Symmetry adapted functions for double point groups II. Cubic point groups

1970 ◽  
Vol 67 (3) ◽  
pp. 647-656 ◽  
Author(s):  
A. P. Cracknell ◽  
S. J. Joshua
Keyword(s):  
Double Point ◽  
Point Group ◽  
Basis Functions ◽  
Kronecker Products ◽  
Symmetry Adapted Functions ◽  
Point Groups

AbstractA method of deriving the basis functions of the double-valued representations of a point group by the reduction of Kronecker products is described. The method has been used to derive expressions for these bases for cubic point groups for which the results are tabulated.

Symmetry adapted functions for double point groups. I. Non-cubic point groups

1969 ◽  
Vol 65 (2) ◽  
pp. 567-578 ◽  
Author(s):  
Arthur P. Cracknell
Keyword(s):  
Double Point ◽  
Basis Functions ◽  
Projection Operators ◽  
Symmetry Adapted Functions ◽  
Point Groups

AbstractBasis functions are derived and tabulated for the double-valued representations of the triclinic, monoclinic, orthorhombic, trigonal, tetragonal and hexagonal crystallographic point groups using the method of projection operators.

Tables of Basis Functions for Double Point Groups

1966 ◽  
Vol 21 (11) ◽  
pp. 2400-2408 ◽  
Author(s):  
Yositaka Onodera ◽  
Makoto Okazaki
Keyword(s):  
Double Point ◽  
Basis Functions ◽  
Point Groups

scholarly journals The determination of point groups from imprecise molecular geometries

2021 ◽  
Author(s):  
Peter J. Knowles
Keyword(s):  
Symmetry Breaking ◽  
Point Group ◽  
Simple Function ◽  
Coordinate Frame ◽  
New Approach ◽  
Measure Of Symmetry ◽  
Point Groups

AbstractWe present a new approach for the assignment of a point group to a molecule when the structure conforms only approximately to the symmetry. It proceeds by choosing a coordinate frame that minimises a measure of symmetry breaking that is computed efficiently as a simple function of the molecular coordinates and point group specification.

scholarly journals Point-group symmetry detection in three-dimensional charge density of biomolecules

2019 ◽  
Vol 36 (7) ◽  
pp. 2237-2243
Author(s):  
Cyril F Reboul ◽  
Simon Kiesewetter ◽  
Dominika Elmlund ◽  
Hans Elmlund
Keyword(s):  
Charge Density ◽  
Single Particle ◽  
Statistical Tests ◽  
Point Group ◽  
Three Dimensional ◽  
Group Symmetry ◽  
Point Group Symmetry ◽  
Density Maps ◽  
Point Groups ◽  
Density Map

Abstract Motivation No rigorous statistical tests for detecting point-group symmetry in three-dimensional (3D) charge density maps obtained by electron microscopy (EM) and related techniques have been developed. Results We propose a method for determining the point-group symmetry of 3D charge density maps obtained by EM and related techniques. Our ab initio algorithm does not depend on atomic coordinates but utilizes the density map directly. We validate the approach for a range of publicly available single-particle cryo-EM datasets. In straightforward cases, our method enables fully automated single-particle 3D reconstruction without having to input an arbitrarily selected point-group symmetry. When pseudo-symmetry is present, our method provides statistics quantifying the degree to which the 3D density agrees with the different point-groups tested. Availability and implementation The software is freely available at https://github.com/hael/SIMPLE3.0.

Colour symmetry double point groups

Pramana ◽  
1989 ◽  
Vol 32 (6) ◽  
pp. 721-730
Author(s):  
K Rama Mohana Rao ◽  
N Nirmala
Keyword(s):  
Double Point ◽  
Point Groups
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