Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Zeitschrift für Kristallographie - Crystalline Materials

Editor-in-Chief: Pöttgen, Rainer

Ed. by Antipov, Evgeny / Boldyreva, Elena V. / Friese, Karen / Huppertz, Hubert / Jahn, Sandro / Tiekink, E. R. T.

IMPACT FACTOR 2017: 1.263
5-year IMPACT FACTOR: 2.057

CiteScore 2017: 2.65

See all formats and pricing
More options …
Volume 233, Issue 9-10


Electrostatic potential in crystals of α-boron, γ-boron and boron carbide

Christian B. Hübschle / Sander van Smaalen
  • Corresponding author
  • Laboratory of Crystallography, University of Bayreuth, Bayreuth 95447, Germany, Tel.: +49-921-553886, Fax: +49-921-553770
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2018-05-29 | DOI: https://doi.org/10.1515/zkri-2018-2080


An overview is given of the recently proposed method for computation of the electrostatic potential (ESP) of dynamic charge densities derived from multipole models [C. B. Hubschle, S. van Smaalen, J. Appl. Crystallogr. 2017, 50, 1627]. The dynamic ESP is presented for the multipole models of the boron polymorphs α-B12 and γ-B28, and stoichiometric boron carbide B13C2. Minimum values of the ESP are conspiciously equal at approximately −1 electron/Å. Regions with the ESP close to its minimum value form an extended network throughout the crystal structures at locations far away from atoms and bonds. Boron and boron carbide are extended solids containing an infinite network of strong chemical bonds. We have shown that for such solids, the ESP can usefully considered on Hirshfeld surfaces encompassing groups of atoms. Accordingly, we discuss bonding in boron and boron carbide with aid of the ESP on the Hirsfeld surface encompassing a B12 icosahedral cluster. The structure of the ESP corroborates the interpretation of the bonding characteristics previously proposed for α-B12, γ-B28 and B13C2.

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

Keywords: dynamic charge density; electron density; electrostatic potential; multipole model

Dedicated to: 75th Birthday of Peter Luger.


  • [1]

    P. Politzer, J. S. Murray, The fundamental nature and role of the electostatic potential in atoms and molecules. Theor. Chem. Acc. 2002, 108, 134.CrossrefGoogle Scholar

  • [2]

    P. Politzer, Y. Ma, P. Lane, M. C. Concha, Computational prediction of standard gas, liquid, and solid-phase heats of formation and heats of vaporization and sublimation. Int. J. Quantum Chem. 2005, 105, 341.CrossrefGoogle Scholar

  • [3]

    A. Kumar, S. D. Yeole, S. R. Gadre, R. Lopez, J. F. Rico, G. Ramirez, I. Ema, D. Zorrilla, DAMQT 2.1.0: a new version of the DAMQT package enabled with the topographical analysis of electron density and electrostatic potential in molecules. J. Comp. Chem. 2015, 36, 2350.CrossrefGoogle Scholar

  • [4]

    R. F. Stewart, Electron population analysis with rigid pseudoatoms. Acta Crystallogr. A 1976, 32, 565.CrossrefGoogle Scholar

  • [5]

    N. K. Hansen, P. Coppens, Testing aspherical atom refinements on small-molecule data sets. Acta Crystallogr. A 1978, 34, 909.CrossrefGoogle Scholar

  • [6]

    Z. Su, P. Coppens, On the mapping of electrostatic properties from the multipole description of the charge density. Acta Crystallogr. A 1992, 48, 188.CrossrefGoogle Scholar

  • [7]

    N. Ghermani, C. Lecomte, N. Bouhmaida, Electrostatic potential from high-resolution X-ray diffraction. Application to a pseudo-peptide molecule. Z. Naturforsch. 1993, 48a, 91.Google Scholar

  • [8]

    R. F. Stewart, B. M. Craven, Molecular eletrostatic potentials from crystal diffraction: the neurotransmitter γ-aminobutyric acid. Biophys. J. 1993, 65, 998.CrossrefGoogle Scholar

  • [9]

    A. Volkov, H. F. King, P. Coppens, L. J. Farrugia, On the calculation of the electrostatic potential, electric field and electric field gradient from the aspherical pseudoatom model. Acta Crystallogr. A 2006, 62, 400.CrossrefWeb of ScienceGoogle Scholar

  • [10]

    J. J. Du, L. Varadi, P. A. Williams, P. W. Groundwater, J. Overgaard, J. A. Platts, D. E. Hibbs, An analysis of the experimental and theoretical charge density distributions of the piroxicam-saccharin co-crystal and its constituents. RSC Adv. 2016, 6, 81578.Web of ScienceCrossrefGoogle Scholar

  • [11]

