Forthcoming article in Acta Crystallographica Section A Foundations and Advances
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Acta Crystallographica Section A: Foundations and Advances covers theoretical and fundamental aspects of the structure of matter. The journal is the prime forum for research in diffraction physics and the theory of crystallographic structure determination by diffraction methods using X-rays, neutrons and electrons. The structures include periodic and aperiodic crystals, and non-periodic disordered materials, and the corresponding Bragg, satellite and diffuse scattering, thermal motion and symmetry aspects. Spatial resolutions range from the subatomic domain in charge-density studies to nanodimensional imperfections such as dislocations and twin walls. The chemistry encompasses metals, alloys, and inorganic, organic and biological materials. Structure prediction and properties such as the theory of phase transformations are also covered.en-gbCopyright (c) 2020 International Union of CrystallographyInternational Union of CrystallographyInternational Union of Crystallographyhttps://journals.iucr.orgurn:issn:0108-7673Acta Crystallographica Section A: Foundations and Advances covers theoretical and fundamental aspects of the structure of matter. The journal is the prime forum for research in diffraction physics and the theory of crystallographic structure determination by diffraction methods using X-rays, neutrons and electrons. The structures include periodic and aperiodic crystals, and non-periodic disordered materials, and the corresponding Bragg, satellite and diffuse scattering, thermal motion and symmetry aspects. Spatial resolutions range from the subatomic domain in charge-density studies to nanodimensional imperfections such as dislocations and twin walls. The chemistry encompasses metals, alloys, and inorganic, organic and biological materials. Structure prediction and properties such as the theory of phase transformations are also covered.text/htmlActa Crystallographica Section A Foundations and Advancestextdaily12002-01-01T00:00+00:00med@iucr.orgActa Crystallographica Section A Foundations and AdvancesCopyright (c) 2020 International Union of Crystallographyurn:issn:0108-7673Forthcoming article in Acta Crystallographica Section A Foundations and Advanceshttp://journals.iucr.org/logos/rss10a.gif
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Still imageIsogonal weavings on the sphere: knots, links, polycatenanes
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We describe non-periodic knotted and linked structures that can be built using one kind of vertex (isogonal) and two kinds of edge (stick). The major types of these structures are identified and reported with optimal embeddings.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733O'Keeffe and Treacydoi:10.1107/S2053273320010669International Union of CrystallographyWe describe non-periodic knotted and linked structures that can be built using one kind of vertex (isogonal) and two kinds of edge (stick). The major types of these structures are identified and reported with optimal embeddings.enWEAVES; KNOTS; LINKS; CATENANESWe describe non-periodic knotted and linked structures that can be built using one kind of vertex (isogonal) and two kinds of edge (stick). The major types of these structures are identified and reported with optimal embeddings.text/htmlIsogonal weavings on the sphere: knots, links, polycatenanestextFast analytical evaluation of intermolecular electrostatic interaction energies using the pseudoatom representation of the electron density. III. Application to crystal structures via the Ewald and direct summation methods
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The exact potential and multipole moment method for fast and accurate evaluation of the intermolecular electrostatic interaction energies using the pseudoatom-based charge distributions is extended to the calculation of energies in molecular crystal structures. The proposed Ewald and direct summation techniques correctly account for the electron density penetration effects that in the benchmark systems constitute 24 – 68% of the total electrostatic interaction energies, and thus cannot be ignored. In agreement with literature, the Ewald summation method offers a higher precision of the evaluated energies (10−5 kJ/mol) and a significantly better computational performance.