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Woińska M, Hoser AA, Chodkiewicz ML, Woźniak K. Enhancing hydrogen positions in X-ray structures of transition metal hydride complexes with dynamic quantum crystallography. IUCRJ 2024; 11:45-56. [PMID: 37990870 PMCID: PMC10833390 DOI: 10.1107/s205225252300951x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2023] [Accepted: 10/31/2023] [Indexed: 11/23/2023]
Abstract
Hirshfeld atom refinement (HAR) is a method which enables the user to obtain more accurate positions of hydrogen atoms bonded to light chemical elements using X-ray data. When data quality permits, this method can be extended to hydrogen-bonded transition metals (TMs), as in hydride complexes. However, addressing hydrogen thermal motions with HAR, particularly in TM hydrides, presents a challenge. At the same time, proper description of thermal vibrations can be vital for determining hydrogen positions correctly. In this study, we employ tools such as SHADE3 and Normal Mode Refinement (NoMoRe) to estimate anisotropic displacement parameters (ADPs) for hydrogen atoms during HAR and IAM refinements performed for seven structures of TM (Fe, Ni, Cr, Nb, Rh and Os) and metalloid (Sb) hydride complexes for which both the neutron and the X-ray structures have been determined. A direct comparison between neutron and HAR/SHADE3/NoMoRe ADPs reveals that the similarity between neutron hydrogen ADPs and those estimated with NoMoRe or SHADE3 is significantly higher than when hydrogen ADPs are refined with HAR. Regarding TM-H bond lengths, traditional HAR exhibits a slight advantage over the other methods. However, combining NoMoRe/SHADE3 with HAR results in a minor decrease in agreement with neutron TM-H bond lengths. For the Cr complex, for which high-resolution X-ray data were collected, an investigation of resolution-related effects was possible.
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Affiliation(s)
- Magdalena Woińska
- Biological and Chemical Research Centre, Chemistry Department, University of Warsaw, Żwirki i Wigury 101, Warsaw 02-089, Poland
| | - Anna A. Hoser
- Biological and Chemical Research Centre, Chemistry Department, University of Warsaw, Żwirki i Wigury 101, Warsaw 02-089, Poland
| | - Michał L. Chodkiewicz
- Biological and Chemical Research Centre, Chemistry Department, University of Warsaw, Żwirki i Wigury 101, Warsaw 02-089, Poland
| | - Krzysztof Woźniak
- Biological and Chemical Research Centre, Chemistry Department, University of Warsaw, Żwirki i Wigury 101, Warsaw 02-089, Poland
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2
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Langmann J, Kepenci H, Eickerling G, Batke K, Jesche A, Xu M, Canfield P, Scherer W. Experimental X-ray Charge-Density Studies─A Suitable Probe for Superconductivity? A Case Study on MgB 2. J Phys Chem A 2022; 126:8494-8507. [DOI: 10.1021/acs.jpca.2c05925] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Affiliation(s)
- Jan Langmann
- CPM, Institut für Physik, Universität Augsburg, 86159Augsburg, Germany
| | - Hasan Kepenci
- CPM, Institut für Physik, Universität Augsburg, 86159Augsburg, Germany
| | - Georg Eickerling
- CPM, Institut für Physik, Universität Augsburg, 86159Augsburg, Germany
| | - Kilian Batke
- CPM, Institut für Physik, Universität Augsburg, 86159Augsburg, Germany
| | - Anton Jesche
- Experimentalphysik VI, Zentrum für Elektronische Korrelation und Magnetismus, Institut für Physik, Universität Augsburg, Augsburg86159, Germany
| | - Mingyu Xu
- The Ames Laboratory, Iowa State University, Ames, Iowa50011, United States
- Department of Physics and Astronomy, Iowa State University, Ames, Iowa50011, United States
| | - Paul Canfield
- The Ames Laboratory, Iowa State University, Ames, Iowa50011, United States
- Department of Physics and Astronomy, Iowa State University, Ames, Iowa50011, United States
| | - Wolfgang Scherer
- CPM, Institut für Physik, Universität Augsburg, 86159Augsburg, Germany
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Hoser AA, Rekis T, Madsen AØ. Dynamics and disorder: on the stability of pyrazinamide polymorphs. ACTA CRYSTALLOGRAPHICA SECTION B STRUCTURAL SCIENCE, CRYSTAL ENGINEERING AND MATERIALS 2022; 78:416-424. [PMID: 35695115 PMCID: PMC9254588 DOI: 10.1107/s2052520622004577] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/11/2022] [Accepted: 04/29/2022] [Indexed: 11/10/2022]
Abstract
The enantiotropic relationship between the four polymorphs of pyrazinamide is analyzed by means of accurate X-ray diffraction measurements, normal-mode refinement and periodic DFT calculations. This article focuses on the structure and relative stability of four pyrazinamide polymorphs. New single crystal X-ray diffraction data collected for all forms at 10 K and 122 K are presented. By combining periodic abinitio DFT calculations with normal-mode refinement against X-ray diffraction data, both enthalpic and entropic contributions to the free energy of all polymorphs are calculated. On the basis of the estimated free energies, the stability order of the polymorphs as a function of temperature and the corresponding solid state phase transition temperatures are anticipated. It can be concluded that the α and γ forms have higher vibrational entropy than that of the β and δ forms and therefore they are significantly more stabilized at higher temperatures. Due to the entropy which arises from the disorder in γ form, it overcomes form α and is the most stable form at temperatures above ∼500 K. Our findings are in qualitative agreement with the experimental calorimetry results.
