op_xyz_list_to_matrix_list: List of matrices and vectors of a specific space group

In cry: Statistics for Structural Crystallography

List of matrices and vectors of a specific space group

Description

Returns 3\times 3 matrices and 3\times 1 vectors corresponding to point group operations, group translations and cell centring of a given space group.

Usage

op_xyz_list_to_matrix_list(op_xyz_list)

Arguments

op_xyz_list

A named list made of two vectors. The first vector, SYMOP, contains strings describing the symmetry operators. The second vector, CENOP, contains strings describing the centring of the unit cell.

Details

A crystallographic space group consists of a series of transformations on a point (x_f,y_f,z_f) in space that are mathematically implemented as the product of a 3\times 3 point-group matrix and the point fractional coordinates, (x_f,y_f,z_f), followed by a sum with a 3\times 1 translation vector. The complete set of points thus produced can be cloned into a new and shifted set translated of an amount represented by a 3\times 1 centring vector.

Value

mat_ops_list A named list consisting of 3 lists. The first list, PG, contains 3\times 3 point group matrices; the second list, T, contains the same number of 3\times 1 translation vectors. The first matrix is always the identity matrix, the first translation vector is always the null vector. The third list, C, consists of centering vectors; the first centering vector is always the null vector. To summarize, the output looks like the following:

[[ [[I,M2,M3,...,Mn]] , [[O,V2,V3,...,Vn]] , [[O,C2,C3,...,Cm]] ]] where: I = identity 3X3 matrix 0 = null 3X1 vector M2,M3,...,Mn = point group 3X3 matrices V2,V3,...,Cn = translation 3X1 vectors C2,C3,...,Cm = centering 3X1 vectors

Examples

# Symmetry operators for space group number 3, P 1 2 1
SG <- "P 1 2 1"
op_xyz_list <- syminfo_to_op_xyz_list(SG)
mat_ops_list <- op_xyz_list_to_matrix_list(op_xyz_list)
names(mat_ops_list)

cry documentation built on Oct. 10, 2022, 9:06 a.m.