Chapter 13.2 Rotation functions

Crystallography of biological macromolecules

Second Online Edition (2012)

Part 13. Molecular replacement

  1. J. Navaza

Published Online: 14 APR 2012

DOI: 10.1107/97809553602060000840

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Navaza, J. 2012. Rotation functions. International Tables for Crystallography. F:13:13.2:340–346.

Author Information

  1. Laboratoire de Génétique des Virus, CNRS‐GIF, 1. Avenue de la Terrasse, 91198 Gif‐sur‐Yvette, France

Publication History

  1. Published Online: 14 APR 2012



The mathematical procedures required to find the relative orientations of the independent but homologous molecules within a crystal, or their absolute orientations if the structure of a similar molecule is known, are discussed in detail. They correspond to the rotational search employed in the molecular‐replacement method.


  • Bessel functions;
  • Dℓm,m′ matrices;
  • Euler parameterization;
  • locked rotation function;
  • molecular replacement;
  • rotation functions;
  • rotation group;
  • rotations in three‐dimensional Euclidean space;
  • spherical Bessel functions;
  • spherical harmonics