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Daniel Nguyen et al.doi:10.1107/S2053273320009584International Union of CrystallographyThe exact potential and multipole moment method for fast and accurate evaluation of the intermolecular electrostatic interaction energies using the pseudoatom-based charge distributions is extended to the calculation of energies in molecular crystal structures. The proposed Ewald and direct summation techniques correctly account for the electron density penetration effects that in the benchmark systems constitute 24 – 68% of the total electrostatic interaction energies, and thus cannot be ignored. In agreement with literature, the Ewald summation method offers a higher precision of the evaluated energies (10−5 kJ/mol) and a significantly better computational performance.enELECTROSTATIC INTERACTION ENERGY; CHARGE DENSITY; PSEUDOATOM MODEL; LOWDIN [ALPHA]-FUNCTION; MULTIPOLE EXPANSION; EWALD SUMMATION; LATTICE SUMS.; ELECTROSTATIC INTERACTION ENERGY; CHARGE DENSITY; PSEUDOATOM MODEL; EWALD SUMMATION; LATTICE SUMSThe exact potential and multipole moment method for fast and accurate evaluation of the intermolecular electrostatic interaction energies using the pseudoatom-based charge distributions is extended to the calculation of energies in molecular crystal structures. The proposed Ewald and direct summation techniques correctly account for the electron density penetration effects that in the benchmark systems constitute 24 – 68% of the total electrostatic interaction energies, and thus cannot be ignored. In agreement with literature, the Ewald summation method offers a higher precision of the evaluated energies (10−5 kJ/mol) and a significantly better computational performance.text/htmlFast analytical evaluation of intermolecular electrostatic interaction energies using the pseudoatom representation of the electron density. III. Application to crystal structures via the Ewald and direct summation methodstextEmbedding-theory-based simulations using experimental electron densities for the environment
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For the first time, the use of experimentally derived molecular electron densities as ρB(r) in calculations based on frozen-density embedding theory (FDET) of environment-induced shifts of electronic excitations for chromophores in clusters is demonstrated. ρB(r) was derived from X-ray restrained molecular wavefunctions of glycylglycine to obtain environment densities for simulating electronic excitations in clusters.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Niccolò Ricardi et al.doi:10.1107/S2053273320008062International Union of CrystallographyFor the first time, the use of experimentally derived molecular electron densities as ρB(r) in calculations based on frozen-density embedding theory (FDET) of environment-induced shifts of electronic excitations for chromophores in clusters is demonstrated. ρB(r) was derived from X-ray restrained molecular wavefunctions of glycylglycine to obtain environment densities for simulating electronic excitations in clusters.enQUANTUM CRYSTALLOGRAPHY; DENSITY EMBEDDING; MULTI-SCALE SIMULATIONS; ELECTRONIC STRUCTURE; CHROMOPHORESFor the first time, the use of experimentally derived molecular electron densities as ρB(r) in calculations based on frozen-density embedding theory (FDET) of environment-induced shifts of electronic excitations for chromophores in clusters is demonstrated. ρB(r) was derived from X-ray restrained molecular wavefunctions of glycylglycine to obtain environment densities for simulating electronic excitations in clusters.text/htmlEmbedding-theory-based simulations using experimental electron densities for the environmenttextX-ray scattering study of water confined in bioactive glasses: experimental and simulated pair distribution function
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Water confined in bioactive glasses is studied by total X-ray scattering. Three structural configurations can be distinguished, from bulk-like water in the pore centre to a strongly distorted layer on the pore surface.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Hassan Khoder et al.doi:10.1107/S2053273320007834International Union of CrystallographyWater confined in bioactive glasses is studied by total X-ray scattering. Three structural configurations can be distinguished, from bulk-like water in the pore centre to a strongly distorted layer on the pore surface.enCONFINED WATER; BIOACTIVE GLASSES; STRUCTURAL ANALYSIS; PAIR DISTRIBUTION FUNCTIONWater confined in bioactive glasses is studied by total X-ray scattering. Three structural configurations can be distinguished, from bulk-like water in the pore centre to a strongly distorted layer on the pore surface.text/htmlX-ray scattering study of water confined in bioactive glasses: experimental and simulated pair distribution functiontextInflation versus projection sets in aperiodic systems: the role of the window in averaging and diffraction
