EQ. 0 ) GO TO 175 PRINT 4 FORMAT ( 8 X , 1 H H » 4 X , 1 H K » 6 X , 4 H F 0 B S , 4 X , 5 7 H 5 . F . C H L 0 R S.F.OXYG S.F.CA 1RB T.F.CHLOR T.F.OXYG T.F.CARB ) DO 5 I = 1. NN  5  PRINT 6* F H U ) . FK(I-). FOBS(I)» FCLI I )> F O ( I ) . F C I I l i TFCL(I). T F O d ) , TFC(I) FORMAT•(5X» 2F5.0, F10.1 • 3F10.2, 3F10.5 ) READ 7• CLX, CLY DQ 8 I = 1» NO . ; READ 7. RADO(I), ANGO(I) DO 171 I = 1, NC READ 7, RADC(I)» ANGC(I) PI = 3.14159 DO 9 I=l» NN SUMHK = F H ( I ) + FK( I ) ' ISUM1 = SUMHK ISUM2 = ISUM1 / 2 * 2 IF (I SUM. .NE. ISUM2 ) GO TO 10 IEVOD(I) = 2 F C L ( I ) = F C L ( I ) * TFCL(I).* 4.0 * COS<2.0 * PI * FH ( I j *CLX ) 1 * COS12.0 * PI * F K ( I ) * CLY ) GO TO 9 IEVODCI) = 1 F C L ( I ) = F C L ( I ) * TFCL ( I ) * (-4 • ) * S IN ( 2 .0 -*PI FH(* I )* CLX. ) 1 * SIN(2.0 * PI * F K ( I ) * CLY ) CONTINUE NOTE THAT FC.L < I ) IS NOW THE CHLORINE@S CONTR. TO STRUCTURE FACTORS S = ABS(THEMAX - THETA)' T = 5 / ABS(THE INC j IDO = T . IDO = IDO + 1 DO 11 I = 1 • NN F O l I ) = F O ( I ) * 4.0 * TFO(I) F C ( I ) = F C ( I ) * 4.0 * T F C ( I ) FH(I) = 2.0 * PI * F H ( I ) F K ( I ) = 2.0 * PI * F K ( I ) NOTE THAT FC(I> NOW CONTAINS THE TEMP. FACTOR AND THE MULTIPLIER 4 NOTE THAT FH AND FK ARE REDEFINED SUMFO = 0.0 THETA = THETA-THE INC DO 27 1=1» NN SUMFO = SUMFO + A B S ( F O B S I I ) ) PRIN. 150» SUMFO FORMAT C/9H SUMFO = * F7.0 ) 1  6 175 8 171  10 9 C  11 C C  27 150  ;  •  PRINT 151, CLX, CLY FORMAT (// IX, 29HCOORDINATES OF CHLORINE ARE (» _X» F5.3,~1H,, 1 IX, F 5 . 3 , IX, 1H) //) PRINT 100 100 FQRMAT(/119H THETA SUMFC R X I Y 1 X 2 Y 2 1 X 3 Y 3 X 4 Y 4 X5 Y 5 X 6 Y 6 ) RM = 2.0 WRITE (11) I DO ; DO 101 K = 1, IDO . THETA = THETA + THEINC DQ 10 2 L = 1, NO ; . . • • ' • " ROTANG = ANGO(L) + THETA XO(L) = ( COS( ROTANG ) •* RADO(L) ) / A + CLX 102 YO(L) = ( SIN( ROTANG ) * RADO(L) ) /B + CLY • DO 172 L = 1, NC ' " " ROTANG = ANGC(L) + THETA XC(L) = ( COS( ROTANG ) » RADC(L) ) 7 A + CLX 172 Y C ( D = ( 5IN( ROTANG ) •* RADC (L) ) /B + CLY SQMFC=0 DQ 24 I = 1 , NN • - . . . - • . FCC = 0.0 ~ FCO = 0.0 IF ( I EVOD ( I ) .EQ. 1) GO TQ 20 DO 21 J. = 1, NO 21 FCO = FCO + COS(FH(I) * X O ( J ) ) * C O S ( F K I I ) * Y O ( J ) ) DO 121 J = 1, NC \ : 121 FCC = FCC + C O S ( F H U ) * XC (J) ) * C O S ( F K ( I ) * Y C ( J ) ) GO TO 22 . v 20 DO 23 J = 1, NO . 23 FCO = FCO - S I N ( F H ( I ) * X O ( J ) ) * S I N ( F K ( I ) * Y O ( J ) ) DO 123 J = 1, NC 123 FCC = FCC - S I N ( F H d ) * XC (J) ) * S I N ( F K d ) * Y C U ) ) 22 F C A L C ( I ) = F C L ( I ) + FCO * F O ( I ) + FCC * F C ( I ) 24 SUMFC = SUMFC + A B S ( F C A L C ( I ) ) SCALE = SUMFC / SUMFO , " R = 0.0 DO 26 I =1 , NN . F O B S S C d ) ' - SCALE * F O B S d ) 26 R = R + ABS( ABS( F O B S S C d ) ) - ABS ( FCALC ( I ) ) ) R = R / SUMFC  .151  :  :  ;  :  s •  127 25 125  126 28 , ' ' 101 128 162  163 164 165 166 167 .161  IF ( R .GE. RM ) GO TO 126 ' . ' DO 127 I = 1> NN FOBSMN(I) = FOBSSC(I) FMIN(I.) = F C A L C ( I ) DO 25 I = 1 > NO . XOM<I) = XOl I ) YOM( I ) = Y0 ( I ) DO 125 I = 1, NC XCM(I ) = XC ( I ) YCM(I) = Y C ( I ) RM = R THETAM = THETA PRINT 28» THETA, SUMFO Rt ( ( X O < I ) , Y O ( I ) ) , I = 1, NO ) F O R M A T ( I X » F 6 . 3 » I X , F 7 . 0 , 2X» F 6 . 3 , 12(2X, F6.3) ) WRITE (11) THETA, R ' . PRINT 128, ( I X C ( I ) , Y C d ) ) , I = 1, NC > £ O R M A T ( 23X, 12(2X, F 6 . 