Chapter 18.1 Introduction to refinement

Crystallography of biological macromolecules

Second Online Edition (2012)

Part 18. Refinement

  1. L. F. Ten Eyck1,
  2. K. D. Watenpaugh2

Published Online: 14 APR 2012

DOI: 10.1107/97809553602060000855

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Ten Eyck, L. F. and Watenpaugh, K. D. 2012. Introduction to refinement. International Tables for Crystallography. F:18:18.1:459–465.

Author Information

  1. 1

    San Diego Supercomputer Center 0505, University of California at San Diego, 9500 Gilman Drive, La Jolla, CA 92093–0505, USA

  2. 2

    Structural, Analytical and Medicinal Chemistry, Pharmacia & Upjohn, Inc., Kalamazoo, MI 49001–0119, USA

Publication History

  1. Published Online: 14 APR 2012



This chapter provides an introduction to refinement and concentrates on the special features of macromolecular crystallography. Topics covered include: least squares and maximum likelihood; optimization methods; resolution, accuracy, completeness and weighting of data; optimization methods; and models and model evaluation.


  • R factors;
  • Rfree;
  • data completeness;
  • data resolution;
  • least‐squares methods;
  • maximum likelihood;
  • model evaluation;
  • optimization methods;
  • refinement;
  • singularity in refinement;
  • weighting