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Can a multipole analysis faithfully reproduce topological descriptors of a total charge density?

Acta Cryst. (2002). A58, 451–459

Ian Bytheway, Graham S. Chandler and Brian N. Figgis

Using a multipole expansion to extract a charge-density distribution from X-ray data is known to show disagreement with theoretical calculations of the same density. The origin of these differences has been attributed to various causes. This paper examines the accuracy of the multipole fitting itself by starting from a precisely known density for crystalline ammonia. This charge density is transformed into thermal-motion-free structure factors, which are then fitted using the usual techniques of multipole analysis.

Through topological analysis it is shown that, except for the Laplacian of the density, agreement to better than 12% can be achieved for the topological parameters. The goodness-of-fit factor and residual plots show that the multipole refinement strategies used are far from perfect, although, when thermal motion refinement is included, they do sample the experimental structure factors of Boese et al. [J. Phys. Chem. (1997). B101, 5794–5799] extremely well.