scholarly journals Magnetic topological quantum chemistry

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Luis Elcoro ◽  
Benjamin J. Wieder ◽  
Zhida Song ◽  
Yuanfeng Xu ◽  
Barry Bradlyn ◽  
...  
Keyword(s):  
Group Theory ◽  
Quantum Chemistry ◽  
Real Space ◽  
Crystalline Solids ◽  
Electronic Band ◽  
Space Groups ◽  
Topological Quantum ◽  
Anomalous Surface ◽  
Theoretic Characterization ◽  
Group Theoretic Characterization

AbstractFor over 100 years, the group-theoretic characterization of crystalline solids has provided the foundational language for diverse problems in physics and chemistry. However, the group theory of crystals with commensurate magnetic order has remained incomplete for the past 70 years, due to the complicated symmetries of magnetic crystals. In this work, we complete the 100-year-old problem of crystalline group theory by deriving the small corepresentations, momentum stars, compatibility relations, and magnetic elementary band corepresentations of the 1,421 magnetic space groups (MSGs), which we have made freely accessible through tools on the Bilbao Crystallographic Server. We extend Topological Quantum Chemistry to the MSGs to form a complete, real-space theory of band topology in magnetic and nonmagnetic crystalline solids – Magnetic Topological Quantum Chemistry (MTQC). Using MTQC, we derive the complete set of symmetry-based indicators of electronic band topology, for which we identify symmetry-respecting bulk and anomalous surface and hinge states.

scholarly journals Topological quantum chemistry

Nature ◽  
2017 ◽  
Vol 547 (7663) ◽  
pp. 298-305 ◽  
Author(s):  
Barry Bradlyn ◽  
L. Elcoro ◽  
Jennifer Cano ◽  
M. G. Vergniory ◽  
Zhijun Wang ◽  
...  
Keyword(s):  
Quantum Chemistry ◽  
Topological Quantum

scholarly journals Graph theory data for topological quantum chemistry

2017 ◽  
Vol 96 (2) ◽  
Author(s):  
M. G. Vergniory ◽  
L. Elcoro ◽  
Zhijun Wang ◽  
Jennifer Cano ◽  
C. Felser ◽  
...  
Keyword(s):  
Graph Theory ◽  
Quantum Chemistry ◽  
Topological Quantum

scholarly journals From space to superspace and back: Superspace Group Finder

2008 ◽  
Vol 41 (6) ◽  
pp. 1182-1186 ◽  
Author(s):  
Ivan Orlov ◽  
Lukas Palatinus ◽  
Gervais Chapuis
Keyword(s):  
Crystal Structure ◽  
Dimensional Space ◽  
Flexible Structures ◽  
Three Dimensional ◽  
Real Space ◽  
Space Group ◽  
Space Groups ◽  
Group A ◽  
Modular Composition ◽  
Three Dimensional Space

The symmetry of a commensurately modulated crystal structure can be described in two different ways: in terms of a conventional three-dimensional space group or using the superspace concept in (3 +d) dimensions. The three-dimensional space group is obtained as a real-space section of the (3 +d) superspace group. A complete network was constructed linking (3 + 1) superspace groups and the corresponding three-dimensional space groups derived from rational sections. A database has been established and is available at http://superspace.epfl.ch/finder/. It is particularly useful for finding common superspace groups for various series of modular (`composition-flexible') structures and phase transitions. The use of the database is illustrated with examples from various fields of crystal chemistry.

Crystallography and Diffraction

2021 ◽  
pp. 220-276
Author(s):  
Kannan M. Krishnan
Keyword(s):  
Rotational Symmetry ◽  
Reciprocal Lattice ◽  
Real Space ◽  
Crystalline Materials ◽  
Space Groups ◽  
Ewald Sphere ◽  
Point Groups ◽  
Diffraction Patterns ◽  
Point Line ◽  
Periodic Arrangement

Crystalline materials have a periodic arrangement of atoms, exhibit long range order, and are described in terms of 14 Bravais lattices, 7 crystal systems, 32 point groups, and 230 space groups, as tabulated in the International Tables for Crystallography. We introduce the nomenclature to describe various features of crystalline materials, and the practically useful concepts of interplanar spacing and zonal equations for interpreting electron diffraction patterns. A crystal is also described as the sum of a lattice and a basis. Practical materials harbor point, line, and planar defects, and their identification and enumeration are important in characterization, for defects significantly affect materials properties. The reciprocal lattice, with a fixed and well-defined relationship to the real lattice from which it is derived, is the key to understanding diffraction. Diffraction is described by Bragg law in real space, and the equivalent Ewald sphere construction and the Laue condition in reciprocal space. Crystallography and diffraction are closely related, as diffraction provides the best methodology to reveal the structure of crystals. The observations of quasi-crystalline materials with five-fold rotational symmetry, inconsistent with lattice translations, has resulted in redefining a crystalline material as “any solid having an essentially discrete diffraction pattern”

scholarly journals ACE-Molecule: An open-source real-space quantum chemistry package

2020 ◽  
Vol 152 (12) ◽  
pp. 124110 ◽  
Author(s):  
Sungwoo Kang ◽  
Jeheon Woo ◽  
Jaewook Kim ◽  
Hyeonsu Kim ◽  
Yongjun Kim ◽  
...  
Keyword(s):  
Quantum Chemistry ◽  
Open Source ◽  
Real Space

Real-space quasi-relativistic quantum chemistry

2020 ◽  
Vol 1175 ◽  
pp. 112711 ◽  
Author(s):  
Joel Anderson ◽  
Robert J. Harrison ◽  
Bryan Sundahl ◽  
W. Scott Thornton ◽  
Gregory Beylkin
Keyword(s):  
Quantum Chemistry ◽  
Relativistic Quantum ◽  
Real Space ◽  
Relativistic Quantum Chemistry

Abinitiostructure solution of nucleic acids and proteins by direct methods: reciprocal-space and real-space approach

2005 ◽  
Vol 38 (1) ◽  
pp. 217-222 ◽  
Author(s):  
Krishna Chowdhury ◽  
Soma Bhattacharya ◽  
Monika Mukherjee
Keyword(s):  
Nucleic Acids ◽  
Direct Method ◽  
Heavy Atom ◽  
Direct Methods ◽  
Disulfide Bridge ◽  
Real Space ◽  
Reciprocal Space ◽  
Space Groups ◽  
Data Resolution ◽  
Modification Procedure

Anab initiomethod for solving macromolecular structures is described. The heavy atom(s) or some disulfide bridge in the structure are located from the phase sets selected on the basis of a figure of merit of a reciprocal-space-based multiple-solution direct method. Subsequent weighted Fourier recycling reveals recognizable structures for two nucleic acids where data resolution is 1.3 Å or better. With lower than 1.3 Å data resolution or sulfur as the heaviest atom in the structure, the phase refinement has been carried out using the density modification procedure (PERP) operating in direct space. The resulting electron density map can readily be interpreted. The methodology has been illustrated with six known nucleic acids and proteins crystallizing in different space groups. It has proved to be fast, simple to use and a very effective tool for solving macromolecular structures with data resolution up to 1.7 Å.

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