3 ) / ) • PRINT 162, THETAM, RM FORMAT (///// IX, 52HC00RDINATES OF VARIOUS ATOMS IN 1/1'20@S FOR f 1HETA = , F 6 . 3 , 9H AND R =., F 6 . 3 , / ) \ CLX = CLX * 120.0 CLY = CLY * 120.0 DO 163 I = 1, NO XOM(I) = XOM(I) * 120.0 YOM(I) = YOM(I) * 120.0 DO 164 I = 1, NC XCM(I) = XCM(I) * 120.0 YCM(I) = YCM(I) * 120.0 PRINT 165* CLX, CLY FORMAT ( 10X, 8HCHL0RINE, 5X, 2(2X, F 6 . 1 ) . / PRINT 166, (( XOM(I), YOM(I) ), I = 1, NO) FORMAT ( 10X, 7H0XYGENS , 6X, 12(2X, F 6 . D PRINT 167, (( X C M ( I ) , YCM(I) ), I = 1, NC ) FORMAT (/10X, 7HCARBONS , 6X, 12(2X, F6.1) / IF ( IFCALC .EQ. 0 ) STOP PRINT 161 FORMAT (//// 3X, 1HH, 4X, 1HK» 5X, 9HF0BSMN ( I ) , - 3X, 8 H F M I N U ) ,//) DO 29 I = 1, NN F H ( I ) = F H ( I ) / ( 1.9999 * PI ) F K ( I ) = F K ( I ) / ( 1.9999 * PI )  \  .  9  £ f S 9  29 160 '  PRINT 160» F H U ) » F K U ) , FOBSMN(I)• FMIN(I) FORMAT (2( IX, F4..0 ), F10.1, 2X, F10.1 ) 5"T"0"P~ END SIBFTC POSN SUBROUTINE POSN ( INPUT,INFILE) ASSIGN 14 TO IENDF CALL EOF (INPUT, IENDF) 12 "RWIT^IWUT : NFILE = INFILE 14 IF (NFILE . L E . 1) GO TO 13 NFTLE = NFILE - 1 18 READ (INPUT) II GO TO 18 TS RTfTTJRTi : : END SENTRY  12.  1 1 '10  9_ 8 7 6 5 4 3  1 8 "  6 |0l  \9  L 8 6 01  TT Zl  CONTUR PROGRAM (THE UTV SUBROUTINE IS A U . B . C . COMPUTING CENIRE PROGRAM 10 RESERVE BUFFERS FOR, AND TO ALLOW THE USE AS VARIABLE^ O F , TAPE UNITS 01 , 02, 03, 04, 11, 12» 13, AND. 14)  12_  1 1_  10  q  SIBFTC  C  CONTUR THIS  START  DECK  PROGRAM W R I T T E N  DATA.LAXI DIMENSION DATA X Y Z ( . R E A L LX,  118 119 120  12.1 123  BY  R. H O G E  = CLOCK(O.O)  REWIND 4 CALL P L O T S DIMENSION DIMENSION DIMENSION DIMENSION  100 101 102 108 117  ' '  A i , I HE UNIV. OF BRITISH C O L U M B I A  " ; " LAXI(3) RHQ(31, 3 1 ) , IDIV(16) LABEL(14)» LQ(12) LIMIT(IO), T D E L I A U O ) , HGHirilu) / 18HX AXjSY A X I 5 / . A A I _ / . XYZ(3) l), XYZ(2)» X Y Z ( 3 ) / 1 H X , 1 H Y , IH/. / LY, L Y S E C T , LYAXI-Uu), L T I U , LVLEFI  ./  • @  INTEGER S I L , 5YMBL(16) . . @ DIMENSION ICYCLX1241), I C Y C L i i 2 4 1 ) @ DIMENSION RH00(61, 6 1 ) , ICONi61» 121) DIMENSION C ( 1 6 ) COMMON IN12, NPASSS, NEWZ, ICON, ICYCLX, LABEL, LIMI 1 ,HGHIY,IDI V,C SYM6L(1) = 0 @ SYMBL(4) = 5 @ SYMBL(7) = 2 • @ SYMBL (10)= 1 < _ SYMBL(13)= 12 @ FORMAT (512) FORMAT U 3 A 6 , A2) FORMAT ( 2 1 1 , 412, 5F10.0) FORMAT I 8F10.0 ) FORMAT ( IX, 12HTAPE UNIT = , 1 2 , 3X, lOHNPASbFb = , 12, 3X, 1 9HNPAIRS = , 12, 3X, 7HNEW_ = , 12 ) FORMAT (9H T I T L E ,13A6, A2) FORMAT ( I X , 5HNA = » I2» 3 A , 5HNB = , 1 2 , 3 A , 9HNC0Ni_ = , 12, 3X, 1 8HI PASS = , 12, 3 A , 7H1LAB = 12, 3X, 6HIPR = » 12) F0RMAT(5X» 8HAAXIS = , F 8 . 3 , 3 A , 1 8HBAXIS = , F 8 . 3 , 3X, 2 8H THE 1A = , F8.2, 3 A , 3 9HSCALER = , F7.2, 3 A , 4 9HCLKMAA = , F6.1) FORMAT ( I X , 12HC0NI0UR- AT 1 6 F 7 . U ) FORMAT (// IX, 94HALL HMEb _HOwN BELOw ARE M I N u i E . ELAP.ED i>INCE  122 52  270  276  281  1 THE BEGINNING .OF EXECUTION OF @CONiuR@ PROGRAM ) FORMAT ( 11H1DATA CARDS /) . • . READ 100, IN12» NPASSS,NPAIRS .NEWZ. • PRINT 122 PRINT117. IN12. NPASSS.NPAIRS , NEW, I F (NEWZ .NE. 0) CALL ALIL REWIND IN 12 READ 101. ( L A B E L ( I ) . I = 1, 14) " PRINT 1 1 8 • ( L A B E L ( I ) . I = 1. 14) READ 102» NA. NB* NCONTU. I PASS. I LAB » IPR» AAXIS».BAXIS» THETA. 