Generation of Basis Vectors for Magnetic Structures and Displacement Modes

Increasing attention is being focused on the use of symmetry-adapted functions to describe magnetic structures, structural distortions, and incommensurate crystallography. Though the calculation of such functions is well developed, significant difficulties can arise such as the generation of too many or too few basis functions to minimally span the linear vector space. We present an elegant solution to these difficulties using the concept of basis sets and discuss previous work in this area using this concept. Further, we highlight the significance of unitary irreducible representations in this method and provide the first validation that the irreducible representations of the crystallographic space groups tabulated by Kovalev are unitary.

MODY – calculation of ordered structures by symmetry-adapted functions

In this paper we focus on the new version of computer program MODY for calculations of symmetryadapted functions based on the theory of groups and representations. The choice of such a functional frame of coordinates for description of ordered structures leads to a minimal number of parameters which must be used for presentation of such structures and investigations of their properties. The aim of this work is to find those parameters, which are coefficients of a linear combination of calculated functions, leading to construction of different types of structure ordering with a given symmetry. A spreadsheet script for simplification of this work has been created and attached to the program.

Application of Over-Sample Policy and Rotated Angle Invariability of Radial Sampling Points in the Isaf Reconstruction Algorithm

ISAF (icosahedral symmetry-adapted functions) algorithm is the new high-resolution algorithm of icosahedral macromolecules. But its running speed is very slow because of the time-consuming operations of mapping sampling points into 3D space. In this paper, a new sampling method is proposed to improve the running speed of this stage. First of all, the angle corresponding to one pixel arc in the maximum Fourier ring is taken as the sampling angle and the same angle sampling is applied in every rings. After that, the sampling points in radius one ring are mapped into 3D space. Finally, the 3D spatial positions of radial sampling points in other rings can be deduced quickly according to the rotate angle invariability of radial sampling points. The HBV (Hepatitis B Virus) Cryo-electron microscopy images are used for validating this strategy. At the high resolution of 6.64 angstrom, the local speedup in the stage of mapping sampling points reaches to 50, and the overall speedup can be improved in an order of magnitude. The overall speedup increases with the increasement number of EM images and the improvement of target resolution.