Phasing in Crystallography

Carmelo Giacovazzo, Professor of Crystallography, Bari University. Director of CNR - IC Institute from 1992 to 2008. President of the European Crystallographic Association from 1997 to 2000. Winner of the European Prize Italgas 1996 for Scientific Research and Innovation; European Crystallographic Association Prize 2003. Editor of the international reviews: Zeitschrift fur Kristallographie and Croatica Chemica Acta. Scientific research: about 300 scientific papers on phasing methods, oriented both to small and to macromolecules. Some of his contributions were quoted in the Nobel Lecture by Herbert Hauptman (1985) as relevant for the solution of the phase problem for small molecules.His theoretical developments allowed to extend to about 2Å the limit of the ab initio crystal structure solution of proteins, and allowed a powerful combination of traditional molecular replacement, isomorphous replacement and anomalous dispersion techniques with suitably designed probabilistic approaches.

• 1. Fundamentals of crystallography ; 2. Wilson statistics ; 3. The origin problem, invariants and seminvariants ; 4. The method of joint probability distribution functions, neighborhoods and representations ; 5. The probabilistic estimation of triplet and quartet invariants ; 6. Traditional direct phasing procedures ; 7. Joint probability distribution functions when a model is available: the Fourier syntheses ; 8. Phase improvement and extension ; 9. Charge flipping and VLD (Vive la difference) ; 10. Patterson methods and direct space properties ; 11. Phasing via electron and neutron diffraction data ; 12. Phasing methods for powder data ; 13. Molecular replacement ; 14. Isomorphous replacement techniques ; 15. Anomalous dispersion techniques ; Mathematical Appendices

This textbook is recommended to those interested in direct methods of solving the "Phase Problem" in order to find the three-dimensional arrangement of atoms within a crystal by use of data from its X-ray diffraction pattern. It explains how best to assess the relative phase of each diffracted beam essential input for the calculation of an electron-density map of a crystal and how to do it correctly and efficiently. Methods used for macromolecules are also discussed. The book contains many excellent well thought-out illustrations and the mathematical equations are also clearly explained in the text.