1 SCALER. CLKMAX ' PRINT 119.NA. NB. NCONTU. IPASS, I LAB. I PR PRINT 120.AAXIS, BAXIS,.THETA. bCALER. C L K M A A READ 108. (C ( I ) » I = 1 . 8 ) . " I T (TfTON'TU .GT. 8) READ 108. ( C l I ) . I = 9. NCONiu) ' PRINT 121» ( C ( I ) . I = 1. NCONiu) PRINT 123 • DO 270 1 = 2 . NCONTU @ I F ( C ( I ) . L T . C H - D ) GO 10 237 @ NP = NPASSS - NPA IRS ; ; ' DO 275 IP = 1. NP IF (NPASSS .NE. 1 .OR. NPAIRs .NE. u) GO lO 276 INPUT1 = 0 ' ' INPUT = IN12 GO TO 277 READ (IN12 ) IZQ, IXO, IYO, IDZ, IPX, IDY, IN_, I N A , I N Y , KK.,1 I , J J _ REWIND 13 WRITE(13) IZQ, IXO, IYO, ID<-» IDA. I D Y . I N<-. I N A . I N Y . K K . H . J J DO 281 K = 1. INZ . READ U N 1 2 ) (( R H O O ( I . J ) . I = 1. I NX), J = 1, INY )• WRITE( 13 ) (( R H O O ( I , J ) , I = 1, I N A ) , J = 1, I N Y ) INPUT = 13 • . ' • • INPUT1 = 0 IF (NPAIRS .EQ. 0) GO TO 277 REWIND 14 " ' INPUT1 = 1 4 READ (IN12 ) IZ0» IXO, IYO, IDZ, IDX, IDY. INZ, INX,.INY» K K . I I . J J WRITE (14) IZQ. IXO. I Y ( J . ID-, I D A . I D T . IN*-, • I N A , INY, K K , I I , J J DO 282 K. = 1, IN-. READ (IN12 ) (( R H O O ( I , J ) , I = 1, I N X ) , J = 1, I N Y ) ;  f  _  '  9  282  WRITE (  14  )  ( ( R H O G M I ,J  REWIND INPUT1 NPAIRS = NPAIRS REWIND INPUT READ (INPUT ) IZ0» IF ( ( N A - I I + NB O R I G I N = 0.0 N P A S S = 1.  277  )»  I  =  1»  INA) »  (IDZ  IF  (INZ .NE.  .NE.  -  t'  'Y  51  1  t2  ho 9  0  5 4 3  L  )  6  I X O , I Y O , I'D-, I D X , - J J ) . N E . 0 ) GO T O  IDY •  IN*:,  INA,  INY»  @  A  •  .OR.  IPX  .NE.  IDAI  .OR.  INX  .NE.  I N x l .OR.  .OR.  I I .NE.  .OR.  I l l .OR.  IDY INY  "' • INZ1» INX1,  '  IDX = IDY IDY = IQ I Q == I N X  INY1»* ' *  .NE.  ID T 1 ) ' 6 0 iO 238S I N Y I ) GO 10 2 3 8 $ .NE. JJ1) GO TO 238$  .NE. JJ  _r_  i.I w  * IDX1»IDY1»  _  TT ~ Zl  KK»H»JJ  239  IDZ1 KKl  _  8  •IF ( IXO _ N E . IXp'l .AND. IYO .NE. IY01 ) . GO TO - 2 3 8 ^ IF ' ( 1 X 0 .EQ. i X O l .AND. IYO •EQ. IY01) GO TO 2 3 8 IF (IZO .NE. IZ01 ) GO TO. 2 3 8 NOTE = II IF(IYO .NE. IY01) NOTE = J J IF (NOTE .NE. NA) GO TO 51 . GO TO 1 Q = AAX1S AAXIS = BAXIS BAXIS = Q IQ = NA NA = NB NB = IQ IF ((NA - NB) .EQ. 1 .OR. (NA - NB) .EQ. (-2)) ORIGIN == 10.0 I ORDER = 0 IF (NA .EQ. I I ) GO TO 3 I ORDER = -1 IQ = IXO IXO = IYO IYO = IQ IQ = IDX  11  6  INT  01  INZ1  IF ' ( . K.K ' • NE •  =•.. 1 *  1  IF (THETA .EQ. 0.0) THETA = 90.00 IF (INPUT1 .LT. 2 ) GO TO 1 NPASS = 2 •_. ^ " READ( INPUTl ) l'ZOl"» IX01» IY01» I DZ 1» 1 KK1» I I I , J J 1 IF  J  $ $ $  $ $ *  •  -  9  •  INX = INY INY = IQ . • ' IQ = II I I = JJ J J = IQ IF UNPUT1 . L T . 2) GO 10 3 IXOl = IY01 IDX1 = 1DY1 .INX1 = INY1 3 REWIND INPUT I F U N P U T 1 «GE« 2) REWIND INPUT1 IF (INPUT1 .GE. 2 .AND. (IXO + IDX * (INX - 1)) .NE. 1X01) GO TO 1 238 TOTAL = CLOCK(START ) / 3600.0 PRINT 103* TOTAL 103 • FORMAT<///9X,39HAXES ADJUSTED FOR PROPER PLOTTER FORMAi, 1 .' 14X, 7HTIME = > F10.2 ) ' P I = 3.14159 RADTHA = PI / 180.0 * IHEIA IF (SCALER .NE. 0.0) GO TO 278 X = (INY - 1) * I D Y SCALER = 25.4 * 120.0/ BAXIS / X / SIN(RADTHA) 278 SCALE = 1.0 / 0.393700 / SCALER C SCALE = ANGSTOMS / INCH Q = ( INX - 1) * IDX LX = 0 * AAXIS / 120.0 / SCAI F Q = ( INY - 1) * IDY LY = Q * BAXIS / 12U.U / sCALE Q = IDY DLY = Q * BAXIS / 120.0 / 5CALE HY = LY * SIN(RADTHA) . DHY = 'DLY * SI N ( RADTHA ) CONSTl = 2 * INY - 2 C0NST2 = 2 * INX - 2 C0NST2 = LX / CONST2 C0NST3 = LY * COS(RADTHA) / C O N b l l CONSTl = HY / CONSTl LYIO = 10.0 / SIN(RADTHA) GRITY = 0.0 IDIV(1) = 2 •  L _) 8 6 01  T T  Zl  * * * $ $  @ @ @ @ @  @. @  .  #  '"  17 S 9  7  232  11 8  9 10  12  14  12  11 9  0  8 7 6  0  5 4 3  104  DO 7 I = 2 » NCONTU IDIV<I) = IDIV( I - 1) * 2 IF (LY . G i . LYIO) GO TO-232 NPARTS = 1 GO TO 10 DO 11 J = 2, INY GRITY = GRITY + DHY IF (GRITY - 10.0 . L E . 0.0) GO TO 11 LIMIT(1) = J - 1 GO TO 8 CONTINUE I J = LIMIT.1) - 1 DO 9 1 = 2» 10 NPARTS = 1 IQ = I * I J + 1 IF (INY - IQ . L E . 0) GO TO 10 L I M I T ( I ) = IQ LIMIT(NPARTS) = INY Q = (-LIMIT ( 1 ) - 1 ) * IDY LYSECT = Q * BAXIS / 120.0 / SCALE DO 12 I = 1,10 L Y A X I S ( I ) = LYSECT Q = NPARTS -1 LYAXIS(NPARTS) = LY - Q * LY5EC1 DO 14 I = 1» 10 T D E L T A ( I ) = L Y A X I S ( I ) *• COS (-RADT+A) HGHTY(I) = L Y A X I S ( I ) * SIN(RADTHA) SHIFT = 0.0 IF' ( THETA .GT. 90.0 ) SHIFT = LYIO * COSIPI - RAD 1 HA) THETA1 = THETA IF ( ORIGIN .EQ. 10.0 ) IHEIA1 = 18U.0 - iHETA RADTH1 = THETA1 * P I / 180.0 STALAB = 0.0 IF ( THETA1 .GT. 90.0 ) STALAB = LYIO * COS(PI - RADIHI) JINIT =1 NINX = 2*INX - 1 NINX2 = NINX - 2 TOTAL = CLOCK(S TART) / 3600.0 PRINT 104, TOTAL FORMAT (/ 9X, 28HVARIOUS CONSTANTS CALCULATED* 25X,  _  @ @ @  -  .  -  @  '  @  1  279 284  .271  280  204  205  7HTIME = » F10.2 ) TOT = 0.0 CALL PLOT ( 2 . 0 . 0.0, -3) IF' (NP •EQ* 1) GO TO 279 IF (IPR.EQ. 1) GO TO 279 CALL SYMBOL (0.0» 0.0, 0.28» 5HPASS-* T H E T A1 » 5) X = 6.0 / 7.0 * 0.28 * 5.0 * COS(RADTHl) Y = 6.0 / 7.0 * 0.28 * 5.0 * SIN(RADIHl) XP = IP CALL NUMBER ( X, Y» 0.28, XP, IHEIA1, -1) CALL PLOT ( 1 . 0 , 0.0» -3 ) IF ( I P .EQ. 1) GO TO 284 IF (IPR * EQ. 1 .OR. ILAB .EQ. (-1) ) GO TO 280 Q = 0.0 @ IF (THETA .NE. 90.0) Q = 1.0/ TAN(RADTH1) @ DO 271 J = 1, NCONTU @ Y = J - 1 c? ' Y = Y * 0.3 @ X = Y * Q + STALAB @ IF ( J .EQ. 1 .OR. J .EQ. 4 .OR. J • EQ'. 7 .OR. J .EQ. 10 .OR. @ 1 J .EQ. 13 ) CALL SYMBOL(X - 0.2» Y + U.u5» 0.1, - Y M B L I J ) , U . U ,-D@ CALL NUMBER (X» Y, 0.1, C«J)» O.U, -1) @ CALL PLOT ( 1.0, 0.0, -3 ) X = 0.1 + STALAB CALL SYMBOL ( X, 0.0, 0._4» LABEL( 1 ) » T H E I A1 » 80 ) DO 15 IPARTS = 1, NPARTS QPARTS = IPARTS LIMJ = LIMIT ( IPARTS) •' . . NINY = 2 * (LIMJ - J I N I 1) +1 N.INY2 = NINY - 2 @ I I NY = LIMJ - JINIT. + 1 NICONY = 2*NINY - 1 NCYCL = 2 * NINX + 2 * NINY - 4 DO 204 I =1, NINX ICYCLX( I) = I ICYCLY( I ) = 1 DO 205 1 = 2 , NINY 1 1 = 1 + NINX - 1 ICYCLX( 11) = NINX ICYCLY( I D = I  206  207  283 J.05  IQ = NINX - 1 DO 206 1= 2, IQ I I = 2*NINX + NINY -1 - I ICYCLXl I I ) = I ICYCLY( I I ) = NINY DO 207 I = 2, NINY I i = 2*NINX + 2*NINY - 2 - 1 ICYCLX( I I ) = 1 . ICYCLY( I D =1 ICYCLX(NCYCL + 1) = 1 ICYCLY (NCYCL + 1) = 1 READ (INPUT) ( L Q I I ) » I = 1» 12) IF (INPUT1 .GE. 2) READ(INPUT1) <LQ ( I ) » 1 = 1 , 12) X = 0.4 + STALAB ' IF (NPARTS .EQ. 1) GO TO 283 CALL SYMBOL ( X , 0.0, 0.14, 5HPART-» THE t Al» 5 ) X = X + 6.0 / 7.0 * 0.14 * 5.0 * COS(RADTHl) . ' Y = 6.0 / 7 . 0 * 0.14 * 5.0 * SIN(RADTHl) CALL NUMBER ( X, Y, 0.14»QPARTS» IHETA1, -1 ) CALL PLOT ( 0.8, 0.0,-3 ) . ' "... ' • TOTAL = CLOCK (START ) /. 