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Rotamers in Crystal Structures of Xylitol, D-Arabitol and L-Arabitol. Int J Mol Sci 2022; 23:ijms23073875. [PMID: 35409233 PMCID: PMC8998848 DOI: 10.3390/ijms23073875] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2022] [Revised: 03/22/2022] [Accepted: 03/28/2022] [Indexed: 02/01/2023] Open
Abstract
Rotamers are stereoisomers produced by rotation (twisting) about σ bonds and are often rapidly interconverting at room temperature. Xylitol-massively produced sweetener-(2R,3r,4S)-pentane-1,2,3,4,5-pentol) forms rotamers from the linear conformer by rotation of a xylitol fragment around the C2-C3 bond (rotamer 1) or the C3-C4 bond (rotamer 2). The rotamers form two distinguishable structures. Small differences in geometry of rotamers of the main carbon chain were confirmed by theoretical calculations; however, they were beyond the capabilities of the X-ray powder diffraction technique due to the almost identical unit cell parameters. In the case of rotamers of similar compounds, the rotations occurred mostly within hydroxyl groups likewise rotations in L-arabitol and D-arabitol, which are discussed in this work. Our results, supported by theoretical calculations, showed that energetic differences are slightly higher for rotamers with rotations within hydroxyl groups instead of a carbon chain.
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Smirnova ES, Alekseeva OA, Dudka AP, Verin IA, Artemov VV, Lyubutina MV, Gudim IA, Frolov KV, Lyubutin IS. Crystal structure of bismuth-containing NdFe 3(BO 3) 4 in the temperature range 20-500 K. ACTA CRYSTALLOGRAPHICA SECTION B, STRUCTURAL SCIENCE, CRYSTAL ENGINEERING AND MATERIALS 2022; 78:1-13. [PMID: 35129115 DOI: 10.1107/s205252062101180x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2021] [Accepted: 11/08/2021] [Indexed: 06/14/2023]
Abstract
Neodymium iron borate NdFe3(BO3)4 is an intensively studied multiferroic with high electric polarization values controlled by a magnetic field. It is characterized by a large quadratic magnetoelectric effect, rigidity in the base plane and a rather strong piezoelectric effect. In this work, the atomic structure of (Nd0.91Bi0.09)Fe3(BO3)4 was studied by single-crystal X-ray diffraction in the temperature range 20-500 K (space group R32, Z = 3). The Bi atoms found in the composition partially substitute the Nd atoms in the 3a position; they entered the structure due to the growth conditions in the presence of Bi2Mo3O12. It was shown that in the temperature range 20-500 K there is no structural phase transition R32→P3121, which occurs in rare-earth iron borates (RE = Eu-Er, Y) with an effective rare-earth cation radius smaller than that of Nd. The temperature dependence of the unit-cell c parameter reveals a slight increase on cooling below 90 K, which is similar to the results obtained previously for iron borates of Gd, Y and Ho. The atomic distances (Nd,Bi)-O, (Nd,Bi)-B, (Nd,Bi)-Fe, Fe-O, Fe-B and Fe-Fe in the iron chains and between chains decrease steadily with decreasing temperature from 500 to 90 K, whereas the B1(3b)-O distance does not change and the average B2(9e)-O distance increases slightly. There is a uniform decrease in the atomic displacement parameters with decreasing temperature, with a more pronounced decrease for the Nd(3a) and O2(9e) atoms. The O2(9e) atoms are characterized by the maximum atomic displacement parameters and the most elongated atomic displacement ellipsoids. The characteristic Debye and Einstein temperatures, and the static component in the atomic displacements were determined for cations using multi-temperature diffraction data. It was shown that the Nd cations have the weakest bonds with the surrounding atoms and the B cations have the strongest.