    C. Kalaiarasi, M. S. Pavan, P. Kumaradhas, Topological characterization of electron density, electrostatic potential and intermolecular interactions of 2-nitroimidazole: an experimental and theoretical study. Acta Crystallogr. B 2016, 72, 775.CrossrefWeb of ScienceGoogle Scholar

  • [12]

    I. L. Kirby, M. Brightwell, M. B. Pitak, C. Wilson, S. J. Coles, P. A. Gale, Systematic experimental charge density analysis of anion receptor complexes. Phys. Chem. Chem. Phys. 2014, 16, 10943.Web of ScienceCrossrefGoogle Scholar

  • [13]

    M. Malinska, Z. Dauter, Transferable aspherical atom model refinement of protein and DNA structures against ultrahigh-resolution X-ray data. Acta Crystallogr. D 2016, 72, 770.Web of ScienceCrossrefGoogle Scholar

  • [14]

    R. Niranjana Devi, C. Jelsch, S. Israel, E. Aubert, C. Anzline, A. A. Hosamani, Charge density analysis of metformin chloride, a biguanide anti-hyperglycemic agent. Acta Crystallogr. B 2017, 73, 10.CrossrefWeb of ScienceGoogle Scholar

  • [15]

    A. Sirohiwal, V. R. Hathwar, D. Dey, R. Regunathan, D. Chopra, Characterization of fluorine-centred ‘F…O’ sigma-hole interactions in the solid state. Acta Crystallogr. B 2017, 73, 140.CrossrefGoogle Scholar

  • [16]

    B. Zarychta, A. Lyubimov, M. Ahmed, P. Munshi, B. Guillot, A. Vrielink, C. Jelsch, Cholesterol oxidase: ultrahigh-resolution crystal structure and multipolar atom model-based analysis. Acta Crystallogr. D 2015, 71, 954.Web of ScienceCrossrefGoogle Scholar

  • [17]

    E. A. Zhurova, V. V. Zhurov, P. Kumaradhas, S. Cenedese, A. A. Pinkerton, Charge density and electrostatic potential study of 16alpha,17beta-estriol and the binding of estrogen molecules to the estrogen receptors ERalpha and ERbeta. J. Phys. Chem. B 2016, 120, 8882.CrossrefGoogle Scholar

  • [18]

    E. F. Bertaut, L’énergie électrostatique de réseaux ioniques. J. Phys. Radium. 1952, 13, 499.CrossrefGoogle Scholar

  • [19]

    E. F. Bertaut, Electrostatic potential, fields and field gradients. J. Phys. Chem. Solids 1978, 39, 97.CrossrefGoogle Scholar

  • [20]

    R. F. Stewart, On the mapping of electrostatic properties from Bragg diffraction data. Chem. Phys. Lett. 1979, 65, 335.CrossrefGoogle Scholar

  • [21]

    M. A. Spackman, R. F. Stewart, Chemical applications of atomic and molecular electrostatic potentials, in Electrostatic Potentials in Crystals, (Eds. P. Politzer and D. G. Truhler) Plenum Press, New York, p. 407, 1981.Google Scholar

  • [22]

    M. A. Spackman, H.-P. Weber, Electrostatic potential in dehydrated sodium zeolite a from low-resolution X-ray diffraton data. J. Phys. Chem. 1988, 92, 794.CrossrefGoogle Scholar

  • [23]

    A. S. Brown, M. A. Spackman, The determination of electric field gradients from X-ray diffration data. Mol. Phys. 1994, 83, 551.CrossrefGoogle Scholar

  • [24]

    M. A. Spackman, Comment on on the calculation of the electrostatic potential, electric field and electric field gradient from the aspherical pseudoatom model by Volkov, King, Coppens and Farrugia (2006). Acta Crystallogr. A 2007, 63, 198.CrossrefWeb of ScienceGoogle Scholar

  • [25]

    M. Franchini, P. Herman T. Philipsen, E. van Lenthe, L. Visscher, Accurate coulomb potentials for periodic and molecular systems through density fitting. J. Chem. Theory Comput. 2014, 10, 1994.Web of ScienceCrossrefGoogle Scholar

  • [26]

    H. Tanaka, Y. Kuroiwa, M. Tanaka, Electrostatic potential of ferroelectric PbTiO3: visualized electron polarization of Pb ion. Phys. Rev. B 2006, 74, 172105.CrossrefGoogle Scholar

  • [27]

    P. P. Ewald, Die berechnung optischer und elektrostatischer gitterpotentiale. Ann. Physik 1921, 64, 258.Google Scholar

  • [28]

    H. Tanaka, Y. Kuroiwa, M. Tanaka, A new method for evaluating the electrostatic potential by using a MEM X-ray diffraction analysis. J. Korean Phys. Soc. 2009, 55, 803.CrossrefGoogle Scholar

