Chapter 8.3 Constraints and restraints in refinement

Mathematical, physical and chemical tables

First Online Edition (2006)

Part 8. Refinement of structural parameters

  1. E. Prince1,
  2. L. W. Finger2,
  3. J. H. Konnert3

Published Online: 1 JAN 2006

DOI: 10.1107/97809553602060000611

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Prince, E., Finger, L. W. and Konnert, J. H. 2006. Constraints and restraints in refinement. International Tables for Crystallography. C:8:8.3:694–701.

Author Information

  1. 1

    NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA

  2. 2

    Geophysical Laboratory, Carnegie Institution of Washington, 5251 Broad Branch Road NW, Washington, DC 20015-1305, USA

  3. 3

    Laboratory for the Structure of Matter, Code 6030, Naval Research Laboratory, Washington, DC 20375-5000, USA

Publication History

  1. Published Online: 1 JAN 2006


In crystallographic refinement a great deal is known about a crystal before any diffraction data are collected. Chapter 8.3 discusses ways to make use of this prior knowledge by applying constraints and restraints to the model. The most obvious constraints, which may be applied either by using Lagrange undetermined multipliers or by reducing the number of variable parameters in the model, are those imposed by space-group symmetry on unit-cell constants, atom positions, and atom-displacement parameters. They may also include site occupancies, molecular shapes, noncrystallographic symmetry, and rigid-body thermal motion. Restraints may be applied when bond distances, bond angles, and relations among motion parameters are not known precisely in advance, but must lie within narrow ranges. The chapter includes a table of typical values of bond distances and angles found in the amino-acid residues in polypeptides and proteins.


  • constrained models;
  • constraints in refinement;
  • Lagrange undetermined multipliers;
  • restraints in refinement;
  • stereochemical constraints