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Affiliation(s)
- Ekaterina S Smirnova
- Shubnikov Institute of Crystallography of Federal Scientific Research Centre Crystallography and Photonics', Russian Academy of Sciences, Moscow 119333, Russian Federation
| | - Olga A Alekseeva
- Shubnikov Institute of Crystallography of Federal Scientific Research Centre Crystallography and Photonics', Russian Academy of Sciences, Moscow 119333, Russian Federation
| | - Alexander P Dudka
- Shubnikov Institute of Crystallography of Federal Scientific Research Centre Crystallography and Photonics', Russian Academy of Sciences, Moscow 119333, Russian Federation
| | - Igor A Verin
- Shubnikov Institute of Crystallography of Federal Scientific Research Centre Crystallography and Photonics', Russian Academy of Sciences, Moscow 119333, Russian Federation
| | - Vladimir V Artemov
- Shubnikov Institute of Crystallography of Federal Scientific Research Centre Crystallography and Photonics', Russian Academy of Sciences, Moscow 119333, Russian Federation
| | - Marianna V Lyubutina
- Shubnikov Institute of Crystallography of Federal Scientific Research Centre Crystallography and Photonics', Russian Academy of Sciences, Moscow 119333, Russian Federation
| | - Irina A Gudim
- Kirensky Institute of Physics, Federal Research Center KSC SB RAS, Krasnoyarsk 660036, Russian Federation
| | - Kirill V Frolov
- Shubnikov Institute of Crystallography of Federal Scientific Research Centre Crystallography and Photonics', Russian Academy of Sciences, Moscow 119333, Russian Federation
| | - Igor S Lyubutin
- Shubnikov Institute of Crystallography of Federal Scientific Research Centre Crystallography and Photonics', Russian Academy of Sciences, Moscow 119333, Russian Federation
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Stanton SA, Du JJ, Lai F, Stanton G, Hawkins BA, Ong JA, Groundwater PW, Platts JA, Hibbs DE. Understanding Hygroscopicity of Theophylline via a Novel Cocrystal Polymorph: A Charge Density Study. J Phys Chem A 2021; 125:9736-9756. [PMID: 34731566 DOI: 10.1021/acs.jpca.0c09536] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The charge density distribution in a novel cocrystal (1) complex of 1,3-dimethylxanthine (theophylline) and propanedioic acid (malonic acid) has been determined. The molecules crystallize in the triclinic, centrosymmetric space group P1̅, with four independent molecules (Z = 4) in the asymmetric unit (two molecules each of theophylline and malonic acid). Theophylline has a notably high hygroscopic nature, and numerous cocrystals have shown a significant improvement in stability to humidity. A charge density study of the novel polymorph has identified interesting theoretical results correlating the stability enhancement of theophylline via cocrystallization. Topological analysis of the electron density highlighted key differences (up to 17.8) in Laplacian (∇2ρ) between the experimental (EXP) and single-point (SP) models, mainly around intermolecular-bonded carbonyls. Further investigation via molecular electrostatic potential maps reaffirmed that the charge redistribution enhanced intramolecular hydrogen bonding, predominantly for N(2') and N(2) (61.2 and 61.8 kJ mol-1, respectively). An overall weaker lattice energy of the triclinic form (-126.1 kJ mol-1) compared to that of the monoclinic form (-133.8 kJ mol-1) suggests a lower energy threshold to overcome to initiate dissociation. Future work via physical testing of the novel cocrystal in both dissolution and solubility will further solidify the correlation between theoretical and experimental results.
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Affiliation(s)
- Stephen A Stanton
- Sydney School of Pharmacy, Faculty of Medicine and Health, The University of Sydney, Sydney, NSW 2006, Australia
| | - Jonathan J Du
- Sydney School of Pharmacy, Faculty of Medicine and Health, The University of Sydney, Sydney, NSW 2006, Australia
| | - Felcia Lai
- Sydney School of Pharmacy, Faculty of Medicine and Health, The University of Sydney, Sydney, NSW 2006, Australia
| | - Gyte Stanton
- Sydney School of Pharmacy, Faculty of Medicine and Health, The University of Sydney, Sydney, NSW 2006, Australia
| | - Bryson A Hawkins
- Sydney School of Pharmacy, Faculty of Medicine and Health, The University of Sydney, Sydney, NSW 2006, Australia
| | - Jennifer A Ong
- Sydney School of Pharmacy, Faculty of Medicine and Health, The University of Sydney, Sydney, NSW 2006, Australia
| | - Paul W Groundwater
- Sydney School of Pharmacy, Faculty of Medicine and Health, The University of Sydney, Sydney, NSW 2006, Australia
| | - James A Platts
- School of Chemistry, Cardiff University, Cardiff CF10 3AT, U.K
| | - David E Hibbs
- Sydney School of Pharmacy, Faculty of Medicine and Health, The University of Sydney, Sydney, NSW 2006, Australia
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7
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Hoser AA, Sztylko M, Trzybiński D, Madsen AØ. Theoretically derived thermodynamic properties can be improved by the refinement of low-frequency modes against X-ray diffraction data. Chem Commun (Camb) 2021; 57:9370-9373. [PMID: 34528955 DOI: 10.1039/d1cc02608a] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Herein, a framework for the estimation of the thermodynamic properties of molecular crystals via the refinement of frequencies from density functional theory calculations against X-ray diffraction data is presented. The framework provides an efficient approach to including the contribution of acoustic modes in the thermodynamic properties. The obtained heat capacities for urea, the α- and β-glycine polymorphs, benzoic acid, and 4'-hydroxyacetophenone are in good agreement with those from adiabatic calorimetry.
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Affiliation(s)
- Anna A Hoser
- Biological and Chemical Research Centre, Faculty of Chemistry, University of Warsaw, Żwirki i Wigury 101, 02-089 Warszawa, Poland.
| | - Marcin Sztylko
- Biological and Chemical Research Centre, Faculty of Chemistry, University of Warsaw, Żwirki i Wigury 101, 02-089 Warszawa, Poland.
| | - Damian Trzybiński
- Biological and Chemical Research Centre, Faculty of Chemistry, University of Warsaw, Żwirki i Wigury 101, 02-089 Warszawa, Poland.