60.0 /6U.0 PRINT 105, IPARTS, TOTAL FORMAT ( / 9X» 14HLABEL FOR PART , 12, 8H WRITTEN , 29X, 1 " 7HTIME = » F10.2 ) ~~ ~ ~ 7~ DO 24 K = 1, INZ IF ( CLKMAX .EQ. 0.0 ) GO TO 25 . • TOTAL = CLOCK(START ) / 3600.0 IF ( CLKMAX - TOTAL -1.00 . L T . TOTAL - 101 ) GO i'O 21 TOT = TOTAL • • . ' • '; QK = ( K - l ) * IDZ + IZO • ' IF (IPR .EQ. 1) QK = IP X = STALAB + 0.2 ' ' CALL NUMBER ( X, 0.0,.0.28, QK, THETA1» -1 ) IF (IPR .EQ. 1) GO TO 272 STATEMENTS LABLED * * * * * ARE INCLUDED BECAUSE rgCALL NUMBER® CANNOT FORM A ZERO ( 0 ) IF (QK .EQ. 0.0) CALL SYMBOL I X, O.U, U.28» 1HU, I H E l A l * 1 ) IF ( K .NE. L A N D . K .NE. IN-.) GO JO 272 X = X + 6.0 / 7.0 * 0.28 * C O b i R A D l H l ) * 3.u Y = 6.0 / 7.0 * 0.28 * SIN ( RADTH1 ) * .3.0  @ @ *  :  25  C C  $  ***** ***** ***** @  e f  s 9  272  CALL SYMBOL ( X, Y, 0.14, 10H/120 ALONG, T H E T A 1 , 1 0 ) X = X + 6.0 / 7.0 * 0.14 * COS(RADTHl) * 12.0 Y = Y + 6.0 / 7.0 # 0.14 *.SINIRADTH1) * 12.0 CALL SYMBOL ( X, Y, 0.28, XYZ.IK.K), ' l HE T Al» 1 ) CALL PLOT ( 0.8, ORIGIN, -3 ) DO 24 M = 1, NPASS IF IK. ..NE. L A N D . K .NE. INZ) GO IQ 234 X = SHIFT + LX/2.0-0.34 Y = -0.24 IF (ORIGIN .NE. 0.0) Y = +10.1CALL SYMBOL (X, Y , '0.14» L A A I i I I ) , u.u, 6) X = LX + SHIFT - 0.32 Q = IXO + ..( INX - 1 ) * IDX IF (M .NE. 1) IQ = 1X01+ (INX1- 1) * IDX1 IF (NPASS .NE. 2 •OR. M .NE, 1 ) l.CALL NUMBER .( X, Y, 0.14, Q, 0.0, -1) IF (Q .EQ. 0.0) CALL SYMBOL ( X , Y » 0.14, IHO,. u.u 1 ) IF ( •M .NE. 1) GO TO. 2 34 : Q = IXO ' , ' • -• CALL NUMBER ( SHIFT, Y, 0.14, Q, O . O , -1 IF (Q .EQ. 0.0) CALL SYMBOL (5HIFI» r , u.14» l H u , u.u , 1 ) X = SHIFT -V0.1 Y = 0.0 Q = IYO + ( J I N I T - 1) * IDY IF (ORIGIN .NE..0) X= SHIFT - 0.32 * COS(RADTH1) - 0.1 IF ( ORIGIN .NE..0) Y = 9.68 CALL NUMBER (X, Y , 0.14, Q, THETA1, -1 ) IF (Q .EQ. 0.0) CALL SYMBOL ( X , Y , 0.14, IHO, IHETA1, 1 ) X = TDELTA<IPARTS) + SHIFT - 0.32 * COS(RAD fHI) - u, Y .= HGHT Y ( IPARTS) - 0.32 IF (ORIGIN .NE. 0.0) Y = 10.0 - HGHTY(IPARTS) IF (ORIGIN .NE. 0.0) X =. TDELTA(IPARTS) + SHIFT - U. 10 Q. = IYO + (LIMJ - 1 ) * IDY CALL NUMBER (X, Y, 0.14, Q, THEIA1, -1) IF (Q .EQ. 0.0) CALL SYMBOL ( X , r , u.l4»-lHu»' i H E i A l , 1 ) X' = SHIFT + TDELTA(IPARTS) / 2.- 0.34 * COSlRADIHl) - u . l Y = HGHTY(IPARTS) / 2 . - 0 . 3 4 . * SIN(RADTH1) IF (ORIGIN .NE.0.0) Y= 10.0-HGHTY(I PARTS) / 2 . - 0 . 3 4 * SIN(RADTH1) CALL SYMBOL (X, Y, 0.14, LAX I ( J J ) , THE! A1 »' 6 )  L 8 6  Oil TT Zl  *  :  12 _  _'_  010  9  •:  i  8  0  7 6 • 5  • 04 3  *****  *****  *****  234  109  C A L L P L O T ( S H I F T , O R I G I N , +3 ) Y = HGH T Y( I P A R T S ) I F ( O R I G I N .EQ. 1 0 . 0 ) Y = 1 0 . 0 - Y X = JDEL'TA ( I P A R T S ) + S H I F T IF ( M .NE. 1) 1 C A L L P L O T ( X , Y» + 3 ) C A L L P L O T ( X , Y, +2 ) X •= T D E L T A ( I P A R T S ) + L X + S H I F T C A L L PLOT ( X, Y, +1 ) X = LX + SHIFT I F ( N P A S S .NE. 1 .AND. M-.NE. 2 ) 1CALL PLOT ( X, O R I G I N , +3 ) CALL PLOT ( X» O R I G I N , + 2 ) C A L L PLOT ( S H I F T , O R I G I N , +1 ) • . TOTAL = CLOCK(START) / 3600.0 P R I N T 1 0 9 * K» M» T O T A L FORMAT , ( / 1 2 X , 1 8 H L A Y O U T FOR S E C T I O N , 1 2 , 5H 1 , 9H 2 7 H T I M E "=. , F 1 0 . 2 ) INPU = INPUT' I F (M .GT. 1 ) I N P U = INPUT1 I F I I O R D E R . E Q . 0 ) GO TO 2 0 READ (INPU ) ( ( R H O O ( J , I ) , I = 1 , I N Y ) , J = G O TO 2 3 • ^~ ' ~ ~ ~ R E A D ( I N P U ) ( ( R H O O ( I , J ) , I = 1 , I N X ) , J .= DO 2 3 3 I = 1 , I N X N = 0 DO 2 3 3 J = J I N I T , L.IMJ : N .