Chapter 16.1 Ab initio phasing

Crystallography of biological macromolecules

Second Online Edition (2012)

Part 16. Direct methods

  1. G. M. Sheldrick1,
  2. C. J. Gilmore2,
  3. H. A. Hauptman3,
  4. C. M. Weeks3,
  5. R. Miller3,
  6. I. Usón4

Published Online: 14 APR 2012

DOI: 10.1107/97809553602060000850

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Sheldrick, G. M., Gilmore, C. J., Hauptman, H. A., Weeks, C. M., Miller, R. and Usón, I. 2012. Ab initio phasing. International Tables for Crystallography. F:16:16.1:413–432.

Author Information

  1. 1

    Lehrstuhl für Strukturchemie, Georg-August-Universität Göttingen, Tammannstrasse 4, D-37077 Göttingen, Germany

  2. 2

    Department of Chemistry, University of Glasgow, Glasgow G12 8QQ, UK

  3. 3

    Hauptman–Woodward Medical Research Institute, Inc., 700 Ellicott Street, Buffalo, NY 14203–1102, USA

  4. 4

    Institució Catalana de Recerca i Estudis Avançats at IBMB-CSIC, Barcelona Science Park. Baldiri Reixach 15, 08028 Barcelona, Spain

Publication History

  1. Published Online: 14 APR 2012


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.


  • Fourier refinement;
  • Patterson functions;
  • ab initio phasing;
  • anomalous scattering;
  • ‘baking’;
  • computer programs;
  • constraints;
  • data completeness;
  • data resolution;
  • direct methods;
  • false minima;
  • isomorphous replacement;
  • minimal function;
  • multiple-beam diffraction and direct methods;
  • normalized structure factors;
  • parameter-shift method;
  • peak picking;
  • peaklist optimization;
  • phase expansion in reciprocal space;
  • phase refinement;
  • phasing;
  • random omit maps;
  • real-space constraints;
  • ‘shaking’;
  • structure factors;
  • structure invariants;
  • tangent formula;
  • ‘twice baking’