| | - Anders Ø Madsen
- Department of Pharmacy, University of Copenhagen, Universitetsparken 2, Copenhagen 2100, Denmark
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Tomaschitz R. Thermodynamics of lattice vibrations in non-cubic crystals: the zinc structure revisited. Acta Crystallogr A Found Adv 2021; 77:420-432. [PMID: 34473096 DOI: 10.1107/s2053273321005507] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2021] [Accepted: 05/26/2021] [Indexed: 05/31/2023] Open
Abstract
A phenomenological model of anisotropic lattice vibrations is proposed, using a temperature-dependent spectral cutoff and varying Debye temperatures for the vibrational normal components. The internal lattice energy, entropy and Debye-Waller B factors of non-cubic elemental crystals are derived. The formalism developed is non-perturbative, based on temperature-dependent linear dispersion relations for the normal modes. The Debye temperatures of the vibrational normal components differ in anisotropic crystals; their temperature dependence and the varying spectral cutoff can be inferred from the experimental lattice heat capacity and B factors by least-squares regression. The zero-point internal energy of the phonons is related to the low-temperature limits of the mean-squared vibrational amplitudes of the lattice measured by X-ray and γ-ray diffraction. A specific example is discussed, the thermodynamic variables of the hexagonal close-packed zinc structure, including the temperature evolution of the B factors of zinc. In this case, the lattice vibrations are partitioned into axial and basal normal components, which admit largely differing B factors and Debye temperatures. The second-order B factors defining the non-Gaussian contribution to the Debye-Waller damping factors of zinc are obtained as well. Anharmonicity of the oscillator potential and deviations from the uniform phonon frequency distribution of the Debye theory are modeled effectively by the temperature dependence of the spectral cutoff and Debye temperatures.
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9
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The Mixed-Layer Structures of Ikunolite, Laitakarite, Joséite-B and Joséite-A. MINERALS 2021. [DOI: 10.3390/min11090920] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
We used high-angle annular dark field scanning transmission electron microscopy (HAADF STEM) to image the crystal structures of four minerals in the Bi4X3 isoseries (X = Te, Se, S), a subgroup of the tetradymite homologous series: ikunolite (Bi4S3), laitakarite (Bi4Se2S), joséite-B (Bi4Te2S), and joséite-A (Bi4TeS2). The four minerals are isostructural and interpretable in terms of regular stacking of seven-atom packages: [Bi–S–Bi–S–Bi–S–Bi], [Bi–Se–Bi–S–Bi–Se–Bi], [Bi–Te–Bi–S–Bi–Te–Bi], and [Bi–S–Bi–Te–Bi–S–Bi], respectively. The four phases are mixed-layer structures representing the Bi2kTe3 (k = 2) module within the tetradymite series. Diffraction patterns confirm they are seven-fold superstructures of a rhombohedral subcell with c/3 = d~1.89–1.93 Å. Modulation along the d* interval matches calculations of reflection intensity using the fractional shift method for Bi4X3. Internal structures can be discerned by high-resolution HAADF STEM imaging and mapping. Paired bismuth atoms are positioned at the outside of each seven-atom layer, giving the minerals a modular structure that can also be considered as being composed of five-atom (X–Bi–X–Bi–X) and two-atom (Bi–Bi) sub-modules. The presence of mixed sites for substituting cations is shown, particularly for Pb. Moreover, Pb may be important in understanding the incorporation of Ag and Au in Bi–chalcogenides. Visualisation of crystal structures by HAADF STEM contributes to understanding relationships between phases in the tetradymite homologous series and will play an invaluable role in the characterization of potential additional members of the series.
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Wanat M, Malinska M, Hoser AA, Woźniak K. Further Validation of Quantum Crystallography Approaches. Molecules 2021; 26:molecules26123730. [PMID: 34207308 PMCID: PMC8233966 DOI: 10.3390/molecules26123730] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2021] [Revised: 06/14/2021] [Accepted: 06/14/2021] [Indexed: 11/16/2022] Open
Abstract
Quantum crystallography is a fast-developing multidisciplinary area of crystallography. In this work, we analyse the influence of different charge density models (i.e., the multipole model (MM), Hirshfeld atom refinement (HAR), and the transferable aspherical atom model (TAAM)), modelling of the thermal motion of hydrogen atoms (anisotropic, isotropic, and with the aid of SHADE or NoMoRe), and the type of radiation used (Mo Kα and Cu Kα) on the final results. To achieve this aim, we performed a series of refinements against X-ray diffraction data for three model compounds and compared their final structures, geometries, shapes of ADPs, and charge density distributions. Our results were also supported by theoretical calculations that enabled comparisons of the lattice energies of these structures. It appears that geometrical parameters are better described (closer to the neutron values) when HAR is used; however, bonds to H atoms more closely match neutron values after MM or TAAM refinement. Our analysis shows the superiority of the NoMoRe method in the description of H-atom ADPs. Moreover, the shapes of the ADPs of H atoms, as well as their electron density distributions, were better described with low-resolution Cu Kα data in comparison to low-resolution Mo Kα data.
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Affiliation(s)
- Monika Wanat
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, 101 Żwirki i Wigury, 02-089 Warszawa, Poland; (M.W.); (M.M.); (A.A.H.)
- College of Inter-Faculty Individual Studies in Mathematics and Natural Sciences (MISMaP), University of Warsaw, 2C Stefana Banacha, 02-097 Warszawa, Poland
| | - Maura Malinska
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, 101 Żwirki i Wigury, 02-089 Warszawa, Poland; (M.W.); (M.M.); (A.A.H.)
| | - Anna A. Hoser
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, 101 Żwirki i Wigury, 02-089 Warszawa, Poland; (M.W.); (M.M.); (A.A.H.)
| | - Krzysztof Woźniak
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, 101 Żwirki i Wigury, 02-089 Warszawa, Poland; (M.W.); (M.M.); (A.A.H.)
