New Techniques for Direct Methods in X-Ray Crystallography

Henderson, Allan Nisbet (1994) New Techniques for Direct Methods in X-Ray Crystallography. PhD thesis, University of Glasgow.

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Abstract

The principal aim of this thesis is the further development of the methods of solution of crystal structures using the techniques of direct methods. All the research undertaken has used either a Bayesian approach to the statistics or has used the more specific maximum entropy technique. Much of the work results in an implementation to the MITHRIL program which is then used as part of the testing strategy, and is mentioned throughout this thesis. The first chapter is an introduction to direct methods to give the reader an overview in the techniques which will be expanded upon later in the thesis. In addition to explaining the major techniques used in the field a section on the maximum entropy method is included along with a brief explanation of the function of the maximum entropy program MICE. The second chapter details the maximum entropy method and presents the results from the entropy maximisation of maps produced using phase sets generated from random starting phases by the SAYTAN program. A small protein Avian Pancreatic Polypeptide (App) was used as the test structure. No conventional figure of merit was able to discriminate between the phase sets yet by applying standard maximum entropy procedures using the MICE program and examining the log likelihood gain (LLO) the correct phase sets were identified. The third chapter details a Bayesian method of obtaining temperature factors, scale factors and estimated standard deviations on these figures for use in the normalisation of structure factors to normalised structure factors. A full derivation of the new formula using Bayesian methods and the Wilson statistics is provided along with details of the implementation into the MITHRIL90 program. A full set of test results based on selections of x-ray diffraction data for seventeen test structures is given. The results show that this is a perfectly adequate method that provides reasonable standard deviations of the normalised structure factors. The greatest advantage of this new theory is that it has the ability to be extended to use Bayesian priors to generate better normalisation equations. The fourth chapter details a likelihood based figure of merit, LOGLIK, designed to compare observed and calculated E-magnitudes for the reflections that are not involved in the direct methods phasing procedure. This gives a measure of the internal consistency of the three phase invariants used in phasing. A derivation of the formula that yields the calculated E-magnitudes is given. The results are given for twenty two test structures and correlations between LOGLIK and conventional figures of merit. The results show that while LOGLIK contains new information it has no new advantage over conventional figures of merit, and indeed can only be used for ranking phase sets into a preferred order not the determination of correctness. Also included in the thesis is an appendix that contains the manual for the use of the MITHRIL90 program, that incorporates the new normalisation method and the LOGLIK figure of merit.

Item Type: Thesis (PhD)
Qualification Level: Doctoral
Additional Information: Adviser: Chris Gilmore
Keywords: Physical chemistry, Computational chemistry
Date of Award: 1994
Depositing User: Enlighten Team
Unique ID: glathesis:1994-75825
Copyright: Copyright of this thesis is held by the author.
Date Deposited: 19 Dec 2019 09:15
Last Modified: 19 Dec 2019 09:15
URI: http://theses.gla.ac.uk/id/eprint/75825

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