= N + l •• R H O I I , N) = RHOO(I» J ) 1 1 = L I M J - J I N I T +1 DO 2 0 1 I = 1 , I N X DO 2 0 1 J = 1 , I 1 RhOOl2*1-1»2*J-1) = RHO(I,J) IF(I.NE«INX) RHOO(2*I» 2 * J ~ 1 ) = U» 5 * t R H O ( I »  » .  •  PASS, 12, COMPLETE , 1 4 X , .  -  :  ,20 23  233  201  IFU.NE.Il  1  IFd.NE.INX DO'202 DO 2 0 2  I = J =  )•" R H O O ( 2 * I - l »  1, INX ) ' '.- '• 1 , I NY )  ,  J)  +  --  RHO  (1 + 1 , J ) )  2 * J ) = 0 . 5 * i R H O i I » J ) + RHO  iI,J+l))  '  .AND.. J . N E . I l ) KHuu ( 2 I » 2 * J ) = \>. 2 5 * . ( ' K H u ( I , J ) + r\HGtI + l , J ) + :-.H: . I , J + l ) + RH0( 1 + 1 , J + l ) ) W  1»NINX 1,NICONY  * * *  * *  •  .  .  s ~ 9  202'  208  264  261  262  f W  V  12 _1_  f 10 9 i  9  8 7  6 5 ¥ 4 3  265  ICON (I»J) = ITYPE = 1 LEFTX = 1 STL = 1 DO 260 I = LEFTX. NCYCL* 2 I IX = ICYCLX( 1 i I 1Y = ICYCLY( I ) I2X = ICYCLX( I + 2 ) I2Y = ICYCLY( I + 2 ) IF ( R H O Q d l X , I1YI . L T . RH00II2X, I 2 Y ) ) GO TO 264 STL = 1 GO TO 260 IF (STL .GT. NCONTU) GO TO 260 DO 261 L = STL* NCONTU T F "fRTTOQlTTX~» ITY) .GE. C ( L ) ) GO TO 261 STL = L IF (RHOO (I2X » I2Y) . L T . C ( L ) ) GO TO 260 STL = L + 1 LINCL = L GO TO 262 CONTINUE STL = 'NCONTU + 1 GO TO 260 IMINX = ICYCLX( 1+1) I MI NY = ICYCLY( 1+1) IMAXX = I2X IMAXY = 12 Y IF(RHOO (IMINX, IMINY) .LT. C ( L I N C L ) ) G O TO 265 IMAXX = IMINX IMAXY = IMINY IMINX = I IX IMINY = I 1Y 13 = (IMAXX + IMINX ) •/ 2 14 = I MAXY + IMINY - 1 LEFTX = I ICONtI3» 14) = I C O N U 3 , 14) + I D I V ( L I N C L ) / 2 13 = 1 •IF ( 14/2 * 2 .EQ. 14) 13 = -1 IDIRX (IMAXY - IMINY ) * 13 IDIRY (IMAXX - IMINX ) *. 13  ] L  I  @ @ @  @  @ @ @  @ @ @ @ @  @ @ @ @ •  @ @  ra .  @ @  @ @ @ @ @  @ @  8  I 6  iOl( jTT~ "121  260  . 218  257  254  251  2 52  255  GO TO 213 CONTINUE I TYPE = 2 LEFTX = 3 LEFTY = 1 STL = 1 DO 250 I - L E F T X , NINX2, 2 IF I I .EO. LEFTX ) GO TO 257 S1 L = 1 LEFTY = 1 DO 250 J = LEFTY, NINY2, 2 IF (RHOO( I » J ) . L T . RHOO(I, J + 2 ) ) GO TO 254 STL = 1 GO TO 250 IF ( S T L .GT. NCONTU ) GO TO 250 DO 251 L = S T L , NCONTU IF (RHOO(I,J) .GE. G I L I I GO TO 251 STL = L IF (RHOO(I * J + 2 ) • L T • C ( L ) ) GO TO 250 STL = L + 1 LINCL = L GO TO 252 CONTINUE STL = NCONTU + 1 GO TO. 250 IMAXX = 1 . IMAXY = J + 2 I MINX = I IMINY = J + 1 IF (RHOOdMlNX* IMINY) . L T . C ( L I N C D ) GO TO 255 IMAXY = IMINY IMINY = J I 3 = (IMAXX + IMINX) / 2 14 = IMAXY + IMINY - 1 IF ( I C 0 N ( I 3 , 14) / I D I V ( L I N C L ) * 2 .NE. IC0N(I3» 1 ) / 2 ) ) GO TO 256 LEFTX = 1 LEFTY = J ISTARX = 1 3 ISTARY = 1 4  •  @ @ @ @ @ @ @ . @ @ @ @ @ @ @ @ @ @ @ @ @  @ @ (3  @ @ @ @ . @ _  @ @ 14) / (IDIV(LINCL® @ @ @ @ @  256  250 C C C 220  c .•  226 225  221  C  IDIRX = 1 IDIRY =0 GO TO 213 I F ( S T L .GT. NCONTU) GO TO 250 @ IF IRHOO(I * J + 2) . L T . C ( S T L ) )'GO TO 250 @ LINCL = STL @ STL = STL + 1 @ GO TO 252 . @ CONTINUE @ . @ GO TO 22 THE SECTION BETWEEN ***@S IS AN IMPLIED SUBROUTINE WHICH C O M P L E T E S ® ONE CONTOUR AND THEN RETURNS TO LEAVING POINT @ = IMAXX +IDIRX = IMAXY +IDIRY (RHOO(11,12) .GE'. C ( L I N C L ) ) GO TO 221 L = (IMAXX + I 1) / 2 = IMAXY +12-1 ( I C 0 N ( I 3 , 14) / I D I V ( L I N C L ) * 2 .NE. I C 0 N U 3 * 14) / (IDIV(LINCL@ 1 ) / 2 ) ) GO TO 222 • @ IDIRX = IMAXX - IMINX IDIRY = IMAXY - IMINY • IMAX = IMAX • IMINX = 11 IMINY =12 GO TO 200 o I F ( I TYPE . L Q . l ) GO TO 225 IFUSTARX .EQ. 13 .AND. ISTARY •EQ. 14 ) GO TO 218 GO TO 220 IF (14.EQ. 1 .OR. 14 .EQ. NICONY ) GO TO 208 IF ( 13.NE.LAND. 13 .NE. NINX ) GO TO 220 IF ( 14.EQ. (14/2 *• 2). ) GO TO 208 GO TO 220 I 1 = IMINX + IDIRX 12 = IMINY + IDIRY IF ( R H O O ( I l , I 2 ) .GE. C ( L I N C L ) ) GO TO 222 L I 3 = (IMAXX + 1 1 + IDIRX ) / 2 14 = IMAXY + 12 + IDIRY - 1 IDIR = IDIR IMAXX = IMAXX + IDIRX  •  .  