- Correspondence:
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Chodkiewicz ML, Woińska M, Woźniak K. Hirshfeld atom like refinement with alternative electron density partitions. IUCRJ 2020; 7:1199-1215. [PMID: 33209330 PMCID: PMC7642787 DOI: 10.1107/s2052252520013603] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2020] [Accepted: 10/12/2020] [Indexed: 05/03/2023]
Abstract
Hirshfeld atom refinement is one of the most successful methods for the accurate determination of structural parameters for hydrogen atoms from X-ray diffraction data. This work introduces a generalization of the method [generalized atom refinement (GAR)], consisting of the application of various methods of partitioning electron density into atomic contributions. These were tested on three organic structures using the following partitions: Hirshfeld, iterative Hirshfeld, iterative stockholder, minimal basis iterative stockholder and Becke. The effects of partition choice were also compared with those caused by other factors such as quantum chemical methodology, basis set, representation of the crystal field and a combination of these factors. The differences between the partitions were small in terms of R factor (e.g. much smaller than for refinements with different quantum chemistry methods, i.e. Hartree-Fock and coupled cluster) and therefore no single partition was clearly the best in terms of experimental data reconstruction. In the case of structural parameters the differences between the partitions are comparable to those related to the choice of other factors. We have observed the systematic effects of the partition choice on bond lengths and ADP values of polar hydrogen atoms. The bond lengths were also systematically influenced by the choice of electron density calculation methodology. This suggests that GAR-derived structural parameters could be systematically improved by selecting an optimal combination of the partition and quantum chemistry method. The results of the refinements were compared with those of neutron diffraction experiments. This allowed a selection of the most promising partition methods for further optimization of GAR settings, namely the Hirshfeld, iterative stockholder and minimal basis iterative stockholder.
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Affiliation(s)
- Michał Leszek Chodkiewicz
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, Żwirki i Wigury 101, Warszawa, 02-089 Warszawa, Poland
| | - Magdalena Woińska
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, Żwirki i Wigury 101, Warszawa, 02-089 Warszawa, Poland
| | - Krzysztof Woźniak
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, Żwirki i Wigury 101, Warszawa, 02-089 Warszawa, Poland
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12
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Post-Hartree-Fock methods for Hirshfeld atom refinement: are they necessary? Investigation of a strongly hydrogen-bonded molecular crystal. J Mol Struct 2020. [DOI: 10.1016/j.molstruc.2020.127934] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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13
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Korlyukov AA, Nelyubina YV. Quantum chemical methods in charge density studies from X-ray diffraction data. RUSSIAN CHEMICAL REVIEWS 2019. [DOI: 10.1070/rcr4866] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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14
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Kofoed PM, Hoser AA, Diness F, Capelli SC, Madsen AØ. X-ray diffraction data as a source of the vibrational free-energy contribution in polymorphic systems. IUCRJ 2019; 6:558-571. [PMID: 31316801 PMCID: PMC6608639 DOI: 10.1107/s2052252519003014] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/07/2018] [Accepted: 02/27/2019] [Indexed: 06/10/2023]
Abstract
In this contribution we attempt to answer a general question: can X-ray diffraction data combined with theoretical computations be a source of information about the thermodynamic properties of a given system? Newly collected sets of high-quality multi-temperature single-crystal X-ray diffraction data and complementary periodic DFT calculations of vibrational frequencies and normal mode vectors at the Γ point on the yellow and white polymorphs of di-methyl 3,6-di-chloro-2,5-di-hydroxy-terephthalate are combined using two different approaches, aiming to obtain thermodynamic properties for the two compounds. The first approach uses low-frequency normal modes extracted from multi-temperature X-ray diffraction data (normal coordinate analysis), while the other uses DFT-calculated low-frequency normal mode in the refinement of the same data (normal mode refinement). Thermodynamic data from the literature [Yang et al. (1989), Acta Cryst. B45, 312-323] and new periodic ab initio DFT supercell calculations are used as a reference point. Both approaches tested in this work capture the most essential features of the systems: the polymorphs are enantiotropically related, with the yellow form being the thermodynamically stable system at low temperature, and the white form at higher temperatures. However, the inferred phase transition temperature varies between different approaches. Thanks to the application of unconventional methods of X-ray data refinement and analysis, it was additionally found that, in the case of the yellow polymorph, anharmonicity is an important issue. By discussing contributions from low- and high-frequency modes to the vibrational entropy and enthalpy, the importance of high-frequency modes is highlighted. The analysis shows that larger anisotropic displacement parameters are not always related to the polymorph with the higher vibrational entropy contribution.
