Phasing in crystallography : a modern perspective / Carmelo Giacovazzo.

Includes bibliographical references.

Print version record.

Cover; Acknowledgements; Preface; Contents; Symbols and notation; 1 Fundamentals of crystallography; 1.1 Introduction; 1.2 Crystals and crystallographic symmetry in direct space; 1.3 The reciprocal space; 1.4 The structure factor; 1.5 Symmetry in reciprocal space; 1.5.1 Friedel law; 1.5.2 Effects of symmetry operators in reciprocal space; 1.5.3 Determination of reflections with restricted phase values; 1.5.4 Systematic absences; 1.6 The basic postulate of structural crystallography; 1.7 The legacy of crystallography; 2 Wilson statistics; 2.1 Introduction.

2.B.1 The algebraic form of the structure factor2.B.2 Structure factor statistics for centric and acentric space groups; APPENDIX 2.C THE DEBYE FORMULA; 3 The origin problem, invariants, and seminvariants; 3.1 Introduction; 3.2 Origin, phases, and symmetry operators; 3.3 The concept of structure invariant; 3.4 Allowed or permissible origins in primitive space groups; 3.5 The concept of structure seminvariant; 3.6 Allowed or permissible origins in centred cells; 3.7 Origin definition by phase assignment.

4 The method of joint probability distribution functions, neighbourhoods, and representations4.1 Introduction; 4.2 Neighbourhoods and representations; 4.3 Representations of structure seminvariants; 4.4 Representation theory for structure invariants extended to isomorphous data; APPENDIX 4.A THE METHOD OF STRUCTURE FACTOR JOINT PROBABILITY DISTRIBUTION FUNCTIONS; 4.A.1 Introduction; 4.A.2 Multivariate distributions in centrosymmetric structures: the case of independent random variables.

4.A.3 Multivariate distributions in non-centrosymmetric structures: the case of independent random variables4.A.4 Simplified joint probability density functions in the absence of prior information; 4.A.5 The joint probability density function when some prior information is available; 4.A.6 The calculation of P(E) in the absence of prior information; 5 The probabilistic estimation of triplet and quartet invariants; 5.1 Introduction; 5.2 Estimation of the triplet structure invariant via its first representation: the P1 and the P.

Modern crystallographic methods originate from the synergy of two main research streams, the small-molecule and the macro-molecular streams. The first stream was able to definitively solve the phase problem for molecules up to 200 atoms in the asymmetric unit. The achievements obtained by the macromolecular stream are also impressive. A huge number of protein structures have been deposited in the Protein Data Bank. The solution of them is no longer reserved to an elite group ofscientists, but may be attained in a large number of laboratories around the world, even by young scientists. New prob.

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