A Computer Program Package for Multipole Refinement and Analysis of Electron Densities from Diffraction Data

This work was initially undertaken as a project of the IUCr Commission on Charge, Spin and Momentum Densities . The programming group consists of:

T. Koritsanszky

University of the Witwatersrand, Johannesburg
Email: tibor@hobbes.gh.wits.ac.za

S. Howard

University of Wales Cardiff
Email: howardst@cardiff.ac.uk

P. R. Mallinson

University of Glasgow
Email: paul@chem.gla.ac.uk

Z. Su

State University of New York at Buffalo
Email: che9985@ubvms.cc.buffalo.edu

T. Richter

Freie Universitat Berlin
Email: richter@chemie.fu-berlin.de

N. K. Hansen

Universite Henri Poincare, Nancy I
Email: hansen@lmcpi.u-nancy.fr

Presently the following programs are in the package:

XDLSM

Least-squares refinement of structure parameters, multipole populations, and expansion-contraction parameters from X-ray and/or neutron diffraction data.

XDPROP

Calculation and mapping of electrostatic properties from a multipole model. Critical point location in total density or Laplacian distribution; bond path calculation.

XDFOUR

General Fourier synthesis program for computing density distributions from structure factors.

XDGRAPH

Drawing two and three-dimensional graphics, e.g. contour maps, relief maps, bond paths, isosurfaces, from the output of XDPROP and XDFOUR.

XDGEOM

Molecular geometry calculation from structural parameters. Publication tabulation of structural and thermal displacement parameters, geometry, and multipole population coefficients.

XDINI

Initialisation of XD files from crystallographic information files (CIFs), other systems and crystal structure packages.

Current and planned developments

1. Compatibility of MORPHY and XD. This will add new features to XD, such as automatic CP search in the whole unit cell, gradient path mapping, integration over zero flux surfaces.
2. Making XDLSM applicable for larger systems by introducing FFT in building the lsq matrix.
3. Making available a databank file containing easy-to-use information on intramolecular displacement amplitudes.
4. Extension to heavier atoms using relativistic scattering factors.
5. XDVIB (the program for analysing adps) and XDSTAT (the statistical program).
6. Inclusion of charge density parameters in the Crystallographic Information File (CIF) data definitions.
Click here to download January 2001 updates for XD installation.

Acknowledgements

The work is made possible through the financial support of the following institutions:

The University of Glasgow under its New Initiatives Scheme.

The International Union of Crystallography.

The package is available by subscription of US$1000 (for academic users). Information on obtaining the package is available from Tibor Koritsanszky.

Links to other relevant pages

International Union of Crystallography

TOPXD program for topological analysis of experimental static electron density based on the Hansen-Coppens multipole formalism, by Anatoliy Volkov and Carlo Gatti.

Computing School on Practical Aspects of Charge Density Determination

Overview of charge density distributions

Chemical crystallography and quantum chemistry encompass our knowledge about the detailed structure of molecules, their properties and reactions, and the distribution of electronic charge in their atoms and chemical bonds. On this insight are based all modern theories of chemical reactivity, and the design principles for new materials and drugs. Great advances in the last two decades have led to the present theoretical and experimental methods for determining molecular structure at the electronic level; we can in principle (and increasingly in practice) obtain not just the positions of atoms in molecules but all other topological properties of the associated electron distribution.

A beam of X-rays is diffracted by the electrons in a crystalline material, just as visible light is diffracted by larger objects. Recombination of diffracted light by means of lenses can give a magnified image of the object; X-rays, having a wavelength about four orders of magnitude shorter than that of visible light, produce an image of the electron or charge density distribution characteristic of the diffracting crystal. There exist no lenses as such for X-rays, but recombination of diffracted rays into an image can be brought about by suitable detection followed by computational Fourier transformation. The experiment is effectively an X-ray microscope for the disposition of electronic charge.

In practice we can bypass the Fourier transformation, because quantum mechanics enables us to construct a mathematical model of the charge density in a crystal. The parameters of such a model can be adjusted to reproduce the experimentally-measured pattern of diffracted X-rays, given prior knowledge of the arrangement of atomic nuclei in the crystal lattice. For chemical (as distinct from biological) molecules this can usually be found routinely using the methods of conventional crystal structure analysis programmed in widely available computer packages. This leads to a ``ball and stick'' model of the atoms and bonds representing the topology of the charge density at the level of its most salient features, found at the positions of the atomic nuclei. It is obtained by Fourier transformation of the diffracted X-ray pattern at relatively low resolution. Next we can proceed with a far more elaborate, so-called ``multipole'' model of the crystalline density, fitting it to a diffraction experiment carried out at high resolution, such that two points as close together as 0.4 x 10^{-10} m can be distinguished. As mentioned earlier, we need no Fourier transformation at this stage because the charge density in fine detail can be computed directly from the fitted multipole model. One major component of the XD package is the program for least squares fitting of a multipole model to the experimental data.

Once a charge distribution has been obtained experimentally, various chemical and physical properties that depend on the distribution can be derived. The chemical structure of molecules can be extracted from an analysis of the topology of the charge distribution, the features of which are summarized by the curvatures of the charge density at its critical points. Each feature, maximum, minimum or saddle has associated with it a point in space called a critical point, where the density is flat. One type of critical point has all three curvatures in 3-D space negative; it is found at the sites of atomic nuclei. Other types, with both positive and negative curvatures, are associated with bonding interactions between atoms. Because the strength and nature of the interactions are characterized by topology, the chemistry of the molecule can be recovered as a property of its charge distribution. A program for deriving molecular properties from the multipole model of the charge distribution is thus another major component of XD. Many of these properties can be displayed pictorially, using the 2-D and 3-