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Affiliation(s)
| | - Anna A. Hoser
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, Żwirki i Wigury 101, Warszawa 02-089, Poland
| | - Frederik Diness
- Department of Chemistry, University of Copenhagen, Copenhagen Denmark
| | - Silvia C. Capelli
- ISIS Neutrons and Muons Facility, Science and Technical Facility Council, Rutherford Appleton Laboratory, Harwell Science Campus, Didcot OX11 OQX, UK
| | - Anders Østergaard Madsen
- Department of Pharmacy, University of Copenhagen, Universitetsparken 2, Copenhagen 2100, Denmark
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15
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Genoni A, Bučinský L, Claiser N, Contreras-García J, Dittrich B, Dominiak PM, Espinosa E, Gatti C, Giannozzi P, Gillet JM, Jayatilaka D, Macchi P, Madsen AØ, Massa L, Matta CF, Merz KM, Nakashima PNH, Ott H, Ryde U, Schwarz K, Sierka M, Grabowsky S. Quantum Crystallography: Current Developments and Future Perspectives. Chemistry 2018; 24:10881-10905. [PMID: 29488652 DOI: 10.1002/chem.201705952] [Citation(s) in RCA: 83] [Impact Index Per Article: 13.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2017] [Revised: 02/27/2018] [Indexed: 11/09/2022]
Abstract
Crystallography and quantum mechanics have always been tightly connected because reliable quantum mechanical models are needed to determine crystal structures. Due to this natural synergy, nowadays accurate distributions of electrons in space can be obtained from diffraction and scattering experiments. In the original definition of quantum crystallography (QCr) given by Massa, Karle and Huang, direct extraction of wavefunctions or density matrices from measured intensities of reflections or, conversely, ad hoc quantum mechanical calculations to enhance the accuracy of the crystallographic refinement are implicated. Nevertheless, many other active and emerging research areas involving quantum mechanics and scattering experiments are not covered by the original definition although they enable to observe and explain quantum phenomena as accurately and successfully as the original strategies. Therefore, we give an overview over current research that is related to a broader notion of QCr, and discuss options how QCr can evolve to become a complete and independent domain of natural sciences. The goal of this paper is to initiate discussions around QCr, but not to find a final definition of the field.
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Affiliation(s)
- Alessandro Genoni
- Université de Lorraine, CNRS, Laboratoire LPCT, 1 Boulevard Arago, F-57078, Metz, France
| | - Lukas Bučinský
- Institute of Physical Chemistry and Chemical Physics, Slovak University of Technology, FCHPT SUT, Radlinského 9, SK-812 37, Bratislava, Slovakia
| | - Nicolas Claiser
- Université de Lorraine, CNRS, Laboratoire CRM2, Boulevard des Aiguillettes, BP 70239, F-54506, Vandoeuvre-lès-Nancy, France
| | - Julia Contreras-García
- Sorbonne Universités, UPMC Université Paris 06, CNRS, Laboratoire de Chimie Théorique (LCT), 4 Place Jussieu, F-75252, Paris Cedex 05, France
| | - Birger Dittrich
- Anorganische und Strukturchemie II, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225, Düsseldorf, Germany
| | - Paulina M Dominiak
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, ul. Żwirki i Wigury 101, 02-089, Warszawa, Poland
| | - Enrique Espinosa
- Université de Lorraine, CNRS, Laboratoire CRM2, Boulevard des Aiguillettes, BP 70239, F-54506, Vandoeuvre-lès-Nancy, France
| | - Carlo Gatti
- CNR-ISTM Istituto di Scienze e Tecnologie Molecolari, via Golgi 19, Milano, I-20133, Italy.,Istituto Lombardo Accademia di Scienze e Lettere, via Brera 28, 20121, Milano, Italy
| | - Paolo Giannozzi
- Department of Mathematics, Computer Science and Physics, University of Udine, Via delle Scienze 208, I-33100, Udine, Italy
| | - Jean-Michel Gillet
- Structure, Properties and Modeling of Solids Laboratory, CentraleSupelec, Paris-Saclay University, 3 rue Joliot-Curie, 91191, Gif-sur-Yvette, France
| | - Dylan Jayatilaka
- School of Molecular Sciences, University of Western Australia, 35 Stirling Highway, Perth, WA, 6009, Australia
| | - Piero Macchi
- Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH-3012, Bern, Switzerland
| | - Anders Ø Madsen
- Department of Pharmacy, University of Copenhagen, Universitetsparken 2, 2100, Copenhagen, Denmark
| | - Lou Massa
- Hunter College & the Ph.D. Program of the Graduate Center, City University of New York, New York, USA
| | - Chérif F Matta
- Department of Chemistry and Physics, Mount Saint Vincent University, Halifax, Nova Scotia, B3M 2J6, Canada.,Department of Chemistry, Dalhousie University, Halifax, Nova Scotia, B3H 4J3, Canada.,Department of Chemistry, Saint Mary's University, Halifax, Nova Scotia, B3H 3C3, Canada.,Département de Chimie, Université Laval, Québec, QC G1V 0A6, Canada
| | - Kenneth M Merz
- Department of Chemistry and Department of Biochemistry and Molecular Biology, Michigan State University, 578 South Shaw Lane, East Lansing, Michigan, 48824, USA.,Institute for Cyber Enabled Research, Michigan State University, 567 Wilson Road, Room 1440, East Lansing, Michigan, 48824, USA
| | - Philip N H Nakashima
- Department of Materials Science and Engineering, Monash University, Victoria, 3800, Australia
| | - Holger Ott
- Bruker AXS GmbH, Östliche Rheinbrückenstraße 49, 76187, Karlsruhe, Germany
| | - Ulf Ryde
- Department of Theoretical Chemistry, Lund University, Chemical Centre, P.O. Box 124, SE-22100, Lund, Sweden
| | - Karlheinz Schwarz
- Technische Universität Wien, Institut für Materialwissenschaften, Getreidemarkt 9, A-1060, Vienna, Austria
| | - Marek Sierka
- Otto Schott Institute of Materials Research, Friedrich Schiller University Jena, Löbdergraben 32, 07743, Jena, Germany
| | - Simon Grabowsky
- Fachbereich 2-Biologie/Chemie, Institut für Anorganische Chemie und Kristallographie, Universität Bremen, Leobener Str. 3, 28359, Bremen, Germany
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16
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George J, Wang R, Englert U, Dronskowski R. Lattice thermal expansion and anisotropic displacements in urea, bromomalonic aldehyde, pentachloropyridine, and naphthalene. J Chem Phys 2018; 147:074112. [PMID: 28830176 DOI: 10.1063/1.4985886] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Anisotropic displacement parameters (ADPs) are commonly used in crystallography, chemistry, and related fields to describe and quantify thermal motion of atoms. Within the very recent years, these ADPs have become predictable by lattice dynamics in combination with first-principles theory. Here, we study four very different molecular crystals, namely, urea, bromomalonic aldehyde, pentachloropyridine, and naphthalene, by first-principles theory to assess the quality of ADPs calculated in the quasi-harmonic approximation. In addition, we predict both the thermal expansion and thermal motion within the quasi-harmonic approximation and compare the predictions with the experimental data. Very reliable ADPs are calculated within the quasi-harmonic approximation for all four cases up to at least 200 K, and they turn out to be in better agreement with the experiment than those calculated within the harmonic approximation. In one particular case, ADPs can even reliably be predicted up to room temperature. Our results also hint at the importance of normal-mode anharmonicity in the calculation of ADPs.
