New Approaches to Direct Methods in X-Ray Crystallography

[摘要] This thesis is concerned with the use of direct methods to solve crystal structures from X-ray data. Particular interest is centred upon why certain structures should be difficult to determine and what steps can be taken to remove or overcome such problems. Throughout the thesis use is made of the direct methods computer program MITHRIL. Many of the new techniques discussed in this thesis have now been incorporated into the program. The first chapter contains an introduction to direct methods - it lays the groundwork for the techniques used elsewhere in the thesis. As well as explaining the theory of direct methods the chapter also includes a discussion of why direct methods fail in certain cases. Direct methods are based on a few simple phase relationships. From the point of view of solving the phase problem it is obviously vital that these relationships are accurate. Chapter 2 is concerned with making phase relationships more reliable. The chapter is in two parts: the first part deals with schemes based on the (sin2theta/lambda2) values of reflections participating in phase relationships while the second part investigates quartet reliability in relation to the frequency of three new cross terms. Although the (sin2theta/lambda2) based schemes are very simple they are shown to be highly effective and extremely useful. Rather disappointingly no link could be established between quartet reliability and the occurrence of the new cross terms. Chapter 3 discusses the implementation of a symbolic addition module, LSAM, into the MITHRIL system. In its original form LSAM was among the first complete systems of computer programs devised for the automatic solution of crystal structures. MITHRIL now contains a substantially upgraded form of LSAM, however, the method remains essentially unaltered. A drawback of LSAM is that it deals only with centrosymmetric structures but, even so, it still provides an alternative to the multisolution method already present in MITHRIL. It is shown that the introduction of LSAM has been very successful and, in particular, that it is often highly advantageous to use symbolic addition when dealing with heavy atom structures. The results and conclusions of using MITHRIL to attempt to solve all twenty five structures on the database of structures resistant to direct methods compiled by Sheldrick are given in Chapter 4. Detailed accounts of the strategies and tactics employed on each structure are given and the results are summarised in tabular form. Conclusions are drawn on the substituent parts of MITHRIL that performed well and those that did not. MITHRIL has already been improved in the light of the experience gained in this chapter and two new options, REVIEW and MISS have been added to the program. REVIEW is a module which enables the best phase sets produced by the program to be identified more readily. The MISS command, located in the normalisation module, adds missing weak reflections to incomplete data sets and assigns structure factors to them in accordance with their (sintheta/lambda) values. In addition, advice is provided on what steps to take when confronted with a difficult structure. The final step in a direct methods analysis is the calculation and interpretation of an E-map. When dealing with difficult structures the E-maps are often complex and difficult to interpret. Chapter 5 is concerned with the use of colour computer graphics routines to aid the interpretation. Two separate modules, MITHGRAPH and CONTOUR, have been written for use in conjunction with MITHRIL. MITHGRAPH performs a series of display and edit routines as well as allowing the user to manipulate molecular fragments in various ways. As the name suggests, CONTOUR, displays contoured sections of an E-map or weighted Fourier map so allowing direct observation of the three dimensional map. It is shown how the contouring routine was of great value in the determination of two of the difficult structures from the database mentioned above. The final chapter also discusses SUBMIT, a program which runs on a colour graphics workstation - it incorporates both MITHGRAPH and CONTOUR modules. SUBMIT can perform Fourier recycling of known fragments, E-map and weighted Fourier map calculations as well as allowing direct observation of previously stored E-maps. Instructions for using MITHGRAPH, CONTOUR and SUBMIT are included in the chapter.

[发布机构] University:University of Glasgow

[关键词] Analytical chemistry