Tables for
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C, ch. 8.7, p. 713

Section 8.7.1. Outline of this chapter

P. Coppens,a Z. Sub and P. J. Beckerc

a732 NSM Building, Department of Chemistry, State University of New York at Buffalo, Buffalo, NY 14260-3000, USA,bDigital Equipment Co., 129 Parker Street, PKO1/C22, Maynard, MA 01754-2122, USA, and cEcole Centrale Paris, Centre de Recherche, Grand Voie des Vignes, F-92295 Châtenay Malabry CEDEX, France

8.7.1. Outline of this chapter

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Knowledge of the electron distribution is crucial for our understanding of chemical and physical phenomena. It has been assumed in many calculations (e.g. Thomas, 1926[link]; Fermi, 1928[link]; and others), and formally proven for non-degenerate systems (Hohenberg & Kohn, 1964[link]) that the electronic energy is a functional of the electron density. Thus, the experimental measurement of electron densities is important for our understanding of the properties of atoms, molecules and solids. One of the main methods to achieve this goal is the use of scattering techniques, including elastic X-ray scattering, Compton scattering of X-rays, magnetic scattering of neutrons and X-rays, and electron diffraction.

Meaningful information can only be obtained with data of the utmost accuracy, which excludes most routinely collected crystallographic data sets. The present chapter will review the basic concepts and expressions used in the interpretation of accurate data in terms of the charge and spin distributions of the electrons. The structure-factor formalism has been treated in Chapter 1.2[link] of Volume B (IT B, 2001[link]).


Fermi, E. (1928). Eine statitische Methode zur Bestimmung einiger Eigenschaften des Atoms und ihre Anwendung auf die Theorie des periodischen Systems der Elemente. Z. Phys. 48, 73–79.
Hohenberg, P. & Kohn, W. (1964). Inhomogeneous electron gas. Phys. Rev. B, 136, 864–867.
International Tables for Crystallography (2001). Vol. B, edited by U. Shmueli. Dordrecht: Kluwer Academic Publishers.
Thomas, L. H. (1926). Proc. Cambridge Philos. Soc. 23, 542–548.

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