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Direct Phasing in Crystallography
Fundamentals and Applications

Carmelo Giacovazzo

Price: £139.00 (hardback)
ISBN-13: 978-0-19-850072-8
Publication date: 26 November 1998
792 pages, 234 figures, 246x189 mm
 Series: International Union of Crystallography Monographs on Crystallography number 8
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Reviews
  • '' This book offers both a comprehensive description of the field and a invaluable reference tool and so will appeal to a wide variety of scientists from undergraduate physics, chemistry, biochemistry and minerology students to the professional crystallographer' Zeitschrift fur Kristallographie' -
  • '' an immense work of scholarship...There is very little of the subject that has been missed and not scrutinized' Acta Crystallographica' -

Description
  • A useful reference text for the daily work of professional crystallographers
  • A multipurpose introduction to the topic for people interested in fundamental crystallography
  • Contains a wide source of references for further reading
  • An accessible text for teaching the basics of direct methods
  • A source of suggestions for future research work
Direct methods are, at present, applied to a large variety of cases: X-ray, neutron or electron data; single crystal and powder data; small molecules and macromolecules. While direct methods solved in practice the phase problem for small molecules, their application to macromolecules is recent and still undergoing strong development. The fundamentals of the methods are described: in particular it is shown how the methods can be optimized for powder, neutron or electron data, and how they can be integrated with isomorphous replacement, molecular replacement and anomalous dispersion techniques. Maximum Entropy methods are also described and discussed. Sets of test structures are used to verify, throughout the various chapters, the mathematical techniques there described and to provide practical examples of applications. This book will appeal to a wide variety of readers - offering both a comprehensive description of direct methods in crystallography and an invaluable reference tool. The first three chapters can be considered as an introduction to the field, with sufficient material to constitute a university course and for allowing the expert use of most direct methods programs. Subsequent chapters are aimed at graduate students and working crystallographers. Basic results are described and discussed in the main body of the text, while the appendices compliment these with in depth mathematical details. The quoted literature is extremely wide and the interested reader can find suggestions for future work and further reading throughout the book.

Readership: Professional crystallographers in academia, research and industry. Upper level undergraduates and postgraduates in chemistry, physics, biochemistry and mineralogy will also find this book useful.

Contents
1. Wilson statistics
1.A. About pseudosymmetries
1.B. Fourier series of representation
1.C. A modified Wilson plot procedure
2. Structure invariants and semi-invariants and the origin problem
3. Triplet invariant estimation and classical direct phasing procedures
3.A. Other multi-solution methods
4. Direct methods and real space properties
4.A. Direct methods and Patterson map properties: additional approaches
4.B. Estimating structures semi-invariants from Harker sections
4.C. Patterson deconvolution methods
5. The method of joint probability distributions
5.A. P(E) and the saddle point method
6. Representations of structure invariants and semi-invariants
6.A. Two algebraic propositions
7. The probabilistic estimation of triplet invariants
7.A. The probabilistic estimation of quartet invariants
8.A. Mathematical derivation of the phase relationship
8.B. Mathematical derivation of the sign relationship
8.C. Special quartets
9. The probabilistic estimation of quintet invariants
10. The probabilistic estimation of 1- and 2- phase structure semi-invariants
10.A. Some mathematical details about the (1 estimates
11. Probabilistic determinantal approaches
12. Phasing neutron and electron data
12.A. About the elastic scattering of electrons: the kinematical approximation
12.B. About HREM image formation
13. Direct phasing from powder data
14. Macromolecular crystallography techniques and traditional direct methods
14.A. Crick and Magdoff relation
14.B. Protein phase estimate incorporating the treatment of errors
14.C. Solvent flattening
14.D. About Fourier synthesis of large use in macromolecular crystallography
14.E. Solvent content according to Matthews
14.F. Ab initio calculation of low-resolution envelopes
15. The integration of direct methods with isomorphous replacement techniques
15.A. Karle's Algebraic rule Riso
15.B. About local scaling
16. The integration of direct methods with anomalous dispersion techniques
16.A. Probabilistic treatment of the errors in the SIRAS case
16.B. Coefficients in the distribution
16.C. The maximal SAS principle
17. Molecular replacement techniques and direct methods

Authors, editors, and contributors


Carmelo Giacovazzo, Professor of Crystallography, University of Bari


Links to web resources and related information
More in the same subject area:
Geochemistry
Crystallography
Physics

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