Chapter 16.1 Ab initio phasing

Crystallography of biological macromolecules

First Online Edition (2006)

Part 16. Direct methods

  1. G. M. Sheldrick3,
  2. H. A. Hauptman2,
  3. C. M. Weeks2,
  4. R. Miller2,
  5. I. Usón1

Published Online: 1 JAN 2006

DOI: 10.1107/97809553602060000689

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Sheldrick, G. M., Hauptman, H. A., Weeks, C. M., Miller, R. and Usón, I. 2006. Ab initio phasing. International Tables for Crystallography. F:16:16.1:333–345.

Author Information

  1. 1

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

  2. 2

    Hauptman–Woodward Medical Research Institute, Inc., 73 High Street, Buffalo, NY 14203-1196, USA

  3. 3

    Institut für Anorganisch Chemie, Universität Göttingen, Tammannstrasse 4, D-37077 Göttingen, Germany

Publication History

  1. Published Online: 1 JAN 2006


The background and use of dual-space direct methods (also known as Shake-and-Bake) for the ab initio phasing of small proteins as well as the phasing of heavy-atom substructures of large proteins is described. Basic concepts include normalized structure factors, multisolution procedures, random trial structures, phase-refinement formulas, peak-picking techniques, alternation of phase improvement in reciprocal and real space, and recognizing solutions. Two independent computer programs which implement the Shake-and-Bake algorithm, SnB and SHELXD, are compared and typical parameters are given. Other topics discussed are the use of Patterson information to get better starting phases, avoiding false minima, the effects of data resolution and completeness, special features of space group P1, and refinement strategies.


  • 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’