Chapter 8.7 Analysis of charge and spin densities

Mathematical, physical and chemical tables

First Online Edition (2006)

Part 8. Refinement of structural parameters

  1. P. Coppens1,
  2. Z. Su2,
  3. P. J. Becker3

Published Online: 1 JAN 2006

DOI: 10.1107/97809553602060000615

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Coppens, P., Su, Z. and Becker, P. J. 2006. Analysis of charge and spin densities. International Tables for Crystallography. C:8:8.7:713–734.

Author Information

  1. 1

    732 NSM Building, Department of Chemistry, State University of New York at Buffalo, Buffalo, NY 14260‐3000, USA

  2. 2

    Digital Equipment Co., 129 Parker Street, PKO1/C22, Maynard, MA 01754‐2122, USA

  3. 3

    Ecole Centrale Paris, Centre de Recherche, Grand Voie des Vignes, F‐92295 Châtenay Malabry CEDEX, France

Publication History

  1. Published Online: 1 JAN 2006



This chapter describes the interaction of X‐rays, unpolarized and polarized neutrons with the charge and spin densities of a periodic system. The methods developed for analysis of the electron densities from the diffraction intensities are described in detail and the concepts used in the interpretation of the results are defined.


  • n‐particle wavefunction;
  • approximations;
  • atom‐centred expansion;
  • charge densities;
  • crystal‐field approximation;
  • cusp constraint;
  • dipolar approximation;
  • elastic scattering;
  • electron density;
  • electroneutrality constraint;
  • electrostatic moments;
  • electrostatic potential;
  • external vibrations;
  • extinction;
  • Hellmann–Feynman constraint;
  • magnetic scattering;
  • magnetic structure factors;
  • moments of a charge distribution;
  • multipole expansions;
  • neutron scattering;
  • physical constraints;
  • polarized neutron scattering;
  • pseudo‐atom moments;
  • radial constraint;
  • scattering;
  • spin density;
  • structure factors;
  • thermal smearing;
  • X‐ray scattering