  • [29]

    K. Kato, H. Tanaka, Visualizing charge densities and electrostatic potentials in materials by synchrotron X-ray powder diffraction. Adv. Phys. X 2016, 1, 55.Web of ScienceGoogle Scholar

  • [30]

    C. B. Hubschle, S. van Smaalen, The electrostatic potential of dynamic charge densities. J. Appl. Crystallogr. 2017, 50, 1627.CrossrefWeb of ScienceGoogle Scholar

  • [31]

    S. van Smaalen, L. Palatinus, M. Schneider, The maximum-entropy method in superspace. Acta Crystallogr. A 2003, 59, 459.CrossrefGoogle Scholar

  • [32]

    S. Mondal, S. J. Prathapa, S. van Smaalen, Experimental dynamic electron densities of multipole models at different temperatures. Acta Crystallogr. A 2012, 68, 568.Web of ScienceCrossrefGoogle Scholar

  • [33]

    V. Domnich, S. Reynaud, R. A. Haber, M. Chhowalla, Boron carbide: structure, properties, and stability under stress. J. Am. Cer. Soc. 2011, 94, 3605.CrossrefGoogle Scholar

  • [34]

    B. Albert, H. Hillebrecht, Boron: elementary challenge for experimenters and theoreticians. Angew. Chem. Int. Ed. 2009, 48, 8640.CrossrefWeb of ScienceGoogle Scholar

  • [35]

    K. Shirai, Phase diagram of boron crystals. Jpn. J. Appl. Phys. 2017, 56, 05FA06.Web of ScienceCrossrefGoogle Scholar

  • [36]

    P. Coppens, X-ray Charge Densities and Chemical Bonding, Oxford University Press, Oxford, 1997.Google Scholar

  • [37]

    P. Becker, P. Coppens, About the coulomb potential in crystals. Acta Crystallogr. A 1990, 46, 254.CrossrefGoogle Scholar

  • [38]

    S. Mondal, S. van Smaalen, A. Schonleber, Y. Filinchuk, D. Chernyshov, S. Simak, A. Mikhaylushkin, I. Abrikosov, E. Zarechnaya, L. Dubrovinsky, N. Dubrovinskaia, Electron-deficient and polycenter bonds in the high-pressure γ-B28 phase of boron. Phys. Rev. Lett. 2011, 106, 215502.CrossrefGoogle Scholar

  • [39]

    S. Mondal, S. van Smaalen, G. Parakhonskiy, S. J. Prathapa, L. Noohinejad, E. Bykova, N. Dubrovinskaia, D. Chernyshov, L. Dubrovinsky, Experimental evidence of orbital order in α-B12 and γ-B28 polymorphs of elemental boron. Phys. Rev. B 2013, 88, 024118.CrossrefGoogle Scholar

  • [40]

    S. Mondal, E. Bykova, S. Dey, S. I. Ali, N. Dubrovinskaia, L. Dubrovinsky, G. Parakhonskiy, S. van Smaalen, Disorder and defects are not intrinsic to boron carbide. Scientific Reports 2016, 6, 19330.Web of ScienceCrossrefGoogle Scholar

  • [41]

    M. A. Spackman, P. G. Byrom, A novel definition of a molecule in a crystal. Chem. Phys. Lett. 1997, 267, 215.CrossrefGoogle Scholar

  • [42]

    J. J. McKinnon, A. S. Mitchell, M. A. Spackman, Hirshfeld surfaces: a new tool for visualising and exploring molecular crystals. Chem. Eur. J. 1998, 4, 2136.CrossrefGoogle Scholar

  • [43]

    P. Politzer, J. S. Murray, Z. Preralta-Inga, Molecular surface electostatic potentials in relation to noncovalent interactions in biological systems. Int. J. Quantum Chem. 2001, 85, 676.CrossrefGoogle Scholar

  • [44]

    E. Nishibori, H. Hyodo, K. Kimura, M. Takata, Revisit: high resolution charge density study of α-rhombohedral boron using third-generation SR data at SPring-8. Solid State Sci. 2015, 47, 27.Web of ScienceCrossrefGoogle Scholar

About the article

Received: 2018-03-01

Accepted: 2018-05-02

Published Online: 2018-05-29

Published in Print: 2018-09-25

Citation Information: Zeitschrift für Kristallographie - Crystalline Materials, Volume 233, Issue 9-10, Pages 663–673, ISSN (Online) 2196-7105, ISSN (Print) 2194-4946, DOI: https://doi.org/10.1515/zkri-2018-2080.

Export Citation

©2018 Walter de Gruyter GmbH, Berlin/Boston.Get Permission

Supplementary Article Materials

Comments (0)

Please log in or register to comment.
Log in