11 12 IF 13 14 IF  I  2'22 C  I MAXY IMINX IMINY  = IMAXY =11 = 12  GO  200  TO  IDIRY -  '  • •  '  . @  CONTINUE " I I AND 12 A R E 13= (IMINX* 14 = IMINY * 15 = IMINX 16 = IMINY IDIRX IDIRY IMAXX IMAXY  C C C 213 200  +  " F U T U R E I M I N S , NO 2 + IDIRX)/ 2 2 + IDIRY - 1 + IDIRX + IDIRY  = IMINX = IMINY =15 =16  -  IMAXX IMAXY  CHECK  ' I S . N E E D E D -TO ' E S T A B L I S H • T H I S ' ' - ' • •  "  "  GO T O 2 0 0 '213 F O R S T A R T I N G C O N T O U R , I . E . , P O S I T I O N I N G P E N C O N T O U R N U M B E R S 1, 4 , 7, 1 0 , AND. 2 2 3 FOR C O N T I N U I N G CONTOUR INQU = 0 XMAXX = IMAXX XMAXY = IMAXY. XMINX = IMINX XMINY = IMINY 1  Q=(C(LINCL)-RHOO( IMINY))  IMINX",  POSIT1  +  =  XMINX  I M I NY ) ) / U R H O O ( I M A X X ,  (XMAXX  •  -XMINX  .  \  . @ (WITH 13)  IMAXY)  SYMBOL  FOR  @ @  RHOO(IMINX.  )#"Q  P O S I T 2 = XMINY + (XMAXY -XMINY )* Q X = CONST2 * ( P O S I T 1 - 1.0) + C O N S T 3 * ( P O S I T 2 - 1.0) + S H I F T • Y = C O N S T 1 * ( P O S I T 2 - 1.0 ) IF ( O R I G I N .GT. 5.0 ) Y = 1 0 . 0 - Y I F ( I N Q U . N E . 0 ) GO T O 2 2 3 INQU = 1 I F ( L I N C L . E Q . 1 .OR. L I N C L . E Q . 4 .OR. L I N C L .EQ.. 7 . O R . LINCL 1 . E Q . 1 0 .OR. L I N C L . E Q . 13 ) C A L L S Y M B O L ( X , Y, 0 . 1 , 2 S Y M B L ( L I N C L ) » 0.0, -1) C A L L P L O T ( X , Y, + 3 ) C A L L PLOT ( X . Y . +2) 223  GO T O 2 2 0 CALL PLOT(X,  Y,  ICON(I3,  =  14)  +1) ICON(I3,  14)  +  L  ID+V(LINCL)  /  2  (?  @ @ @ @ @ @ @  @ @  I i  c  GO TO 226  22  |  FY 12  1 1  1-10 9 8  f  X = LX + 1.0 @ IF (NPASS .EQ. 2 .AND. M .EQ. 1) X = LX * TOTAL = CLOCK(START) / 3600.0 PRINT 107* K» M* TOTAL * 107 FORMAT I 12X* 7HSECTI ON » 12. 5H PASS. 12, * 1 10H COMPLETED . 24X. @ 2 7HTIME = • F10.2 ) * 24 CALL PLOT ( X. 0.0. -3 ) J I N I T = L l M I T i IPARTS) IF (INPUT1 .GT. 1) REWIND INPUT! 15 REWIND INPUT 275 . CONTINUE CALL SYMBOL ( STALAB. 0.0. 0.28.:17HEND OF ALL PASSES,THETA1, 17 ) IF (IPASS .EQ.' 1) GO TO "52 • 21 21 CALL PLOT NO ra TOTAL = 37.5 * TOTAL I = TOTAL IHR = 1 / 6 0 IMN = I - IHR * 60 PRINT 124. IHR. IMN 124 FORMAT (/// IX. 45HAPPROXI MAT E TIME NEEDED FOR PLOTTING ABOVE I S . 1 14. 4H HR., 15, 5H MIN. ) STOP 238 PRINT 114 • $ 114 FORMAT ( 81H ERROR.... TWO PASSES ARE INCAPABLE OF BEING JOINED 1$ IN ANY MANNER BY THIS PROGRAM ) $ STOP 239 PRINT 115 @ 115 FORMAT ( 56H ERROR.... SECTIONS IN CONTUR AND IN FOURIE ARE NOT SA@ 1ME ) @ STOP 237 . PRINT 116 @ 116 FORMAT ( 43H ERROR.... CONTOURS NOT IN INCREASING ORDER ) STOP $ END JIBMAP UTV DECK FTL27890 ENTRY UTVAR. FTL27900 EXTERN ERLOC. FTL27910 v  7  5 6 W 4 • 3  1  MACRO FOR G E N E R A T I N G V A R I A B L E U N I T S AND C O R R E S P O N D I N G E X T E R N S UNITS CNT  CNT  MACRO SET IRP DUP PZE PZE EXTERN SET  TABLE  • • ••  .  "A 0 A. 1»@A@-CNT FIL@A@. FIL@A_. _A_ + 1  IRP ENDM  ** E N T R Y  FROM  MAIN  PROGRAM  TO D E F I N E  A  V A R I A B L E UNIT  .  • *  UTVAR.  UTVX  USTOP  .  