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A Real Space Solution to the Phase Problem in X-Ray Crystallography

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A Real Space Solution to the Phase Problem in X-Ray Crystallography Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1984 A real space solution to the phase problem in X-ray crystallography: ALCAMPS (Ames Laboratory Computer-aided Analysis of Multi-solution Patterson Superpositions) James Wyman Richardson Jr. Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Physical Chemistry Commons Recommended Citation Richardson, James Wyman Jr., "A real space solution to the phase problem in X-ray crystallography: ALCAMPS (Ames Laboratory Computer-aided Analysis of Multi-solution Patterson Superpositions) " (1984). Retrospective Theses and Dissertations. 9024. https://lib.dr.iastate.edu/rtd/9024 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. INFORMATION TO USERS This reproduction was made from a copy of a document sent to us for microfilming. While the most advanced technology has been used to photograph and reproduce this document, the quality of the reproduction is heavily dependent upon the quality of the material submitted. The following explanation of techniques is provided to help clarify markings or notations which may appear on this reproduction. 1.The sign or "target" for pages apparently lacking from the document photographed is "Missing Page(s)". If it was possible to obtain the missing page(s) or section, they are spliced into the film along with adjacent pages. This may have necessitated cutting through an image and duplicating adjacent pages to assure complete continuity. 2. 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These prints are available upon request from the Dissertations Customer Services Department. 5. Some pages in any document may have indistinct print. In all cases the best available copy has been filmed. UniversiW MicriSilms International 300 N. Zeeb Road Ann Arbor, Ml 48106 8423669 Richardson, James Wyman, Jr. A REAL SPACE SOLUTION TO THE PHASE PROBLEM IN X-RAY CRYSTALLOGRAPHY: ALCAMPS (AMES LABORATORY COMPUTER-AIDED ANALYSIS OF MULTI-SOLUTION PATTERSON SUPERPOSITIONS) Iowa State University PH.D. 1984 University Microfilms Int6rnsti0n£ll 300 N. Zeeb Road, Ann Arbor, Ml 48106 PLEASE NOTE: In all cases this material has been filmed in the best possible way from the available copy. Problems encountered with this document have been identified here with a check mark V . 1. Glossy photographs or pages 2. Colored illustrations, paper or print 3. Photographs with dark background 4. Illustrations are poor copy 5. Pages with black marks, not original copy ^ 6. 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Other University Microfilms International A real space solution to the phase problem in X-ray crystallography; ALCAMPS (Ames Laboratory Computer-aided Analysis of Multi-solution Patterson Superpositions) by James Wyman Richardson, Jr. A Dissertation Submitted to the Graduate Faculty in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY Department; Chemistry Major; Physical Chemistry Approved: Signature was redacted for privacy. or Work Signature was redacted for privacy. t the Major' De^â^ment Signature was redacted for privacy. For the Graduate College Iowa State University Ames, Iowa 1984 ii TABLE OF CONTENTS PAGE 1. INTRODUCTION 1 2. THE PHASE PROBLEM 6 2.1. Discussion of the Problem 6 2.1.1. A physical problem 6 2.1.2. A computational problem 10 2.2. Direct Methods 12 2.2.1. Solving the phase problem 12 2.2.2. Development of methods 13 2.3. Real Space Methods 18 2.3.1. Solving the phase problem 18 2.3.2. Development of methods 22 2.4. Introduction to ALCAMPS 33 3. SOLUTION OF THE HYPOTHETICAL "ELEPHANTINE" STRUCTURE 37 4. DETAILS OF THE ALCAMPS PROCEDURE 53 4.1. Input 54 4.2. HarJcer Vector Analysis 57 4.3. Elimination of Incorrect Solutions 63 