Tables for
Volume G
Definition and exchange of crystallographic data
Edited by S. R. Hall and B. McMahon

International Tables for Crystallography (2006). Vol. G, ch. 3.5, p. 141

Section 3.5.1. Introduction

P. R. Mallinsona* and I. D. Brownb

aDepartment of Chemistry, University of Glasgow, Glasgow G12 8QQ, Scotland, and bBrockhouse Institute for Materials Research, McMaster University, Hamilton, Ontario, Canada L8S 4M1
Correspondence e-mail:

3.5.1. Introduction

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Modern high-resolution X-ray diffraction methods enable the electron density distributions in many crystals to be accurately determined, allowing one to explore the interactions that hold crystals and molecules together (Coppens, 1997[link]; Koritsanszky & Coppens, 2001[link]). For example, Bader's (1990[link]) theory of atoms in molecules gives a description of chemical bonding in terms of the topology of the electron density, but it requires an accurate knowledge of the electron density. [Note that the terms `electron density' (or distribution) and `charge density' tend to be used interchangeably in the literature. The term `electron density' is used here since `charge density' strictly includes both positive (nuclear) and negative (electronic) charge. Properties such as electrostatic potential, electric fields and their gradients, and molecular electric moments are derived from the charge density distribution, which includes the contribution of the nuclear charge (Spackman & Brown, 1994[link]).] The advent of area detectors, more powerful laboratory computing facilities and developments in software have combined to produce a rapid increase in the number of accurate electron density determinations now available. While such studies are not yet routine, they are sufficiently common to justify defining a structure for a secure and systematic archive. This in turn requires a method of representing the electron density acceptable to the crystallographic community.

The CIF standard which has been adopted by the IUCr and is in common use in macromolecular and small-molecule crystallography is the obvious choice for such a file structure. At the Sagamore XIII conference held at Stare Jablonki, Poland, in 2000, the IUCr Commission on Charge, Spin and Momentum Densities decided to prepare a CIF dictionary for reporting electron densities in crystals. The result is the rhoCIF dictionary described in this chapter. It was prepared in conjunction with members of the Commission and other members of the community. [The name rhoCIF for this dictionary was chosen over the more obvious choice of edCIF to avoid any possible confusion with electron diffraction. The symbol [\rho({\bf r})] conventionally represents the electron density in real space at the point defined by the position vector r.]

The distribution of electron density in a molecule or crystal can also be calculated theoretically, and the results are usually compared with experiment. The Hohenberg–Kohn theorem (Hohenberg & Kohn, 1964[link]) shows that the ground-state energy is a unique functional of the electron density, thus providing a theoretical justification for relating chemical and physical properties directly to the observable electron density. Density functional theory has been applied to chemical problems for some time (see, for example, Labanowski & Andzelm, 1991[link]; Ziegler, 1991[link]; Kohn et al., 1996[link]; Nagy, 1998[link]). Although the current version of the rhoCIF dictionary is intended to record the results of experimental measurements, it can also be used to represent a theoretical electron density that has been fitted with an appropriate model.


Bader, R. F. W. (1990). Atoms in molecules: a quantum theory. Oxford University Press.
Coppens, P. (1997). X-ray charge densities and chemical bonding. Oxford University Press.
Hohenberg, P. & Kohn, W. (1964). Inhomogeneous electron gas. Phys. Rev. (Second Series), 136, B864–B871.
Kohn, W., Becke, A. D. & Parr, R. G. (1996). Density functional theory of electronic structure. J. Phys. Chem. 100, 12974–12980.
Koritsanszky, T. S. & Coppens, P. (2001). Chemical applications of X-ray charge density analysis. Chem. Rev. 101, 1583–1627.
Labanowski, J. K. & Andzelm, J. W. (1991). Density-functional methods in chemistry. New York: Springer-Verlag.
Nagy, A. (1998). Density functional. Theory and application to atoms and molecules. Phys. Rep. 298, 2–79.
Spackman, M. A. & Brown, A. S. (1994). Charge densities from X-ray diffraction data. R. Soc. Chem. Ann. Rep. Sect. C, pp. 175–212.
Ziegler, T. (1991). Approximate density functional theory as a practical tool in molecular energetics and dynamics. Chem. Rev. 91, 651–667.

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