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Affiliation(s)
- Janine George
- Institute of Inorganic Chemistry, RWTH Aachen University, 52056 Aachen, Germany
| | - Ruimin Wang
- Institute of Inorganic Chemistry, RWTH Aachen University, 52056 Aachen, Germany
| | - Ulli Englert
- Institute of Inorganic Chemistry, RWTH Aachen University, 52056 Aachen, Germany
| | - Richard Dronskowski
- Institute of Inorganic Chemistry, RWTH Aachen University, 52056 Aachen, Germany
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17
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Wahlberg N, Madsen AØ. Implications of X-ray thermal diffuse scattering in integrated Bragg intensities of silicon and cubic boron nitride. J Appl Crystallogr 2017. [DOI: 10.1107/s1600576717014376] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022] Open
Abstract
This article describes a theoretical quantification of the thermal diffuse scattering (TDS) contribution to the integrated intensities of single-crystal diffraction from silicon and cubic boron nitride. The TDS intensity is calculatedab initioand the intensity contribution to the Bragg peak determined by integration of a volume of appropriate size. The effect of including TDS in the structure factors is assessed in a subsequent refinement, where the effect on the atomic displacement parameters and the residual Fourier maps is inspected. In both compounds changes caused solely by the TDS inclusion are observed. Particularly, adding TDS to the structure factors of silicon produces significant features in the residual Fourier maps and a change in the atomic displacement parameter. Significant effects are also present at low temperatures. Thus, it is important to address the effect of TDS when pursuing high-accuracy charge densities or if analyzing the atomic displacement parameters.
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18
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Grabowsky S, Genoni A, Bürgi HB. Quantum crystallography. Chem Sci 2017; 8:4159-4176. [PMID: 28878872 PMCID: PMC5576428 DOI: 10.1039/c6sc05504d] [Citation(s) in RCA: 96] [Impact Index Per Article: 13.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2016] [Accepted: 03/03/2017] [Indexed: 12/12/2022] Open
Abstract
Approximate wavefunctions can be improved by constraining them to reproduce observations derived from diffraction and scattering experiments. Conversely, charge density models, incorporating electron-density distributions, atomic positions and atomic motion, can be improved by supplementing diffraction experiments with quantum chemically calculated, tailor-made electron densities (form factors). In both cases quantum chemistry and diffraction/scattering experiments are combined into a single, integrated tool. The development of quantum crystallographic research is reviewed. Some results obtained by quantum crystallography illustrate the potential and limitations of this field.
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Affiliation(s)
- Simon Grabowsky
- Universität Bremen , Fachbereich 2 - Biologie/Chemie , Institut für Anorganische Chemie und Kristallographie , Leobener Str. NW2 , 28359 Bremen , Germany .
| | - Alessandro Genoni
- CNRS , Laboratoire SRSMC , UMR 7565 , Vandoeuvre-lès-Nancy , F-54506 , France
- Université de Lorraine , Laboratoire SRSMC , UMR 7565 , Vandoeuvre-lès-Nancy , F-54506 , France .
| | - Hans-Beat Bürgi
- Universität Bern , Departement für Chemie und Biochemie , Freiestr. 3 , CH-3012 Bern , Switzerland .