SXA LAC SXA LXA LAS TRA NOP PAC CLA PAX TXL AXT STO TRA  U T V X ,4 UTVX»4 ERLOC.>4 U T V X »4 NFILES. USTOP  LXA CLA* TSL PZE  UTVXt4 -1»4 FEXEM. ' EXIT»»32  *  RETURN  INDEX '  STOP I F L O G I C A L T A P E NUMBER E X C E E D S . NUMBER OF F I L E S I N T A B L E . •  • 4 I0U,4 . »4. UST0P-2»4»0. **»4 2,4 1,4  * I N P U T -- O U T P U T •.ADDITIONS  SAVE  OR  LOGICAL  ADDRESS  OF  FCB  POINTER  STOP I F UNIT I S UNDEFINED RESTORE RETURN INDEX S E T L O C A T I O N OF F C B / R E T U R N TO M A I N P R O G R A M •  *  UNIT  DELETIONS  PICKUP  RESTORE UNIT DESIGNATION ERROR, I L L E G A L UNIT REQUESTED. NO O P T I O N A L RETURN  TABLE  SHOULD  BE MADE  TO  CARD  IOU  FOLLOWING  FTL27912 FTL27913 FTL27914 FTL27915 FTL27916 FTL27917 FTL27918 FTL27919 FTL27920 FTL27921 FTL27922 FTL27923 FTL27924 FTL27925 FTL27930 FTL27940 FTL27950 FTL27960 FTL27970 FTL27980 FTL27990 FTL28000 FTL28010 FTL28020 FTL28030 FTL2804O FTL28050 FTL28060 FTL28070 ' FTL28080 FTL28090 FTL28100 FTL28U0 . FTL28120 FTL281.30 •FTL28140 FTL28150 FTL28160 FTL28170  i  1 #  IOU UNITS N F I L E S PZE  (01,02.03 *04* 11*12*13*14) . *-IOU-l  FTL28180 FTL2827Q  6  FEXEM..EXIT EXTERN FTL28300 END FTL28310 SIBFTC ALT Z DECK SUBROUTINE ALTZ DIMENSION RHO(31 * 31» 8)» L A X I ( 3 ) ' COMMON INPUT, NPASS* NEWZ, RHO INTEGER OUTPUT __• • DATA LAXI / 18HX AXISY AXISZ A X I S / REWIND INPUT REWIND 1 • . ' DO 1 L = r7~NP A_~S" ' ~* " REWIND 13 . REWIND 14 ____ • • " READ (INPUT) 1X10* 1X20* 1X30* IDX1* IDX2* IDX3* I P 1 * I P 2 . I P 3 * 1 I I * J J * KK IF ( NEWZ. »NE« I I ) GO TO 14 PT^ITTT T5T~irAX"H"NE¥ZT : ' 15 FORMAT ( // 16H WARNING... THE » A6» 32H IS ALREADY THE AXIS OF SE _^ 1CTIONS 7 5QH THE PROGRAM CONTINUES WITHOUT ALTERATION OF AXES ) RETURN 14 I P H = IP1 / 2 IP12 == IP1 - I P H IP120 = I P H + 1 DO 16 IK = 1.2 LIM = I P H IF ( I K .EQ. 2) L I M = LP 12 ITAPE = 13 IF ( I K .EQ. 2) ITAPE = 14 DO 2 K = 1. LIM 2 READ ( I N P U T ) ( ( R H O ( I . J . K ) . J == 1 , IP2 ) » I= :1. I P 3 ) 3 IF ( NEWZ .NE. J J ) GO TO 5 DO 6 J = 1. I P 2 6 WRITE ( I T A P E ) ( ( R H O ( I . J , K)» K == 1» L I M ) . I == 1. IP3 ) GO TO 16 5 IF ( NEWZ .NE. KK ) GO TO 9 DO 10 I = 1, I P 3  Old TT  Zl A  12 1  1  10 9  8 7 6  5 . 4 3  !  •  • •  _|  1^  -  -  9  L | e  -  e  s  10 16  WRITE (1TAPE ) ( I R H O l I , J *K), J = 1, IP2) , K = 1• LIM ) CONTINUE REWIND 13 REWIND 14 IF (NEWZ .NE, J J ) GO TO 17 WRITE ( 01 ) 1X20, 1X10, 1X30, IDX2» IDX1, IDX3, I P 2 , I P l ,IP3, 1 J J , I I , KK DO 18 , K. = 1, I P2 READ (13) ((RHO(I , J , 1 ) , J = 1 , I P 1 1 ) , I = 1, IP3) READ (14) ( ( R H O ( I , J , 1 ) , J= IP120, I P l ) , I = 1, IP3) 18 WRITE(01) I ( R H O ( I , J , 1) , J = 1» I P l ) , I = 1, IP3) GO TO 11 17 WRITE I PI ) 1X30, 1X20, 1X10, IDX3» IDX2» IDX1, IP3» IP2» I P l * 1 K.K » J J » I I DO 19 K = 1> IP3 READ (13) ( ( R H O ( I , J , 1 ) , J = 1, I P 2 ) , I = 1»IP 11) ' READ (14) ( ( R H O ( I , J , 1) , J = 1» IP2) , I = IP120, I P l ) 19 WRITE (1) ( ( R H O ( I , J , l ) , J = 1, I P 2 ) , I = 1, I P l ) 11 PRINT 7, LAXI(NEWZ) FORMAT (5X» 6H (THE , A6» 30H IS NOW THE AXIS OF SECTIONS) 7 ) 1 CONTINUE REWIND INPUT . INPUT = 1 RETURN ' 9 PRINT 4, NEWZ FORMAT ( 13H ERROR—AXIS » 12, 15H DOES NOT EXIST ) 4 STOP END SENTRY  y  '6  01  A  TT  Zl  1 •  •  

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