New Techniques for Direct Methods in X-ray Crystallography

[摘要] The research presented in this thesis involves the development of both new and existing techniques in direct methods. All of the techniques investigated were integrated into a test version of the direct methods program MITHRIL94 and then tested on structures that are known to be difficult to solve. For every technique the results produced were compared to those obtained from the previous version of MITHRIL94. Chapter 1 is an introduction to direct methods - the underlying principles of the method and a comprehensive summary of the techniques employed, some of which are discussed and expanded in later chapters. This chapter also contains a section on the limitations of direct methods and a flowchart of the modules which are present in the MITHRIL94 version of the program. The reliability of the phase relationships used in direct methods is an essential step in obtaining the correct structure solution. Chapter 2 discusses the measure of reliability of the triplets (K) and quartets (Keq) that exist in MITHRIL94. Since the use of Keq is relatively slow, this chapter investigates other methods of measuring the reliability of the quartets that are quicker but still produce an accurate measure. The two methods investigated were derived from the variable B, used in the conditional probability equation P1/7. These two methods, B1 and B2, differed in their treatment of the cross terms. Comparison of these methods with Keq was achieved by plotting the average phase error against increasing reliability for each of Keq, B1 and B2, with K also being plotted as a standard. To test the methods fully, negative and positive quartets were treated separately. This chapter provides details of the implementation of these methods into a test version of MITHRIL94 and presents the results for some of the structures tested. The results showed that all three methods provided an accurate measure of reliability, and since the use of B1 increased the speed of the program by an approximate factor of 10 it was used to measure the reliability of the negative quartets in subsequent investigations. The third chapter details the principles of optimisation techniques, namely that of simulated annealing and discusses how this technique is applied to crystallography in the form of phase annealing. This chapter includes a detailed account of the implementation of phase annealing into MITHRIL94. Centric and acentric phases are treated differently during phase annealing and flowcharts for these processes are provided. The phase annealing algorithm was integrated into three of the tangent refinement modules in MITHRIL94 - FASTAN and SWTR, the principles of which are discussed in chapter one, and X-Y which is discussed in this chapter. The phase annealing code was tested on structures from the Sheldrick database of difficult structures. The results for each tangent refinement module employing phase annealing are displayed in separate tables. These show that phase annealing in MITHRIL94 was a definite success for FASTAN and SWTR, especially SWTR where phase annealing produced a dramatic improvement in results compared to the original module. Phase permutation involves the assignment of values to the phases in the starting set of reflections. Various methods of phase permutation exist including those of magic integer and random phasing, both of which are discussed in chapter 1. Chapter 4 discusses the use of error correcting codes as a phase permutation technique. The first pai t of this chapter details the background theory of error correcting codes, discussing their relevance to experimental design and the properties required of the error correcting codes for efficient phase permutation. Two error correcting codes were investigated - the Hadamard code and the binary [24,12,8] Golay code. Detailed descriptions of how they were used to permute phases is provided. The error correcting codes were incorporated into a trial version of MITHRIL94 and used with the FASTAN and SWTR tangent refinement modules. The results for each code, employed with each module, are displayed. Again the results are provided from tests on the Sheldrick database of difficult structures and are compared with the results produced using a previous version of MITHRIL94. The results show that the Golay and Hadamard error correcting codes are capable of producing structure solutions and are therefore viable phase permutation techniques. Since the results gained from error correcting codes and phase annealing were successful the next obvious step was to combine these two techniques. Chapter 5 discusses how these techniques were combined.

[发布机构] University:University of Glasgow

[关键词] Computational chemistry, Analytical chemistry