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 3.5.2. Dictionary design considerations

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:

3.5.2. Dictionary design considerations

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The rhoCIF dictionary contains the definitions of data items used to report accurate electron densities in crystals. The structure of these definitions conforms to the CIF rules and conventions, and selected data items reflect those currently needed in the field. In any field of science, the nature of the data used to describe the experiment and the results changes with time, and accurate electron density studies are no exception. The items defined in this dictionary describe the density representation approach used most often today – the atom-centred multipole expansion model introduced by Stewart (1973[link]) and refined by Hansen & Coppens (1978[link]). In this model, the electron density is expressed as the sum of three components. Two are the partial contributions of the core and valence shell of the spherical free atom, usually taken from the paper by Clementi & Roetti (1974[link]). The third component is an aspherical multipole expansion of the remaining electron density. This is an atom-centred function, flexible enough to describe most electron density distributions likely to be encountered in a crystal, and with components that have the same symmetries as the atom-centred wave functions (orbitals) frequently used by chemists when describing chemical bonding.


Clementi, E. & Roetti, C. (1974). Roothan–Hartree–Fock atomic wavefunctions. Basis functions and their coefficients for ground and certain excited states of neutral and ionized atoms. At. Data Nucl. Data Tables, 14, 177–478.
Hansen, N. K. & Coppens, P. (1978). Testing aspherical atom refinements on small-molecule data sets. Acta Cryst. A34, 909–921.
Stewart, R. F. (1973). Electron population analysis with generalized X-ray scattering factors: higher multipoles. J. Chem. Phys. 58, 1668–1676.

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