- Universität Zürich , Institut für Chemie , Winterthurerstrasse 190 , CH-8057 Zürich , Switzerland
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19
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Dittrich B, Lübben J, Mebs S, Wagner A, Luger P, Flaig R. Accurate Bond Lengths to Hydrogen Atoms from Single-Crystal X-ray Diffraction by Including Estimated Hydrogen ADPs and Comparison to Neutron and QM/MM Benchmarks. Chemistry 2017; 23:4605-4614. [PMID: 28295691 PMCID: PMC5434951 DOI: 10.1002/chem.201604705] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2016] [Revised: 11/21/2016] [Indexed: 11/21/2022]
Abstract
Amino acid structures are an ideal test set for method-development studies in crystallography. High-resolution X-ray diffraction data for eight previously studied genetically encoding amino acids are provided, complemented by a non-standard amino acid. Structures were re-investigated to study a widely applicable treatment that permits accurate X-H bond lengths to hydrogen atoms to be obtained: this treatment combines refinement of positional hydrogen-atom parameters with aspherical scattering factors with constrained "TLS+INV" estimated hydrogen anisotropic displacement parameters (H-ADPs). Tabulated invariom scattering factors allow rapid modeling without further computations, and unconstrained Hirshfeld atom refinement provides a computationally demanding alternative when database entries are missing. Both should incorporate estimated H-ADPs, as free refinement frequently leads to over-parameterization and non-positive definite H-ADPs irrespective of the aspherical scattering model used. Using estimated H-ADPs, both methods yield accurate and precise X-H distances in best quantitative agreement with neutron diffraction data (available for five of the test-set molecules). This work thus solves the last remaining problem to obtain such results more frequently. Density functional theoretical QM/MM computations are able to play the role of an alternative benchmark to neutron diffraction.
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Affiliation(s)
- Birger Dittrich
- Heinrich-Heine Universität DüsseldorfInstitut für Anorganische Chemie und Strukturchemie, Material- und Strukturforschung, Gebäude: 26.42Universitätsstraße 140225DüsseldorfGermany
| | - Jens Lübben
- Heinrich-Heine Universität DüsseldorfInstitut für Anorganische Chemie und Strukturchemie, Material- und Strukturforschung, Gebäude: 26.42Universitätsstraße 140225DüsseldorfGermany
| | - Stefan Mebs
- Institut für Chemie und Biochemie–Anorganische Chemie derFreien Universität Berlin14195BerlinGermany
| | - Armin Wagner
- Diamond Light SourceHarwell Science and Innovation CampusDidcotOX11 0DEUK
| | - Peter Luger
- Institut für Chemie und Biochemie–Anorganische Chemie derFreien Universität Berlin14195BerlinGermany
| | - Ralf Flaig
- Diamond Light SourceHarwell Science and Innovation CampusDidcotOX11 0DEUK
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20
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Hoser AA, Madsen AØ. Dynamic quantum crystallography: lattice-dynamical models refined against diffraction data. II. Applications to L-alanine, naphthalene and xylitol. ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES 2017; 73:102-114. [PMID: 28248659 DOI: 10.1107/s2053273316018994] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/02/2016] [Accepted: 11/28/2016] [Indexed: 11/10/2022]
Abstract
In the first paper of this series [Hoser & Madsen (2016). Acta Cryst. A72, 206-214], a new approach was introduced which enables the refinement of frequencies of normal modes obtained from ab initio periodic computations against single-crystal diffraction data. In this contribution, the performance of this approach is tested by refinement against data in the temperature range from 23 to 205 K on the molecular crystals of L-alanine, naphthalene and xylitol. The models, which are lattice-dynamical models derived at the Γ point of the Brillouin zone, are able to describe the atomic vibrations of L-alanine and naphthalene to a level where the residual densities are similar to those obtained from the independent atom model. For the more flexible molecule xylitol, larger deviations are found. Hydrogen ADPs (anisotropic displacement parameters) derived from the models are in similar or better agreement with neutron diffraction results than ADPs obtained by other procedures. The heat capacity calculated after normal mode refinement for naphthalene is in reasonable agreement with the heat capacity obtained from calorimetric measurements (to less than 1 cal mol-1 K-1 below 300 K), with deviations at higher temperatures indicating anharmonicity. Standard uncertainties and correlation of the refined parameters have been derived based on a Monte Carlo procedure. The uncertainties are quite small and probably underestimated.
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Affiliation(s)
- Anna A Hoser
- Department of Chemistry, Biological and Chemical Research Centre, University of Warsaw, Żwirki i Wigury 101, 02-089 Warsaw, Poland
| | - Anders Ø Madsen
- Department of Chemistry, University of Copenhagen, Universitetsparken 5, Copenhagen 2100, Denmark
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21
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Wolny J, Buganski I, Kuczera P, Strzalka R. Pushing the limits of crystallography. J Appl Crystallogr 2016; 49:2106-2115. [PMID: 27980514 PMCID: PMC5139996 DOI: 10.1107/s160057671601637x] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2016] [Accepted: 10/14/2016] [Indexed: 11/25/2022] Open
Abstract
A very serious concern of scientists dealing with crystal structure refinement, including theoretical research, pertains to the characteristic bias in calculated versus measured diffraction intensities, observed particularly in the weak reflection regime. This bias is here attributed to corrective factors for phonons and, even more distinctly, phasons, and credible proof supporting this assumption is given. The lack of a consistent theory of phasons in quasicrystals significantly contributes to this characteristic bias. It is shown that the most commonly used exponential Debye-Waller factor for phasons fails in the case of quasicrystals, and a novel method of calculating the correction factor within a statistical approach is proposed. The results obtained for model quasiperiodic systems show that phasonic perturbations can be successfully described and refinement fits of high quality are achievable. The standard Debye-Waller factor for phonons works equally well for periodic and quasiperiodic crystals, and it is only in the last steps of a refinement that different correction functions need to be applied to improve the fit quality.
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Affiliation(s)
- Janusz Wolny
- Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Krakow, Poland
| | - Ireneusz Buganski
- Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Krakow, Poland
| | - Pawel Kuczera
- Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Krakow, Poland
| | - Radoslaw Strzalka
- Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Krakow, Poland
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