International Tables for Crystallography

Ab initio phasing
G. M. Sheldrick, C. J. Gilmore, H. A. Hauptman, C. M. Weeks, R. Miller and I. Usón. International Tables for Crystallography (2012). Vol. F, ch. 16.1, pp. 413-432  [ doi:10.1107/97809553602060000850 ]


The background and use of dual-space direct methods for the ab initio phasing of small macromolecules as well as the phasing of heavy-atom substructures of larger biological structures are described. Basic concepts include normalized structure factors, multisolution procedures, random trial structures, phase-refinement formulas, peak-picking techniques, density modification including charge flipping, and recognizing solutions. Other topics discussed are the use of Patterson information to get better starting phases, avoiding false minima, the effects of data resolution, data quality and completeness, special features of space group P1, refinement strategies, and future possibilities. Several independent computer programs that implement these concepts are then briefly described.

Access, prices and ordering

International Tables for Crystallography is available online as a full set of volumes through Wiley.


If you have already registered and are using a computer listed in your registration details, please email for assistance.

About International Tables for Crystallography

International Tables for Crystallography is the definitive resource and reference work for crystallography. The series consists of nine volumes and comprises articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the structure and properties of materials.