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Averaged quantities such as mean shelling numbers, scaling behaviour or diffraction for cut-and-project sets can conveniently be computed in internal space, also for systems with fractally bounded windows.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Baake and Grimmdoi:10.1107/S2053273320007421International Union of CrystallographyAveraged quantities such as mean shelling numbers, scaling behaviour or diffraction for cut-and-project sets can conveniently be computed in internal space, also for systems with fractally bounded windows.enQUASICRYSTALS; PROJECTION METHOD; INFLATION RULES; DIFFRACTION; HYPERUNIFORMITYAveraged quantities such as mean shelling numbers, scaling behaviour or diffraction for cut-and-project sets can conveniently be computed in internal space, also for systems with fractally bounded windows.text/htmlInflation versus projection sets in aperiodic systems: the role of the window in averaging and diffractiontextOn Cayley graphs of {\bb Z}^4
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Cayley graphs of {\bb Z}^4 with valency 10 have been enumerated which correspond to generating sets of integral vectors with components −1, 0, 1 and which are embedded in a four-dimensional Euclidean space without edge intersections.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Igor A. Baburindoi:10.1107/S2053273320007159International Union of CrystallographyCayley graphs of {\bb Z}^4 with valency 10 have been enumerated which correspond to generating sets of integral vectors with components −1, 0, 1 and which are embedded in a four-dimensional Euclidean space without edge intersections.enCAYLEY GRAPHS; FREE ABELIAN GROUPS; COMPUTATIONAL GROUP THEORY; VERTEX-TRANSITIVE GRAPHS; ISOTOPYCayley graphs of {\bb Z}^4 with valency 10 have been enumerated which correspond to generating sets of integral vectors with components −1, 0, 1 and which are embedded in a four-dimensional Euclidean space without edge intersections.text/htmlOn Cayley graphs of {\bb Z}^4textMultiplicity-weighted Euler's formula for symmetrically arranged space-filling polyhedra
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For many tested cases of identical space-filling polyhedra, such as the space-group-specific asymmetric units or Dirichlet domains, the numbers of their faces (Fn), edges (En) and vertices (Vn), in each case normalized by division by the multiplicity of their (potentially special) symmetry position, fulfill a modified Euler's formula Fn − En + Vn = 1.Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Dauter and Jaskolskidoi:10.1107/S2053273320007093International Union of CrystallographyFor many tested cases of identical space-filling polyhedra, such as the space-group-specific asymmetric units or Dirichlet domains, the numbers of their faces (Fn), edges (En) and vertices (Vn), in each case normalized by division by the multiplicity of their (potentially special) symmetry position, fulfill a modified Euler's formula Fn − En + Vn = 1.enASYMMETRIC UNIT; UNIT CELL; EULER'S FORMULA; SPACE-FILLING POLYHEDRA; DIRICHLET DOMAINSFor many tested cases of identical space-filling polyhedra, such as the space-group-specific asymmetric units or Dirichlet domains, the numbers of their faces (Fn), edges (En) and vertices (Vn), in each case normalized by division by the multiplicity of their (potentially special) symmetry position, fulfill a modified Euler's formula Fn − En + Vn = 1.text/htmlMultiplicity-weighted Euler's formula for symmetrically arranged space-filling polyhedratextA Journey into Reciprocal Space: A Crystallographer's Perspective. By A. M. Glazer. Morgan & Claypool, 2017. Paperback, pp. 190. Price USD 55.00. ISBN 9781681746203.
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Copyright (c) 2020 International Union of Crystallographyurn:issn:2053-2733Berthold Stögerdoi:10.1107/S2053273319006983International Union of CrystallographyenBOOK REVIEW; RECIPROCAL SPACEtext/htmlA Journey into Reciprocal Space: A Crystallographer's Perspective. By A. M. Glazer. Morgan & Claypool, 2017. Paperback, pp. 190. Price USD 55.00. ISBN 9781681746203.text