4.4. Accumulation of Atom Lists 66 4.5. Calculation of Structure Factors 69 4.6. Averaging of Images 71 4.7. Distance - Angle Calculation 79 5. APPLICATION OF ALCAMPS TO THE SOLUTION OF UNKNOWN STRUCTURES 80 iii 5.1. Vector Verification Solution of W3(CCHGC(CH3)3)OJCR^(H^O)3(OGCC(CH3)3)83 5.1.1. Discussion 83 5.1.2. Evaluation 91 5.2. ALCAMPS Solution of C^H^Fe(CO)2(CS)FF^ 92 5.2.1. Discussion 92 5.2.2. Evaluation 101 5.3. ALCAMPS Solution of Fe(CO)(C^H^)Fe(CO)3 - 5.3.1. Discussion 102 5.3.2. Evaluation 114 5.4. ALCAMPS Solution of Cu( N2C3^3^Hg ( OH)2 )2^2 " 2^2° 115 5.4.1. Discussion 115 5.4.2. Evaluation 125 5.5. ALCAMPS Solution of Cd^^(SCH2CH2OH)- (ClO^i^'SHgO 126 5.5.1. Discussion 126 5.5.2. Evaluation 134 5.6. ALCAMPS Solution of (N(CH3 ) 3CH2(C^H^) ) 2M05CI^^3 136 5.5.1. Discussion 136 5.6.2. Evaluation 153 5.7. ALCAMPS Solution of ( ClHgNC5H3^2Cl > 2"^2^^5 154 5.7.1. Discussion 154 5.7.2. Evaluation 163 5.8. ALCAMPS Solution of HgAl(P04)3 164 5.8.1. Discussion 164 iv 5.8.2. Evaluation 172 5.9. Structures Solved by ÀLCAMPS 173 6. CONCLUSION 175 7. IDEAS FOR FUTURE WORK 178 8. APPENDIX A. CRYSTAL STRUCTURE DETERMINATIONS 182 8.1. Structure Determination of (CCHgC(CH3)3)OgCrg(H^O)3(OgCC(CH3 >3)12^ 183 8.1.1. Introduction 183 8.1.2. Collection and reduction of X-ray data 183 8.1.3. Solution and refinement of structure 184 8.1.4. Discussion of structure 186 8.2. Structure Determinations of Cu(N2C^^Hg(0H)2)2" Cl2*4H20 and Cu(N2C^j^Hg(0H) 2 ) 2<N03 )2* 2H2O 203 8.2.1. Introduction 203 8.2.2. Collection and reduction of X-ray data 203 8.2.3. Solution and refinement of structures 204 8.2.4. Discussion of structures 212 8.3. Structure Determination of Cd^Q( SCH2CH2OH) ( CIO4 )4 • 8H2O 220 8.3.1. Introduction 220 8.3.2. Collection and reduction of X-ray data 220 8.3.3. Solution and refinement of structure 221 8.3.4. Discussion of structure 224 8.4. Structure Determinations of (ClHgNCgHj^2^1 ^2 ~ Hg2Clg and (ClHgNCgHj^2Cl)2"^^^4^^6"6*^2° 238 8.4.1. Introduction 238 V 8.4.2. Collection and reduction of X-ray data 238 8.4.3. Solution and refinement of structures 243 8.4.4-. Discussion of structures 244 9. APPENDIX B. OTHER STRUCTURES SOLVED 260 9.1. Structures Published 261 9.2. Structures to be Published 263 10. APPENDIX C. PIKR 264 10.1. Introduction 264 10.2. Identification of Local Maxima 267 10.3. Gaussian Refinement 269 10.3.1. Introduction 269 10.3.2. Theory 269 10.3.3. Programming details 272 10.4. Half-height Refinement 273 10.4.1. Introduction 273 10.4.2. Theory 274 10.4.3. Programming details 275 10.5. Molecular Fragment Search 276 11. APPENDIX D. THE INTERACTIVE COMMAND PROCEDURE CHES.CAT 278 12. APPENDIX E. LOW TEMPERATURE APPARATUS FOR SINGLE-CRYSTAL DATA COLLECTION 282 13. LITERATURE CITED 286 14. ACKNOWLEDGEMENTS 291 1 1. INTRODUCTION In the early 19503, there was a revolution, of sorts, in the field of X-ray crystallography. Since 1934, when À.L. Patterson derived what is now known as the Patterson function, crystal structures had been solved, almost exclusively, from analysis of this function. Such structure solutions were accomplished by obtaining the atomic positions of constituent atoms from a search for characteristic interatomic vectors in the Patterson function, usually using two-dimensional projections. The revolution began, however, in 1952 with a series of elegant derivations which revealed that crystal structures could, in theory, be solved from the direct manipulation of the phases of Bragg reflections. These approaches became known as direct methods. The immediate popularity of the direct methods approach stems from its relatively low computational requirements and its capacity to solve equal atom structures which were previously somewhat difficult to handle. Since that time the solutions of a large majority of all crystal structures have been attempted first using direct methods.
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