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Zeitschrift für Kristallographie - Crystalline Materials

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Volume 233, Issue 9-10


On avoiding negative electron density in Gram-Charlier refinements of anharmonic motion: the example of glutathione

Christian B. Hübschle / Charlotte Ruhmlieb
  • Institut für Physikalische Chemie der Universität Hamburg, Martin-Luther-King-Platz 6, 20146 Hamburg, Germany
  • Other articles by this author:
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/ Anja Burkhardt / Sander van Smaalen / Birger Dittrich
  • Corresponding author
  • Heinrich-Heine Universität Düsseldorf, Institut für Anorganische Chemie und Strukturchemie, Universitätsstraße 1, 40225 Düsseldorf, Germany
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  • Other articles by this author:
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Published Online: 2018-09-03 | DOI: https://doi.org/10.1515/zkri-2018-2060


The structure of glutathione, γ-l-Glutamyl-l-cysteinyl-glycine (C10H17N3O6S), was studied by multi-temperature single-crystal X-ray diffraction. Residual density maps from conventional independent atom model refinement gave indication of anharmonic motion in the molecule. This was further investigated by invariom refinement with anisotropic displacement parameters for all atoms, which described asphericity due to chemical bonding and lone pairs; afterwards only the residual-density signal of anharmonic motion remained. Treating anharmonicity with third-order Gram-Charlier displacement parameters led to regions with unphysical negative electron density. In contrast, a maximum entropy method (MEM) determination of the electron density successfully takes the features into account. Respective difference electron density plots (MEM minus prior and [Invariom+GC] minus invariom) agree well with each other. Challenges in treating and understanding the phenomenon are discussed. A procedure is proposed how unphysical negative electron density can be avoided. It is closely related to the free lunch algorithm.

This article offers supplementary material which is provided at the end of the article.

Keywords: anharmonic motion; invariom refinement; maximum entropy method


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About the article

Received: 2018-01-17

Accepted: 2018-06-02

Published Online: 2018-09-03

Published in Print: 2018-09-25

Citation Information: Zeitschrift für Kristallographie - Crystalline Materials, Volume 233, Issue 9-10, Pages 695–706, ISSN (Online) 2196-7105, ISSN (Print) 2194-4946, DOI: https://doi.org/10.1515/zkri-2018-2060.

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